Texas Instruments TI-82 STATS User manual

Texas Instruments TI-82 STATS User manual

TI-82 STATS

GRAPHING CALCULATOR

GUIDEBOOK

© 1996, 2000, 2005 Texas Instruments Incorporated.

IBM is a registered trademark of International Business Machines Corporation

Macintosh is a registered trademark of Apple Computer, Inc.

82STAT~2.DOC TI-83 Intl English, Title Page Bob Fedorisko Revised: 10/28/05 11:55 AM Printed: 10/28/05

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Important

US FCC

Information

Concerning

Radio Frequency

Interference

Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “as-is” basis.

In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas

Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

This equipment has been tested and found to comply with the limits for a

Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation.

If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures:

Reorient or relocate the receiving antenna.

Increase the separation between the equipment and receiver.

Connect the equipment into an outlet on a circuit different from that to which the receiver is connected.

Consult the dealer or an experienced radio/television technician for help.

Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment.

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Table of Contents

This manual describes how to use the TI-82 STATS Graphing Calculator. Getting

Started is an overview of TI-82 STATS features. Chapter 1 describes how the

TI-82 STATS operates. Other chapters describe various interactive features. Chapter

17 shows how to combine these features to solve problems.

Getting Started:

Do This First!

TI-82 STATS Keyboard

.....................................................................................

TI-82 STATS Menus

............................................................................................

First Steps

....................................................................................................................

Entering a Calculation: The Quadratic Formula

.................................

Converting to a Fraction: The Quadratic Formula

............................

Displaying Complex Results: The Quadratic Formula

...................

Defining a Function: Box with Lid

.............................................................

9

Defining a Table of Values: Box with Lid

.............................................

10

7

8

5

6

2

4

Zooming In on the Table: Box with Lid

..................................................

11

Setting the Viewing Window: Box with Lid

.........................................

12

Displaying and Tracing the Graph: Box with Lid

.............................

13

Zooming In on the Graph: Box with Lid

.................................................

15

Finding the Calculated Maximum: Box with Lid

..............................

16

Other TI-82 STATS Features

..........................................................................

17

Chapter 1:

Operating the

TI-82 STATS

Turning On and Turning Off the TI-82 STATS

.................................

1-2

Setting the Display Contrast

............................................................................

1-3

The Display

................................................................................................................

1-4

Entering Expressions and Instructions

......................................................

1-6

TI-82 STATS Edit Keys

.....................................................................................

1-8

Setting Modes

...........................................................................................................

1-9

Using TI-82 STATS Variable Names

.......................................................

1-13

Storing Variable Values

.....................................................................................

1-14

Recalling Variable Values

................................................................................

1-15

ENTRY (Last Entry) Storage Area

..............................................................

1-16

Ans (Last Answer) Storage Area

..................................................................

1-18

TI-82 STATS Menus

............................................................................................

1-19

VARS and VARS Y.VARS

Menus

..............................................................

1-21

Equation Operating System (EOSé)

.........................................................

1-22

Error Conditions

......................................................................................................

1-24

Introduction iii

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Table of Contents

(continued)

Chapter 2:

Math, Angle, and

Test Operations

Getting Started: Coin Flip

.................................................................................

2-2

Keyboard Math Operations

..............................................................................

2-3

MATH Operations

...................................................................................................

2-5

Using the Equation Solver

................................................................................

2-8

MATH NUM (Number) Operations

..............................................................

2-13

Entering and Using Complex Numbers

....................................................

2-16

MATH CPX

(Complex) Operations

............................................................

2-18

MATH PRB

(Probability) Operations

........................................................

2-20

ANGLE

Operations

................................................................................................

2-23

TEST

(Relational) Operations

........................................................................

2-25

TEST LOGIC

(Boolean) Operations

..........................................................

2-26

Chapter 3:

Function

Graphing

Getting Started: Graphing a Circle

..............................................................

3-2

Defining Graphs

......................................................................................................

3-3

Setting the Graph Modes

...................................................................................

3-4

Defining Functions

................................................................................................

3-5

Selecting and Deselecting Functions

..........................................................

3-7

Setting Graph Styles for Functions

..............................................................

3-9

Setting the Viewing Window Variables

...................................................

3-11

Setting the Graph Format

..................................................................................

3-13

Displaying Graphs

..................................................................................................

3-15

Exploring Graphs with the Free-Moving Cursor

................................

3-17

Exploring Graphs with

TRACE

.....................................................................

3-18

Exploring Graphs with the

ZOOM

Instructions

..................................

3-20

Using

ZOOM MEMORY

....................................................................................

3-23

Using the CALC (Calculate) Operations

..................................................

3-25

Chapter 4:

Parametric

Graphing

Chapter 5:

Polar Graphing

Getting Started: Path of a Ball

Exploring Parametric Graphs

........................................................................

Defining and Displaying Parametric Graphs

........................................

..........................................................................

4-2

4-4

4-7

Getting Started: Polar Rose

..............................................................................

5-2

Defining and Displaying Polar Graphs

.....................................................

5-3

Exploring Polar Graphs

......................................................................................

5-6

iv Introduction

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Chapter 6:

Sequence

Graphing

Chapter 7:

Tables

Chapter 8:

DRAW

Operations

Chapter 9:

Split Screen

Getting Started: Forest and Trees

.................................................................

6-2

Defining and Displaying Sequence Graphs

...........................................

6-3

Selecting Axes Combinations

.........................................................................

6-8

Exploring Sequence Graphs

.............................................................................

6-9

Graphing Web Plots

..............................................................................................

6-11

Using Web Plots to Illustrate Convergence

...........................................

6-12

Graphing Phase Plots

...........................................................................................

6-13

Comparing TI-82 STATS and TI.82 Sequence Variables

...........

6-15

Keystroke Differences Between TI-82 STATS and TI-82

..........

6-16

Getting Started: Roots of a Function

..........................................................

7-2

Setting Up the Table

.............................................................................................

7-3

Defining the Dependent Variables

...............................................................

7-4

Displaying the Table

.............................................................................................

7-5

Getting Started: Drawing a Tangent Line

...............................................

8-2

Using the

DRAW

Menu

......................................................................................

8-3

Clearing Drawings

.................................................................................................

8-4

Drawing Line Segments

.....................................................................................

8-5

Drawing Horizontal and Vertical Lines

...................................................

8-6

Drawing Tangent Lines

......................................................................................

8-8

Drawing Functions and Inverses

...................................................................

8-9

Shading Areas on a Graph

................................................................................

8-10

Drawing Circles

.......................................................................................................

8-11

Placing Text on a Graph

.....................................................................................

8-12

Using Pen to Draw on a Graph

......................................................................

8-13

Drawing Points on a Graph

..............................................................................

8-14

Drawing Pixels

.........................................................................................................

8-16

Storing Graph Pictures ( Pic )

............................................................................

8-17

Recalling Graph Pictures ( Pic )

.......................................................................

8-18

Storing Graph Databases ( GDB )

...................................................................

8-19

Recalling Graph Databases ( GDB )

..............................................................

8-20

Getting Started: Exploring the Unit Circle

.............................................

9-2

Using Split Screen

..................................................................................................

9-3

Horiz (Horizontal) Split Screen

.....................................................................

9-4

G-T (Graph-Table) Split Screen

....................................................................

9-5

TI-82 STATS Pixels in Horiz and G-T Modes

....................................

9-6

Introduction v

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Table of Contents

(continued)

Chapter 10:

Matrices

Chapter 11:

Lists

Chapter 12:

Statistics

Chapter 13:

Inferential

Statistics and

Distributions

Getting Started: Systems of Linear Equations

.....................................

10-2

Defining a Matrix

...................................................................................................

10-3

Viewing and Editing Matrix Elements

......................................................

10-4

Using Matrices with Expressions

.................................................................

10-7

Displaying and Copying Matrices

................................................................

10-8

Using Math Functions with Matrices

.........................................................

10-9

Using the

MATRX MATH

Operations

.......................................................

10-12

Getting Started: Generating a Sequence

..................................................

11-2

Naming Lists

..............................................................................................................

11-3

Storing and Displaying Lists

...........................................................................

11-4

Entering List Names

.............................................................................................

11-6

Attaching Formulas to List Names

..............................................................

11-7

Using Lists in Expressions

................................................................................

11-9

LIST OPS

Menu

......................................................................................................

11-10

LIST MATH

Menu

..................................................................................................

11-17

Getting Started: Pendulum Lengths and Periods

................................

12-2

Setting up Statistical Analyses

.......................................................................

12-10

Using the Stat List Editor

..................................................................................

12-11

Attaching Formulas to List Names

..............................................................

12-14

Detaching Formulas from List Names

......................................................

12-16

Switching Stat List Editor Contexts

............................................................

12-17

Stat List Editor Contexts

....................................................................................

12-18

STAT EDIT

Menu

..................................................................................................

12-20

Regression Model Features

..............................................................................

12-22

STAT CALC Menu

................................................................................................

12-24

Statistical Variables

...............................................................................................

12-29

Statistical Analysis in a Program

..................................................................

12-30

Statistical Plotting

...................................................................................................

12-31

Statistical Plotting in a Program

....................................................................

12-37

Getting Started: Mean Height of a Population

.....................................

13-2

Inferential Stat Editors

.........................................................................................

13-6

STAT TESTS Menu

.............................................................................................

13-9

Inferential Statistics Input Descriptions

...................................................

13-26

Test and Interval Output Variables

..............................................................

13-28

Distribution Functions

.........................................................................................

13-29

Distribution Shading

.............................................................................................

13-35

vi Introduction

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Chapter 14:

Financial

Functions

Chapter 15:

CATALOG

,

Strings,

Hyperbolic

Functions

Chapter 16:

Programming

Chapter 17:

Applications

Getting Started: Financing a Car

...................................................................

14-2

Getting Started: Computing Compound Interest

................................

14-3

Using the TVM Solver

.........................................................................................

14-4

Using the Financial Functions

........................................................................

14-5

Calculating Time Value of Money ( TVM )

..............................................

14-6

Calculating Cash Flows

......................................................................................

14-8

Calculating Amortization

...................................................................................

14-9

Calculating Interest Conversion

....................................................................

14-12

Finding Days between Dates/Defining Payment Method

.......................

14-13

Using the

TVM

Variables

...................................................................................

14-14

Browsing the TI-82 STATS

CATALOG

..................................................

15-2

Entering and Using Strings

...............................................................................

15-3

Storing Strings to String Variables

..............................................................

15-4

String Functions and Instructions in the

CATALOG

........................

15-6

Hyperbolic Functions in the

CATALOG

..................................................

15-10

Getting Started: Volume of a Cylinder

.....................................................

16-2

Creating and Deleting Programs

...................................................................

16-4

Entering Command Lines and Executing Programs

........................

16-5

Editing Programs

....................................................................................................

16-6

Copying and Renaming Programs

...............................................................

16-7

PRGM CTL

(Control) Instructions

..............................................................

16-8

PRGM I/O

(Input/Output) Instructions

.....................................................

16-16

Calling Other Programs as Subroutines

...................................................

16-22

Comparing Test Results Using Box Plots

...............................................

17-2

Graphing Piecewise Functions

.......................................................................

17-4

Graphing Inequalities

...........................................................................................

17-5

Solving a System of Nonlinear Equations

..............................................

17-6

Using a Program to Create the Sierpinski Triangle

..........................

17-7

Graphing Cobweb Attractors

..........................................................................

17-8

Using a Program to Guess the Coefficients

...........................................

17-9

Graphing the Unit Circle and Trigonometric Curves

......................

17-10

Finding the Area between Curves

................................................................

17-11

Using Parametric Equations: Ferris Wheel Problem

........................

17-12

Demonstrating the Fundamental Theorem of Calculus

..................

17-14

Computing Areas of Regular N-Sided Polygons

................................

17-16

Computing and Graphing Mortgage Payments

...................................

17-18

Introduction vii

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Table of Contents

(continued)

Chapter 18:

Memory

Management

Appendix A:

Tables and

Reference

Information

Appendix B:

General

Information

Checking Available Memory

..........................................................................

18-2

Deleting Items from Memory

.........................................................................

18-3

Clearing Entries and List Elements

.............................................................

18-4

Resetting the TI-82 STATS

.............................................................................

18-5

Chapter 19:

Communication

Link

Getting Started: Sending Variables

.............................................................

19-2

TI-82 STATS

LINK

...............................................................................................

19-3

Selecting Items to Send

.......................................................................................

19-4

Receiving Items

.......................................................................................................

19-5

Transmitting Items

.................................................................................................

19-6

Transmitting Lists to a TI-82

..........................................................................

19-8

Transmitting from a TI-82 to a TI-82 STATS

.....................................

19-9

Backing Up Memory

............................................................................................

19-10

Table of Functions and Instructions

Menu Map

Variables

Statistical Formulas

............................................................

...................................................................................................................

.......................................................................................................................

...............................................................................................

A-2

A-39

A-49

A-50

Financial Formulas

................................................................................................

A-54

Battery Information

...............................................................................................

B-2

In Case of Difficulty

.............................................................................................

B-4

Error Conditions

......................................................................................................

B-5

Accuracy Information

..........................................................................................

B-10

Support and Service Information

..................................................................

B-12

Warranty Information

..........................................................................................

B-13

Index

viii Introduction

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Contents

Getting Started:

Do This First!

TI-82 STATS Keyboard

.....................................................................................

TI-82 STATS Menus

............................................................................................

First Steps

....................................................................................................................

Entering a Calculation: The Quadratic Formula

.................................

Converting to a Fraction: The Quadratic Formula

............................

Displaying Complex Results: The Quadratic Formula

...................

Defining a Function: Box with Lid

.............................................................

9

Defining a Table of Values: Box with Lid

.............................................

10

7

8

5

6

2

4

Zooming In on the Table: Box with Lid

..................................................

11

Setting the Viewing Window: Box with Lid

.........................................

12

Displaying and Tracing the Graph: Box with Lid

.............................

13

Zooming In on the Graph: Box with Lid

.................................................

15

Finding the Calculated Maximum: Box with Lid

..............................

16

Other TI-82 STATS Features

..........................................................................

17

Getting Started 1

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TI-82 STATS Keyboard

Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.

Keyboard Zones

Graphing keys access the interactive graphing features.

Editing keys allow you to edit expressions and values.

Advanced function keys display menus that access the advanced functions.

Scientific calculator keys access the capabilities of a standard scientific calculator.

Graphing Keys

Editing Keys

Advanced

Function Keys

Scientific

Calculator Keys

2 Getting Started

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Using the

Color.Coded

Keyboard

The keys on the TI-82 STATS are color-coded to help you easily locate the key you need.

The gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs.

The primary function of each key is printed in white on the key.

For example, when you press , the

MATH

menu is displayed.

Using the

y

and

ƒ Keys

The secondary function of each key is printed in yellow above the key. When you press the yellow y key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press y and then , the

TEST

menu is displayed. This guidebook describes this keystroke combination as y [

TEST

].

The alpha function of each key is printed in green above the key. When you press the green ƒ key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press ƒ and then

, the letter

A

is entered. This guidebook describes this keystroke combination as ƒ [

A

].

The y key accesses the second function printed in yellow above each key.

The

ƒ key accesses the alpha function printed in green above each key.

Getting Started 3

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TI-82 STATS Menus

Displaying a Menu

While using your TI-82 STATS, you often will need to access items from its menus.

When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , the

MATH

menu is displayed as a full screen.

After you select an item from a menu, the screen where you are working usually is displayed again.

Moving from One Menu to Another

Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press ~ and | to highlight each menu name.

Selecting an Item from a Menu

The number or letter next to the current menu item is highlighted. If the menu continues beyond the screen, a down arrow (

$

) replaces the colon (

:

) in the last displayed item. If you scroll beyond the last displayed item, an up arrow (

#

) replaces the colon in the first item displayed.You can select an item in either of two ways.

¦ Press † or } to move the cursor to the number or letter of the item; press Í.

¦ Press the key or key combination for the number or letter next to the item.

Leaving a Menu without Making a Selection

You can leave a menu without making a selection in any of three ways.

¦ Press ‘ to return to the screen where you were.

¦ Press y [

QUIT

] to return to the home screen.

¦ Press a key for another menu or screen.

4 Getting Started

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First Steps

Before starting the sample problems in this chapter, follow the steps on this page to reset the TI-82 STATS to its factory settings and clear all memory. This ensures that the keystrokes in this chapter will produce the illustrated results.

To reset the TI-82 STATS, follow these steps.

1. Press É to turn on the calculator.

2. Press and release y, and then press [

MEM

]

(above Ã).

When you press y, you access the operation printed in yellow above the next key that you press. [

MEM

] is the y operation of the à key.

The

MEMORY

menu is displayed.

3. Press

5

to select

5:Reset

.

The

RESET

menu is displayed.

4. Press

1

to select

1:All Memory

.

The

RESET MEMORY

menu is displayed.

5. Press

2

to select

2:Reset

.

All memory is cleared, and the calculator is reset to the factory default settings.

When you reset the TI-82 STATS, the display contrast is reset.

¦

If the screen is very light or blank, press and release y, and then press and hold } to darken the screen.

¦

If the screen is very dark, press and release y, and then press and hold † to lighten the screen.

Getting Started 5

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Entering a Calculation: The Quadratic Formula

Use the quadratic formula to solve the quadratic equations 3X 2 + 5X + 2 = 0 and 2X 2

N X + 3 = 0. Begin with the equation 3X

2 + 5X + 2 = 0.

1. Press

3

¿ ƒ [

A

] (above ) to store the coefficient of the X 2 term.

2. Press ƒ [

:

] (above Ë). The colon allows you to enter more than one instruction on a line.

3. Press

5

¿ ƒ [

B

] (above ) to store the coefficient of the X term. Press

ƒ [

:

] to enter a new instruction on the same line. Press

2

¿ ƒ [

C

] (above

) to store the constant.

4. Press Í to store the values to the variables

A, B, and C.

The last value you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entry.

5. Press £ Ì ƒ [

B

] Ã y [

] ƒ [

B

]

¡ ¹

4

ƒ [

A

] ƒ [

C

] ¤ ¤ ¥ £

2

ƒ [

A

] ¤ to enter the expression for one of the solutions for the quadratic formula,

− +

b

2

a ac

6. Press Í to find one solution for the equation 3X 2 + 5X + 2 = 0.

The answer is shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression.

6 Getting Started

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Converting to a Fraction: The Quadratic Formula

You can show the solution as a fraction.

1. Press  to display the

MATH

menu.

2. Press

1

to select

1:4Frac

from the

MATH menu.

When you press

1

,

Ans4Frac

is displayed on the home screen.

Ans

is a variable that contains the last calculated answer.

3. Press Í to convert the result to a fraction.

To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation.

4. Press y [

ENTRY

] (above Í) to recall the fraction conversion entry, and then press y

[

ENTRY

] again to recall the quadratic-formula expression,

− +

b

2

a ac

5. Press } to move the cursor onto the

+

sign in the formula. Press ¹ to edit the quadraticformula expression to become:

− −

b ac

2

a

6. Press Í to find the other solution for the quadratic equation 3X 2 + 5X + 2 = 0.

Getting Started 7

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Displaying Complex Results: The Quadratic Formula

Now solve the equation 2X 2 N X + 3 = 0. When you set

a+b

i complex number mode, the TI-82 STATS displays complex results.

1. Press z † † † † † † (6 times), and then press ~ to position the cursor over

a+b

i.

Press Í to select

a+b

i complex-number mode.

2. Press y [

QUIT

] (above z) to return to the home screen, and then press ‘ to clear it.

3. Press

2

¿ ƒ [

A

] ƒ [

:

] Ì

1

¿ ƒ [

B

] ƒ [

:

]

3

¿ ƒ

[

C

] Í.

The coefficient of the X 2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively.

4. Press y [

ENTRY

] to recall the store instruction, and then press y [

ENTRY

] again to recall the quadratic-formula expression,

− −

b

2

a ac

5. Press Í to find one solution for the equation 2X

2

N X + 3 = 0.

6. Press y [

ENTRY

] repeatedly until this quadratic-formula expression is displayed:

− +

b

2

a ac

7. Press Í to find the other solution for the quadratic equation: 2X

2

N X + 3 = 0.

Note: An alternative for solving equations for real numbers is to use the built-in Equation

Solver (Chapter 2).

8 Getting Started

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Defining a Function: Box with Lid

Take a 20 cm. × 25 cm. sheet of paper and cut X × X squares from two corners. Cut

X × 12.5 cm. rectangles from the other two corners as shown in the diagram below.

Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution.

Begin by defining a function that describes the volume of the box.

From the diagram: 2X + A = 20

2X + 2B = 25

V = A B X

Substituting: V = (20 N 2X) (25à 2 N X) X

X

20 A

X B X B

25

1. Press o to display the

Y= editor, which is where you define functions for tables and graphing.

2. Press £

20

¹

2

„ ¤ £

25

¥

2

¹

„ ¤ „ Í to define the volume function as

Y

1

in terms of

X

.

„ lets you enter

X

quickly, without having to press ƒ. The highlighted

=

sign indicates that

Y

1

is selected.

Getting Started 9

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Defining a Table of Values: Box with Lid

The table feature of the TI-82 STATS displays numeric information about a function.

You can use a table of values from the function defined on page 9 to estimate an answer to the problem.

1. Press y [

TBLSET

] (above p) to display the

TABLE SETUP

menu.

2. Press Í to accept

TblStart=0

.

3. Press

1

Í to define the table increment

@Tbl=1

. Leave

Indpnt: Auto

and

Depend: Auto

so that the table will be generated automatically.

4. Press y [

TABLE

] (above s) to display the table.

Notice that the maximum value for

Y

1

(box’s volume) occurs when

X

is about

4

, between

3

and

5

.

5. Press and hold † to scroll the table until a negative result for

Y

1

is displayed.

Notice that the maximum length of

X

for this problem occurs where the sign of

Y

1

(box’s volume) changes from positive to negative, between

10

and

11

.

6. Press y [

TBLSET

].

Notice that

TblStart

has changed to

6

to reflect the first line of the table as it was last displayed. (In step 5, the first value of

X

displayed in the table is

6

.)

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Zooming In on the Table: Box with Lid

You can adjust the way a table is displayed to get more information about a defined function. With smaller values for

@Tbl

, you can zoom in on the table.

1. Press

3

Í to set

TblStart

. Press Ë

1

Í to set

@Tbl

.

This adjusts the table setup to get a more accurate estimate of

X

for maximum volume

Y

1

.

2. Press y [

TABLE

].

3. Press † and } to scroll the table.

Notice that the maximum value for

Y

1

is

410.26

, which occurs at

X

=

3.7

. Therefore, the maximum occurs where

3.6

<

X

<

3.8

.

4. Press y [

TBLSET

]. Press

3

Ë

6

Í to set

TblStart

. Press Ë

01

Í to set

@Tbl

.

5. Press y [

TABLE

], and then press † and } to scroll the table.

Four equivalent maximum values are shown,

410.60

at

X

=

3.67

,

3.68

,

3.69

, and

3.70

.

6. Press † and } to move the cursor to

3.67

.

Press ~ to move the cursor into the

Y

1

column.

The value of

Y

1

at

X

=

3.67

is displayed on the bottom line in full precision as

410.261226

.

7. Press † to display the other maximums.

The value of

Y

1

at

X

=

3.68

in full precision is

410.264064

, at

X

=

3.69

is

410.262318

, and at

X

=

3.7

is

410.256

.

The maximum volume of the box would occur at

3.68

if you could measure and cut the paper at

.01-cm. increments.

Getting Started 11

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Setting the Viewing Window: Box with Lid

You also can use the graphing features of the TI-82 STATS to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window.

1. Press p to display the window editor, where you can view and edit the values of the window variables.

The standard window variables define the viewing window as shown.

Xmin

,

Xmax

,

Ymin

, and

Ymax

define the boundaries of the display.

Xscl

and

Yscl

define the distance between tick marks on the

X

and

Y

axes.

Xres

controls resolution.

2. Press

0

Í to define

Xmin

.

3. Press

20

¥

2

to define

Xmax

using an expression.

Xmin

Ymin

Ymax

Xscl

Yscl

Xmax

4. Press Í. The expression is evaluated, and

10

is stored in

Xmax

. Press Í to accept

Xscl

as

1

.

5. Press

0

Í

500

Í

100

Í

1

Í to define the remaining window variables.

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Displaying and Tracing the Graph: Box with Lid

Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the

TRACE

feature.

1. Press s to graph the selected function in the viewing window.

The graph of

Y

1

=(20N2X)(25à2NX)X

is displayed.

2. Press ~ to activate the free-moving graph cursor.

The

X

and

Y

coordinate values for the position of the graph cursor are displayed on the bottom line.

3. Press |, ~, }, and † to move the freemoving cursor to the apparent maximum of the function.

As you move the cursor, the

X

and

Y

coordinate values are updated continually.

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Displaying and Tracing the Graph: Box with Lid

(cont.)

4. Press r. The trace cursor is displayed on the

Y

1

function.

The function that you are tracing is displayed in the top-left corner.

5. Press | and ~ to trace along

Y

1

, one

X

dot at a time, evaluating

Y

1

at each

X

.

You also can enter your estimate for the maximum value of

X

.

6. Press

3

Ë

8

. When you press a number key while in

TRACE

, the

X=

prompt is displayed in the bottom-left corner.

7. Press Í.

The trace cursor jumps to the point on the

Y

1

function evaluated at

X=3.8

.

8. Press | and ~ until you are on the maximum

Y

value.

This is the maximum of

Y

1

(X)

for the

X

pixel values. The actual, precise maximum may lie between pixel values.

14 Getting Started

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Zooming In on the Graph: Box with Lid

To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the

ZOOM

instructions.

1. Press q to display the

ZOOM

menu.

This menu is a typical TI-82 STATS menu. To select an item, you can either press the number or letter next to the item, or you can press † until the item number or letter is highlighted, and then press Í.

2. Press

2

to select

2:Zoom In

.

The graph is displayed again. The cursor has changed to indicate that you are using a

ZOOM instruction.

3. With the cursor near the maximum value of the function (as in step 8 on page 14), press

Í.

The new viewing window is displayed. Both

Xmax

N

Xmin

and

Ymax

N

Ymin

have been adjusted by factors of 4, the default values for the zoom factors.

4. Press p to display the new window settings.

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Finding the Calculated Maximum: Box with Lid

You can use a

CALCULATE

menu operation to calculate a local maximum of a function.

1. Press y [

CALC

] (above r) to display the

CALCULATE

menu. Press

4

to select

4:maximum

.

The graph is displayed again with a

Left Bound?

prompt.

2. Press | to trace along the curve to a point to the left of the maximum, and then press

Í.

A

4

at the top of the screen indicates the selected bound.

A

Right Bound?

prompt is displayed.

3. Press ~ to trace along the curve to a point to the right of the maximum, and then press

Í.

A

3

at the top of the screen indicates the selected bound.

A

Guess?

prompt is displayed.

4. Press | to trace to a point near the maximum, and then press Í.

Or, press

3

Ë

8

, and then press Í to enter a guess for the maximum.

When you press a number key in

TRACE

, the

X=

prompt is displayed in the bottom-left corner.

Notice how the values for the calculated maximum compare with the maximums found with the free-moving cursor, the trace cursor, and the table.

Note: In steps 2 and 3 above, you can enter values directly for Left Bound and Right Bound, in the same way as described in step 4.

16 Getting Started

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Other TI-82 STATS Features

Getting Started has introduced you to basic TI-82 STATS operation. This guidebook describes in detail the features you used in Getting Started. It also covers the other features and capabilities of the TI-82 STATS.

Graphing

You can store, graph, and analyze up to 10 functions (Chapter

3), up to six parametric functions (Chapter 4), up to six polar functions (Chapter 5), and up to three sequences (Chapter 6).

You can use

DRAW

operations to annotate graphs (Chapter 8).

Sequences

Tables

You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots (Chapter 6).

You can create function evaluation tables to analyze many functions simultaneously (Chapter 7).

Split Screen

Matrices

Lists

Statistics

You can split the screen horizontally to display both a graph and a related editor (such as the

Y=

editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously

(Chapter 9).

You can enter and save up to 10 matrices and perform standard matrix operations on them (Chapter 10).

You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves (Chapter 11).

You can perform one- and two-variable, list-based statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regular box-and-whisker plot, or normal probability plot. You can define and store up to three stat plot definitions (Chapter

12).

Getting Started 17

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Other TI-82 STATS Features (

continued

)

Inferential

Statistics

Financial

Functions

CATALOG

Programming

Linking to a PC or Macintoshë

You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically (Chapter 13).

You can use time-value-of-money (

TVM

) functions to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions (Chapter 14).

The

CATALOG

is a convenient, alphabetical list of all functions and instructions on the TI-82 STATS. You can paste any function or instruction from the

CATALOG

to the current cursor location (Chapter 15).

You can enter and store programs that include extensive control and input/output instructions (Chapter 16).

You can connect your TI-82 STATS to a personal computer using TI Connect™ software and a TI Connectivity cable. The software is included on the CD in the TI-82 STATS package.

When you connect to the TI Connect™ software, the TI-82

STATS calculator will be identified by TI Connect™ as a TI-83 calculator. Everything else should function as expected.

For more information, consult the TI Connect™ Help.

The TI-82 STATS has a port to connect and communicate with another TI-82 STATS, a TI.82, the Calculator-Based

Laboratoryé (CBLé) System, a Calculator-Based Rangeré

(CBRé), or a personal computer. The unit-to-unit link cable is included with the TI-82 STATS (Chapter 19).

18 Getting Started

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Contents

1

Operating the TI-82 STATS

Turning On and Turning Off the TI-82 STATS

.................................

Setting the Display Contrast

............................................................................

The Display

................................................................................................................

Entering Expressions and Instructions

......................................................

TI-82 STATS Edit Keys

.....................................................................................

Setting Modes

...........................................................................................................

Using TI-82 STATS Variable Names

.......................................................

13

Storing Variable Values

.....................................................................................

14

8

9

4

6

2

3

Recalling Variable Values

................................................................................

15

ENTRY

(Last Entry) Storage Area

..............................................................

16

Ans

(Last Answer) Storage Area

.................................................................

18

TI-82 STATS Menus

............................................................................................

19

VARS

and

VARS Y.VARS

Menus

..............................................................

21

Equation Operating System (EOSé)

.........................................................

22

Error Conditions

......................................................................................................

24

Operating the TI-82 STATS 1-1

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Turning On and Turning Off the TI-82 STATS

Turning On the

Calculator

Turning Off the

Calculator

Batteries

To turn on the TI-82 STATS, press É.

If you previously had turned off the calculator by pressing y [

OFF

], the TI-82 STATS displays the home screen as it was when you last used it and clears any error.

If Automatic Power Down™ (APDé) had previously turned off the calculator, the TI-82 STATS will return exactly as you left it, including the display, cursor, and any error.

To prolong the life of the batteries, APD turns off the

TI-82 STATS automatically after about five minutes without any activity.

To turn off the TI-82 STATS manually, press y [

OFF

].

All settings and memory contents are retained by Constant

Memoryé.

Any error condition is cleared.

The TI-82 STATS uses four AAA alkaline batteries and has a user-replaceable backup lithium battery (CR1616 or CR1620).

To replace batteries without losing any information stored in memory, follow the steps in Appendix B.

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Setting the Display Contrast

Adjusting the

Display Contrast

You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from

0

(lightest) to

9

(darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark.

Note: The TI-82 STATS has 40 contrast settings, so each number

0

through 9 represents four settings.

The TI-82 STATS retains the contrast setting in memory when it is turned off.

To adjust the contrast, follow these steps.

1. Press and release the y key.

2. Press and hold † or }, which are below and above the contrast symbol (yellow, half-shaded circle).

† lightens the screen.

} darkens the screen.

Note: If you adjust the contrast setting to

0, the display may become completely blank. To restore the screen, press and release y, and then press and hold

} until the display reappears.

When to Replace

Batteries

When the batteries are low, a low-battery message is displayed when you turn on the calculator.

To replace the batteries without losing any information in memory, follow the steps in Appendix B.

Generally, the calculator will continue to operate for one or two weeks after the low-battery message is first displayed. After this period, the TI-82 STATS will turn off automatically and the unit will not operate. Batteries must be replaced. All memory is retained.

Note: The operating period following the first low-battery message could be longer than two weeks if you use the calculator infrequently.

Operating the TI-82 STATS 1-3

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The Display

Types of

Displays

Home Screen

Displaying

Entries and

Answers

The TI-82 STATS displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-82 STATS can display a horizontally or vertically split screen to show graphs and text simultaneously.

The home screen is the primary screen of the TI-82 STATS. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen.

When text is displayed, the TI-82 STATS screen can display a maximum of eight lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the

Y=

editor

(Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left.

When an entry is executed on the home screen, the answer is displayed on the right side of the next line.

Entry

Answer

The mode settings control the way the TI-82 STATS interprets expressions and displays answers (page 1.9).

If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis (

...

) is displayed to the right or left. Press ~ and | to scroll the answer.

Entry

Answer

Returning to the

Home Screen

To return to the home screen from any other screen, press y

[

QUIT

].

Busy Indicator

When the TI-82 STATS is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line.

1-4 Operating the TI-82 STATS

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Display Cursors

In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.

Cursor Appearance Effect of Next Keystroke

Entry Solid rectangle

$

A character is entered at the cursor; any existing character is overwritten

Insert Underline

__

Second Reverse arrow

Þ

A character is inserted in front of the cursor location

A 2nd character (yellow on the keyboard) is entered or a 2nd operation is executed

Alpha Reverse A

Ø

Full Checkerboard rectangle

#

An alpha character (green on the keyboard) is entered or

SOLVE

is executed

No entry; the maximum characters are entered at a prompt or memory is full

If you press ƒ during an insertion, the cursor becomes an underlined

A

(

A

) If you press y during an insertion, the underline cursor becomes an underlined # ( # ).

Graphs and editors sometimes display additional cursors, which are described in other chapters.

Operating the TI-82 STATS 1-5

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Entering Expressions and Instructions

What Is an

Expression?

An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-82 STATS, you enter an expression in the same order as you would write it on paper. For example, pR 2 is an expression.

You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.

Entering an

Expression

Multiple Entries on a Line

To create an expression, you enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press Í, regardless of the cursor location. The entire expression is evaluated according to

Equation Operating System (EOSé) rules (page 1.22), and the answer is displayed.

Most TI-82 STATS functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press «

45

. Do not enter the letters

L

,

O

, and

G

. If you enter

LOG

, the TI-82 STATS interprets the entry as implied multiplication of the variables

L

,

O

, and

G

.

Calculate 3.76 ÷ (L7.9 + ‡5) + 2 log 45.

3

Ë

76

¥ £ Ì

7

Ë

9

à y [

Í

]

5

¤ ¤

Ã

2

«

45

¤

To enter two or more expressions or instructions on a line, separate them with colons (ƒ [

:

]). All instructions are stored together in last entry (

ENTRY

; page 1.16).

1-6 Operating the TI-82 STATS

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Entering a

Number in

Scientific

Notation

To enter a number in scientific notation, follow these steps.

1. Enter the part of the number that precedes the exponent. This value can be an expression.

2. Press y [

EE

]. åååå is pasted to the cursor location.

3. If the exponent is negative, press Ì, and then enter the exponent, which can be one or two digits.

Functions

Instructions

Interrupting a

Calculation

When you enter a number in scientific notation, the

TI-82 STATS does not automatically display answers in scientific or engineering notation. The mode settings (page 1.9) and the size of the number determine the display format.

A function returns a value. For example,

÷

,

L

,

+

,

‡(

, and

log(

are the functions in the example on page 1.6. In general, the first letter of each function is lowercase on the TI-82 STATS. Most functions take at least one argument, as indicated by an open parenthesis (

(

) following the name. For example,

sin(

requires one argument,

sin(

value

)

.

An instruction initiates an action. For example,

ClrDraw

is an instruction that clears any drawn elements from a graph.

Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis (

(

) at the end of the name. For example,

Circle(

requires three arguments,

Circle(

X

,

Y

,

radius

)

.

To interrupt a calculation or graph in progress, which would be indicated by the busy indicator, press É.

When you interrupt a calculation, the menu is displayed.

To return to the home screen, select

1:Quit

.

To go to the location of the interruption, select

2:Goto

.

When you interrupt a graph, a partial graph is displayed.

To return to the home screen, press ‘ or any nongraphing key.

To restart graphing, press a graphing key or select a graphing instruction.

Operating the TI-82 STATS 1-7

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TI-82 STATS Edit Keys

Keystrokes Result

~ or |

Moves the cursor within an expression; these keys repeat.

} or †

Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat.

On the top line of an expression on the home screen, } moves the cursor to the beginning of the expression.

On the bottom line of an expression on the home screen, † moves the cursor to the end of the expression.

y | y ~

Í

Moves the cursor to the beginning of an expression.

Moves the cursor to the end of an expression.

Evaluates an expression or executes an instruction.

On a line with text on the home screen, clears the current line.

On a blank line on the home screen, clears everything on the home screen.

In an editor, clears the expression or value where the cursor is located; it does not store a zero.

{ y [

INS

]

Deletes a character at the cursor; this key repeats.

Changes the cursor to

__

; inserts characters in front of the underline cursor; to end insertion, press y [

INS

] or press |, }, ~, or †.

y

Changes the cursor to Þ; the next keystroke performs a

2nd operation

(an operation in yellow above a key and to the left); to cancel

2nd

, press y again.

ƒ

Changes the cursor to Ø; the next keystroke pastes an alpha character

(a character in green above a key and to the right) or executes

SOLVE

(Chapters 10 and 11); to cancel ƒ, press ƒ or press |, },

~, or †.

y [

A .

LOCK

] Changes the cursor to Ø; sets alpha-lock; subsequent keystrokes (on an alpha key) paste alpha characters; to cancel alpha-lock, press ƒ; name prompts set alpha-lock automatically.

Pastes an

Seq

X

in

Func

mode, a

T

mode with one keystroke.

in

Par

mode, a

q

in

Pol

mode, or an

n

in

1-8 Operating the TI-82 STATS

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Setting Modes

Checking Mode

Settings

Changing Mode

Settings

Mode settings control how the TI-82 STATS displays and interprets numbers and graphs. Mode settings are retained by the

Constant Memory feature when the TI-82 STATS is turned off.

All numbers, including elements of matrices and lists, are displayed according to the current mode settings.

To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.

Normal Sci Eng

Float 0123456789

Radian Degree

Func Par Pol Seq

Connected

Sequential

Dot

Simul

Real a+bi re^qi

Full Horiz G-T

Numeric notation

Number of decimal places

Unit of angle measure

Type of graphing

Whether to connect graph points

Whether to plot simultaneously

Real, rectangular cplx, or polar cplx

Full screen, two split-screen modes

To change mode settings, follow these steps.

1. Press † or } to move the cursor to the line of the setting that you want to change.

2. Press ~ or | to move the cursor to the setting you want.

3. Press Í.

Setting a Mode from a Program

You can set a mode from a program by entering the name of the mode as an instruction; for example,

Func

or

Float

. From a blank command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location.

Operating the TI-82 STATS 1-9

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Setting Modes

(continued)

Normal, Sci, Eng

Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to

10 digits and a two-digit exponent. You can enter a number in any format.

Normal

notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in

12345.67

.

Sci

(scientific) notation mode expresses numbers in two parts.

The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of

E

, as in

1.234567

E

4

.

Eng

(engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal; and the power-of-10 exponent is a multiple of three, as in

12.34567

E

3

.

Note: If you select

Normal notation, but the answer cannot display in

10 digits (or the absolute value is less than .001), the TI-82 STATS expresses the answer in scientific notation.

Float,

0123456789

Float

(floating) decimal mode displays up to 10 digits, plus the sign and decimal.

0123456789

(fixed) decimal mode specifies the number of digits

(

0

through

9

) to display to the right of the decimal. Place the cursor on the desired number of decimal digits, and then press

Í.

The decimal setting applies to

Normal

,

Sci

, and

Eng

notation modes.

The decimal setting applies to these numbers:

An answer displayed on the home screen

Coordinates on a graph (Chapters 3, 4, 5, and 6)

The

Tangent(

DRAW

instruction equation of the line,

x

, and

dy/dx

values (Chapter 8)

Results of

CALCULATE

operations (Chapters 3, 4, 5, and 6)

The regression equation stored after the execution of a regression model (Chapter 12)

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Radian, Degree

Func, Par, Pol,

Seq

Connected, Dot

Angle modes control how the TI-82 STATS interprets angle values in trigonometric functions and polar/rectangular conversions.

Radian

mode interprets angle values as radians. Answers display in radians.

Degree

mode interprets angle values as degrees. Answers display in degrees.

Graphing modes define the graphing parameters. Chapters 3, 4,

5, and 6 describe these modes in detail.

Func

(function) graphing mode plots functions, where

Y

is a function of

X

(Chapter 3).

Par

(parametric) graphing mode plots relations, where

X

and

Y

are functions of

T

(Chapter 4).

Pol

(polar) graphing mode plots functions, where

r

is a function of

q

(Chapter 5).

Seq

(sequence) graphing mode plots sequences (Chapter 6).

Connected

plotting mode draws a line connecting each point calculated for the selected functions.

Dot

plotting mode plots only the calculated points of the selected functions.

Operating the TI-82 STATS 1-11

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Setting Modes

(continued)

Sequential, Simul Sequential

graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted.

Simul

(simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of

X

and then evaluates and plots them for the next value of

X

.

Note: Regardless of which graphing mode is selected, the

TI-82 STATS will sequentially graph all stat plots before it graphs any functions.

Real, a+bi, re^qi

Real

mode does not display complex results unless complex numbers are entered as input.

Two complex modes display complex results.

a+b

i (rectangular complex mode) displays complex numbers in the form a+bi.

re^q

i (polar complex mode) displays complex numbers in the form re^qi.

Full, Horiz, G.T

Full

screen mode uses the entire screen to display a graph or edit screen.

Each split-screen mode displays two screens simultaneously.

Horiz

(horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9).

G.T

(graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).

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Using TI-82 STATS Variable Names

Variables and

Defined Items

Notes about

Variables

On the TI-82 STATS you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings.

The TI-82 STATS uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names.

Variable Type

Real numbers

Complex numbers

Matrices

Lists

Functions

Parametric equations

Polar functions

Sequence functions

Stat plots

Graph databases

Graph pictures

Strings

System variables

Names

A

,

B

, . . . ,

Z

,

q

A

,

B

, . . . ,

Z

,

q

ã

A

ä

,

ã

B

ä

,

ã

C

ä

, . . . ,

ã

J

ä

L

1

,

L

2

,

L

3

,

L

4

,

L

5

,

L

6

, and user-defined names

Y

1

,

Y

2

, . . . ,

Y

9

,

Y

0

X

1T

and

Y

1T

, . . . ,

X

6T

and

Y

6T r

1

,

r

2

,

r

3

,

r

4

,

r

5

,

r

6 u

,

v

,

w

Plot1, Plot2, Plot3

GDB1

,

GDB2

, . . . ,

GDB9

,

GDB0

Pic1

,

Pic2

, . . . ,

Pic9

,

Pic0

Str1

,

Str2

, . . . ,

Str9

,

Str0

Xmin

,

Xmax

, and others

You can create as many list names as memory will allow

(Chapter 11).

Programs have user-defined names and share memory with variables (Chapter 16).

From the home screen or from a program, you can store to matrices (Chapter 10), lists (Chapter 11), strings (Chapter

15), system variables such as

Xmax

(Chapter 1),

TblStart

(Chapter 7), and all

Y=

functions (Chapters 3, 4, 5, and 6).

From an editor, you can store to matrices, lists, and

Y= functions (Chapter 3).

From the home screen, a program, or an editor, you can store a value to a matrix element or a list element.

You can use

DRAW STO

menu items to store and recall graph databases and pictures (Chapter 8).

Operating the TI-82 STATS 1-13

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Storing Variable Values

Storing Values in a Variable

Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used.

To store a value to a variable from the home screen or a program using the ¿ key, begin on a blank line and follow these steps.

1. Enter the value you want to store. The value can be an expression.

2. Press ¿. ! is copied to the cursor location.

3. Press ƒ and then the letter of the variable to which you want to store the value.

4. Press Í. If you entered an expression, it is evaluated.

The value is stored to the variable.

Displaying a

Variable Value

To display the value of a variable, enter the name on a blank line on the home screen, and then press Í.

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Recalling Variable Values

Using Recall

(RCL)

To recall and copy variable contents to the current cursor location, follow these steps. To leave

RCL

, press ‘.

1. Press y ã

RCL

ä.

Rcl

and the edit cursor are displayed on the bottom line of the screen.

2. Enter the name of the variable in any of five ways.

Press ƒ and then the letter of the variable.

Press y ã

LIST

ä, and then select the name of the list, or press y [

L

n].

Press , and then select the name of the matrix.

Press  to display the

VARS

menu or  ~ to display the

VARS Y.VARS

menu; then select the type and then the name of the variable or function.

Press  |, and then select the name of the program

(in the program editor only).

The variable name you selected is displayed on the bottom line and the cursor disappears.

3. Press Í. The variable contents are inserted where the cursor was located before you began these steps.

Note: You can edit the characters pasted to the expression without affecting the value in memory.

Operating the TI-82 STATS 1-15

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ENTRY (Last Entry) Storage Area

Using ENTRY

(Last Entry)

Accessing a

Previous Entry

When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called

ENTRY

(last entry).

When you turn off the TI-82 STATS,

ENTRY

is retained in memory.

To recall

ENTRY

, press y [

ENTRY

]. The last entry is pasted to the current cursor location, where you can edit and execute it.

On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line.

Because the TI-82 STATS updates

ENTRY

only when you press

Í, you can recall the previous entry even if you have begun to enter the next expression.

5

Ã

7

Í y [

ENTRY

]

The TI-82 STATS retains as many previous entries as possible in

ENTRY

, up to a capacity of 128 bytes. To scroll those entries, press y [

ENTRY

] repeatedly. If a single entry is more than 128 bytes, it is retained for

ENTRY

, but it cannot be placed in the

ENTRY

storage area.

1

¿ ƒ

A

Í

2

¿ ƒ

B

Í y [

ENTRY

]

If you press y [

ENTRY

] after displaying the oldest stored entry, the newest stored entry is displayed again, then the nextnewest entry, and so on.

y [

ENTRY

]

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Reexecuting the

Previous Entry

After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press Í.

To reexecute the displayed entry, press Í again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed.

0

¿ ƒ

N

Í

ƒ

N

Ã

1

¿ ƒ

N

ƒ ã:ä ƒ

N

¡ Í

Í

Í

Multiple Entry

Values on a Line

To store to

ENTRY

two or more expressions or instructions, separate each expression or instruction with a colon, then press

Í. All expressions and instructions separated by colons are stored in

ENTRY

.

When you press y [

ENTRY

], all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press Í.

For the equation A=pr

2

, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess.

8

¿ ƒ

R

ƒ

[

:

] y [ p

] ƒ

R

¡ Í y [

ENTRY

] y |

7

y [

INS

] Ë

95

Í

Continue until the answer is as accurate as you want.

Clearing ENTRY Clear Entries

(Chapter 18) clears all data that the TI-82 STATS is holding in the

ENTRY

storage area.

Operating the TI-82 STATS 1-17

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Ans (Last Answer) Storage Area

Using Ans in an

Expression

Continuing an

Expression

When an expression is evaluated successfully from the home screen or from a program, the TI-82 STATS stores the answer to a storage area called

Ans

(last answer).

Ans

may be a real or complex number, a list, a matrix, or a string. When you turn off the TI-82 STATS, the value in

Ans

is retained in memory.

You can use the variable

Ans

to represent the last answer in most places. Press y [

ANS

] to copy the variable name

Ans

to the cursor location. When the expression is evaluated, the

TI-82 STATS uses the value of

Ans

in the calculation.

Calculate the area of a garden plot 1.7 meters by 4.2 meters.

Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.

1

Ë

7

¯

4

Ë

2

Í

147

¥ y [

Í

ANS

]

You can use

Ans

as the first entry in the next expression without entering the value again or pressing y [

ANS

]. On a blank line on the home screen, enter the function. The TI-82 STATS pastes the variable name

Ans

to the screen, then the function.

5

¥

2

Í

¯

9

Ë

9

Í

Storing Answers

To store an answer, store

Ans

to a variable before you evaluate another expression.

Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V.

y [ p

]

5

¡

Í

¯

3

Ë

3

Í

¿ ƒ

V

Í

1-18 Operating the TI-82 STATS

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TI-82 STATS Menus

Using a

TI-82 STATS

Menu

You can access most TI-82 STATS operations using menus.

When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen.

The menu name on the left side of the top line is highlighted.

Up to seven items in that menu are displayed, beginning with item

1

, which also is highlighted.

A number or letter identifies each menu item’s place in the menu. The order is

1

through

9

, then

0

, then

A

,

B

,

C

, and so on. The

LIST NAMES

,

PRGM EXEC

, and

PRGM EDIT

menus only label items

1

through

9

and

0

.

When the menu continues beyond the displayed items, a down arrow ( $ ) replaces the colon next to the last displayed item.

When a menu item ends in an ellipsis, the item displays a secondary menu or editor when you select it.

To display any other menu listed on the top line, press ~ or | until that menu name is highlighted. The cursor location within the initial menu is irrelevant. The menu is displayed with the cursor on the first item.

Note: The Menu Map in Appendix A shows each menu, each operation under each menu, and the key or key combination you press to display each menu.

Scrolling a Menu

To scroll down the menu items, press †. To scroll up the menu items, press }.

To page down six menu items at a time, press ƒ †. To page up six menu items at a time, press ƒ }. The green arrows on the calculator, between † and }, are the page-down and page-up symbols.

To wrap to the last menu item directly from the first menu item, press }. To wrap to the first menu item directly from the last menu item, press †.

Operating the TI-82 STATS 1-19

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TI-82 STATS Menus

(continued)

Selecting an Item from a Menu

You can select an item from a menu in either of two ways.

Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.

Press † or } to move the cursor to the item you want, and then press Í.

After you select an item from a menu, the TI-82 STATS typically displays the previous screen.

Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items

1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or q, press the key combination for that alpha character or q. If no items begin with that character, then the cursor moves beyond it to the next item.

Calculate 3

‡27.

 † † † Í

27

¤ Í

Leaving a Menu without Making a

Selection

You can leave a menu without making a selection in any of four ways.

Press y [

QUIT

] to return to the home screen.

Press ‘ to return to the previous screen.

Press a key or key combination for a different menu, such as

 or y [

LIST

].

Press a key or key combination for a different screen, such as o or y [

TABLE

].

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VARS and VARS Y.VARS Menus

VARS Menu

You can enter the names of functions and system variables in an expression or store to them directly.

To display the

VARS

menu, press . All

VARS

menu items display secondary menus, which show the names of the system variables.

1:Window

,

2:Zoom

, and

5:Statistics

each access more than one secondary menu.

VARS Y-VARS

1: Window...

2: Zoom...

3: GDB...

4: Picture...

5: Statistics...

6: Table...

7: String...

X/Y

,

T/q

, and

U/V/W variables

ZX/ZY

Graph database

Picture

XY

,

ZT/Zq

, and

ZU variables variables variables

,

G

,

EQ

,

TEST

, and

PTS variables

TABLE variables

String variables

Selecting a

Variable from the

VARS Menu or

VARS Y.VARS

Menu

To display the

VARS Y.VARS

menu, press  ~.

1:Function

,

2:Parametric

, and

3:Polar

display secondary menus of the

Y=

function variables.

VARS Y-VARS

1: Function...

2: Parametric...

3: Polar...

4: On/Off...

Y

n functions

X

n

T

,

Y

n

T

functions

r

n functions

Lets you select/deselect functions

Note: The sequence variables (

u, v, w) are located on the keyboard as the second functions of

¬, −, and ®.

To select a variable from the

VARS

or

VARS Y.VARS

menu, follow these steps.

1. Display the

VARS

or

VARS Y.VARS

menu.

Press  to display the

VARS

menu.

Press  ~ to display the

VARS Y.VARS

menu.

2. Select the type of variable, such as

2:Zoom

from the

VARS menu or

3:Polar

from the

VARS Y.VARS

menu. A secondary menu is displayed.

3. If you selected

1:Window

,

2:Zoom

, or

5:Statistics

from the

VARS

menu, you can press ~ or | to display other secondary menus.

4. Select a variable name from the menu. It is pasted to the cursor location.

Operating the TI-82 STATS 1-21

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Equation Operating System (EOSé)

Order of

Evaluation

The Equation Operating System (EOSé) defines the order in which functions in expressions are entered and evaluated on the

TI-82 STATS. EOS lets you enter numbers and functions in a simple, straightforward sequence.

EOS evaluates the functions in an expression in this order:

1 Single-argument functions that precede the argument, such as

‡(

,

sin(

, or

log(

2 Functions that are entered after the argument, such as

2

,

M1

,

!

,

¡

,

r

, and conversions

3 Powers and roots, such as

2^5

or

5 x

‡32

4 Permutations (

nPr

) and combinations (

nCr

)

5 Multiplication, implied multiplication, and division

6 Addition and subtraction

7 Relational functions, such as

>

or

8 Logic operator

and

9 Logic operators

or

and

xor

Within a priority level, EOS evaluates functions from left to right.

Calculations within parentheses are evaluated first.

Multiargument functions, such as

nDeriv(A

as they are encountered.

2

,A,6)

, are evaluated

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Implied

Multiplication

The TI-82 STATS recognizes implied multiplication, so you need not press ¯ to express multiplication in all cases. For example, the TI-82 STATS interprets

2p

,

4sin(46)

,

5(1+2)

, and

(2

ääää5)7 as implied multiplication.

Note: TI-82 STATS implied multiplication rules differ from those of the

äääX,

Parentheses

All calculations inside a pair of parentheses are completed first.

For example, in the expression

4(1+2)

, EOS first evaluates the portion inside the parentheses,

1+2

, and then multiplies the answer,

3

, by

4

.

Negation

You can omit the close parenthesis (

)

) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or displayconversion instructions.

Note: An open parenthesis following a list name, matrix name, or Y= function name does not indicate implied multiplication. It specifies elements in the list (Chapter 11) or matrix (Chapter 10) and specifies a value for which to solve the

Y= function.

To enter a negative number, use the negation key. Press Ì and then enter the number. On the TI-82 STATS, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.

For example,

MX

2

, evaluates to a negative number (or 0). Use parentheses to square a negative number.

Note: Use the

¹ key for subtraction and the Ì key for negation. If you press

¹ to enter a negative number, as in 9 ¯ ¹ 7, or if you press

Ì to indicate subtraction, as in 9 Ì 7, an error occurs. If you press

ƒ A Ì ƒ B, it is interpreted as implied multiplication

(

A

ääääMB).

Operating the TI-82 STATS 1-23

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Error Conditions

Diagnosing an

Error

The TI-82 STATS detects errors while performing these tasks.

Evaluating an expression

Executing an instruction

Plotting a graph

Storing a value

When the TI-82 STATS detects an error, it returns an error message as a menu title, such as

ERR:SYNTAX

or

ERR:DOMAIN

. Appendix B describes each error type and possible reasons for the error.

Correcting an

Error

If you select

1:Quit

(or press y [

QUIT

] or ‘), then the home screen is displayed.

If you select

2:Goto

, then the previous screen is displayed with the cursor at or near the error location.

Note: If a syntax error occurs in the contents of a Y= function during program execution, then the Goto option returns to the Y= editor, not to the program.

To correct an error, follow these steps.

1. Note the error type (

ERR:

error type).

2. Select

2:Goto

, if it is available. The previous screen is displayed with the cursor at or near the error location.

3. Determine the error. If you cannot recognize the error, refer to Appendix B.

4. Correct the expression.

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Contents

2

Math, Angle, and Test

Operations

Getting Started: Coin Flip

.................................................................................

Keyboard Math Operations

..............................................................................

MATH

Operations

...................................................................................................

Using the Equation Solver

................................................................................

MATH NUM

(Number) Operations

..............................................................

13

5

8

2

3

Entering and Using Complex Numbers

....................................................

16

MATH CPX

(Complex) Operations

............................................................

18

MATH PRB

(Probability) Operations

........................................................

20

ANGLE

Operations

................................................................................................

23

TEST

(Relational) Operations

........................................................................

24

TEST LOGIC

(Boolean) Operations

..........................................................

26

Math, Angle, and Test Operations 2.1

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Getting Started: Coin Flip

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5.

1. Begin on the home screen. Press  | to display the

MATH PRB

menu. Press

7

to select

7:randBin(

(random Binomial).

randBin(

is pasted to the home screen. Press

10

to enter the number of coin flips. Press ¢. Press Ë

5

to enter the probability of heads. Press ¢. Press

40

to enter the number of simulations. Press ¤.

2. Press Í to evaluate the expression. A list of

40 elements is displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.

3. Press ¿ y ã

L1

ä Í to store the data to the list name

L

1

. You then can use the data for another activity, such as plotting a histogram

(Chapter 12).

4. Press ~ or | to view the additional counts in the list. Ellipses (

...

) indicate that the list continues beyond the screen.

Note: Since randBin( generates random numbers, your list elements may differ from those in the example.

2.2 Math, Angle, and Test Operations

Keyboard Math Operations

Using Lists with

Math Operations

Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length.

+ (Addition),

N (Subtraction),

ääää (Multiplication),

à (Division)

You can use

+

(addition, Ã),

N

(subtraction, ¹), ääää

(multiplication, ¯), and

à

(division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use

à

with matrices.

valueA

+

valueB valueA

ääää

valueB

valueA

N

valueB valueA

à

valueB

Trigonometric

Functions

You can use the trigonometric (trig) functions (sine, ˜; cosine, ™; and tangent, š) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.

For example,

sin(30)

in

Radian

mode returns

L.9880316241

; in

Degree

mode it returns

.5

.

sin(

value

) cos(

value

) tan(

value

)

You can use the inverse trig functions (arcsine, y [

SIN

L1

]; arccosine, y [

COS

L1

]; and arctangent, y [

TAN

L1

]) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.

sin

L1

(

value

) cos

L1

(

value

) tan

L1

(

Note: The trig functions do not operate on complex numbers.

value

)

^ (Power),

2

(Square),

‡( (Square Root)

You can use

^

(power, ›),

2

(square, ¡), and

‡(

(square root, y [

]) with real and complex numbers, expressions, lists, and matrices. You cannot use

‡(

with matrices.

value

^

power value

2

‡(

value

)

L1

(Inverse)

You can use

L1

(inverse, —) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1àx.

value

L1

Math, Angle, and Test Operations 2.3

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Keyboard Math Operations

(continued) log(,

10^(, ln(

You can use

log(

(logarithm, «),

10^(

(power of 10, y

[

10

x

]), and

ln(

(natural log, µ) with real or complex numbers, expressions, and lists.

log(

value

) 10^(

power

) ln(

value

) e^( (Exponential) e^(

(exponential, y ã e

x

]) returns the constant

e

raised to a power. You can use

e^(

with real or complex numbers, expressions, and lists.

e^(

power

) e (Constant) e

(constant, y [ e

]) is stored as a constant on the TI-82 STATS

. Press y [ e

] to copy

e

to the cursor location. In calculations, the TI-82 STATS uses 2.718281828459 for

e

.

L (Negation) M

(negation, Ì) returns the negative of value. You can use

M

with real or complex numbers, expressions, lists, and matrices.

M

value

EOS rules (Chapter 1) determine when negation is evaluated.

For example,

LA

2

returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in

(LA)

2

.

p (Pi)

Note: On the TI-82 STATS, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press

¹.

p

(Pi, y [ p

]) is stored as a constant in the TI-82 STATS. In calculations, the TI-82 STATS uses 3.1415926535898 for

p

.

2.4 Math, Angle, and Test Operations

MATH Operations

MATH Menu

4Frac,

4Dec

To display the

MATH

menu, press .

MAT

H

NUM CPX PRB

1: 4Frac

2: 4Dec

3:

3

4:

5:

3

‡( x

6: fMin(

7: fMax(

8: nDeriv(

9: fnInt(

0: Solver...

Displays the answer as a fraction.

Displays the answer as a decimal.

Calculates the cube.

Calculates the cube root.

Calculates the x

th

root.

Finds the minimum of a function.

Finds the maximum of a function.

Computes the numerical derivative.

Computes the function integral.

Displays the equation solver.

4Frac

(display as a fraction) displays an answer as its rational equivalent. You can use

4Frac

with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use

4Frac

following value.

value

4Frac

4Dec

(display as a decimal) displays an answer in decimal form.

You can use

4Dec

with real or complex numbers, expressions, lists, and matrices. You can only use

4Dec

following value.

value

4Dec

Math, Angle, and Test Operations 2.5

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MATH Operations

(continued)

3

(Cube),

3

‡( (Cube Root)

3

(cube) returns the cube of value. You can use

3

with real or complex numbers, expressions, lists, and square matrices.

value

3

3

‡(

(cube root) returns the cube root of value. You can use

3

‡(

with real or complex numbers, expressions, and lists.

3

‡(

value

) x

‡ (Root) fMin(, fMax( x

(x

th

root) returns the x

th

root of value. You can use

x

with real or complex numbers, expressions, and lists.

x th root

x

value

fMin(

(function minimum) and

fMax(

(function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable.

fMin(

and

fMax(

are not valid in

expression. The accuracy is controlled by tolerance (if not specified, the default is 1â

L

5).

fMin(

expression

,

variable

,

lower

,

upper[

,

tolerance]

) fMax(

expression

,

variable

,

lower

,

upper[

,

tolerance]

)

Note: In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]).

2.6 Math, Angle, and Test Operations

nDeriv( nDeriv(

(numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is

L

3).

nDeriv(

is valid only for real numbers.

nDeriv(

expression

,

variable

,

value[

,

H]

) nDeriv(

uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.

f¢( x

) = f( x

+H)Nf( x NH)

2H

As H becomes smaller, the approximation usually becomes more accurate.

fnInt(

You can use

nDeriv(

once in expression. Because of the method used to calculate

nDeriv(

, the TI-82 STATS can return a false derivative value at a nondifferentiable point.

fnInt(

(function integral) returns the numerical integral (Gauss-

Kronrod method) of expression with respect to variable, given

lower limit, upper limit, and a tolerance (if not specified, the default is 1â

L

5).

fnInt(

is valid only for real numbers.

fnInt(

expression

,

variable

,

lower

,

upper[

,

tolerance]

)

Tip: To speed the drawing of integration graphs (when

fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s.

Math, Angle, and Test Operations 2.7

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Using the Equation Solver

Solver Solver

displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero.

Solver

is valid only for real numbers.

When you select

Solver

, one of two screens is displayed.

The equation editor (see step 1 picture below) is displayed when the equation variable

eqn

is empty.

The interactive solver editor (see step 3 picture on page 2.9) is displayed when an equation is stored in

eqn

.

Entering an

Expression in the

Equation Solver

To enter an expression in the equation solver, assuming that the variable

eqn

is empty, follow these steps.

1. Select

0:Solver

from the

MATH

menu to display the equation editor.

2. Enter the expression in any of three ways.

Enter the expression directly into the equation solver.

Paste a

Y=

variable name from the

VARS Y.VARS

menu to the equation solver.

Press y [

RCL

], paste a

Y=

variable name from the

VARS Y.VARS

menu, and press Í. The expression is pasted to the equation solver.

The expression is stored to the variable

eqn

as you enter it.

2.8 Math, Angle, and Test Operations

Entering an

Expression in the

Equation Solver

(continued)

3. Press Í or †. The interactive solver editor is displayed.

The equation stored in

eqn

is set equal to zero and displayed on the top line.

Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed.

The default lower and upper bounds appear in the last line of the editor (

bound={L1

åååå

99,1

åååå

99}

).

A

$

is displayed in the first column of the bottom line if the editor continues beyond the screen.

Tip: To use the solver to solve an equation such as

K=.5MV

2 eqn:0=KN.5MV

2

in the equation editor.

, enter

Entering and

Editing Variable

Values

When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable.

You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration.

You can store equations to any

VARS Y.VARS

variables, such as

Y

1

or

r

6

, and then reference the variables in the equation. The interactive solver editor displays all variables of all

Y=

functions referenced in the equation.

Math, Angle, and Test Operations 2.9

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Using the Equation Solver

(continued)

Solving for a

Variable in the

Equation Solver

To solve for a variable using the equation solver after an equation has been stored to

eqn

, follow these steps.

1. Select

0:Solver

from the

MATH

menu to display the interactive solver editor, if not already displayed.

2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press Í or †.

3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the

TI-82 STATS will attempt to display the solution that is closest to your guess.

The default guess is calculated as

(upper + lower)

2

.

2.10 Math, Angle, and Test Operations

Solving for a

Variable in the

Equation Solver

(continued)

4. Edit

bound={

lower

,

upper

}

. lower and upper are the bounds between which the TI-82 STATS searches for a solution. This is optional, but it may help find the solution more quickly. The default is

bound={L1

åååå

99,1

åååå

99}

.

5. Move the cursor to the variable for which you want to solve and press ƒ [

SOLVE

] (above the Í key).

The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen.

Note: When a number continues beyond the screen, be sure to press

~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent.

The values of the variables are updated in memory.

leftNrt=

diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation. A solid square in the first column next to

leftNrt=

indicates that the equation has been evaluated at the new value of the variable for which you solved.

Math, Angle, and Test Operations 2.11

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Using the Equation Solver

(continued)

Editing an

Equation Stored to eqn

To edit or replace an equation stored to

eqn

when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation.

Equations with

Multiple Roots

Some equations have more than one solution. You can enter a new initial guess (page 2.10) or new bounds (page 2.11) to look for additional solutions.

Further Solutions

After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid squares next to the previous solution and

leftNrt=

diff

disappear. Move the cursor to the variable for which you now want to solve and press ƒ [

SOLVE

].

Controlling the

Solution for

Solver or solve(

The TI-82 STATS solves equations through an iterative process.

To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions.

Using solve( on the Home Screen or from a

Program

The function

solve(

is available only from

CATALOG

or from within a program. It returns a solution (root) of expression for

variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower is

L1â99. The default for upper is 1â99.

solve(

is valid only for real numbers.

solve(

expression

,

variable

,

guess[

,{

lower

,

upper

}

]

)

expression is assumed equal to zero. The value of variable will not be updated in memory. guess may be a value or a list of two values. Values must be stored for every variable in expression, except variable, before expression is evaluated. lower and upper must be entered in list format.

2.12 Math, Angle, and Test Operations

MATH NUM (Number) Operations

MATH NUM Menu

To display the

MATH NUM

menu, press  ~.

MATH NU

M

1: abs(

2: round(

3: iPart(

4: fPart(

5: int(

6: min(

7: max(

8: lcm(

9: gcd(

CPX PRB

Absolute value

Round

Integer part

Fractional part

Greatest integer

Minimum value

Maximum value

Least common multiple

Greatest common divisor

abs( abs(

(absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices.

abs(

value

) round(

Note:

abs( is also available on the MATH CPX menu.

round(

returns a number, expression, list, or matrix rounded to

#decimals (9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits.

round(

value[

,

#decimals]

)

Math, Angle, and Test Operations 2.13

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MATH NUM (Number) Operations

(continued) iPart(, fPart( iPart(

(integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices.

iPart(

value

) fPart(

(fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices.

fPart(

value

) int( int(

(greatest integer) returns the largest integer  real or complex numbers, expressions, lists, and matrices.

int(

value

)

Note: For a given value, the result of

int( is the same as the result of

iPart( for nonnegative numbers and negative integers, but one integer less than the result of

iPart( for negative noninteger numbers.

2.14 Math, Angle, and Test Operations

min(, max( min(

(minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listA and listB are compared,

min(

returns a list of the smaller of each pair of elements. If list and value are compared,

min(

compares each element in list with value.

max(

(maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared,

max(

returns a list of the larger of each pair of elements. If list and value are compared,

max(

compares each element in list with value.

min(

valueA

,

valueB

) min(

list

) min(

listA

,

listB

) min(

list

,

value

) max(

valueA

,

valueB

) max(

list

) max(

listA

,

listB

) max(

list

,

value

) lcm(, gcd(

Note:

min( and max( also are available on the LIST MATH menu.

lcm(

returns the least common multiple of valueA and valueB, both of which must be nonnegative integers. When listA and

listB are specified,

lcm(

returns a list of the lcm of each pair of elements. If list and value are specified,

lcm(

finds the lcm of each element in list and value.

gcd(

returns the greatest common divisor of valueA and valueB, both of which must be nonnegative integers. When listA and

listB are specified,

gcd(

returns a list of the gcd of each pair of elements. If list and value are specified,

gcd(

finds the gcd of each element in list and value.

lcm(

valueA

,

valueB

) lcm(

listA

,

listB

) lcm(

list

,

value

) gcd(

valueA

,

valueB

) gcd(

listA

,

listB

) gcd(

list

,

value

)

Math, Angle, and Test Operations 2.15

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Entering and Using Complex Numbers

Complex-Number

Modes

The TI-82 STATS displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes.

a+b

i (rectangular-complex mode)

re^q

i (polar-complex mode)

On the TI-82 STATS, complex numbers can be stored to variables. Also, complex numbers are valid list elements.

In

Real

mode, complex-number results return an error, unless you entered a complex number as input. For example, in

Real

mode

ln(L1)

returns an error; in

a+b

i mode

ln(L1)

returns an answer.

Real

mode

a+b

i mode

$ $

Entering

Complex

Numbers

Note about

Radian versus

Degree Mode

Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed.

Radian mode is recommended for complex number calculations.

Internally, the TI-82 STATS converts all entered trig values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.

In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^( ) are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as

e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode.

2.16 Math, Angle, and Test Operations

Interpreting

Complex Results

Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction (page 2.19).

In the example below,

re^q

i and

Radian

modes are set.

Rectangular-

Complex Mode

Rectangular-complex mode recognizes and displays a complex number in the form a+b

i, where a

is the real component, b

is the imaginary component, and i is a constant equal to

-1

.

To enter a complex number in rectangular form, enter the value of a (real component), press à or ¹, enter the value of b

(imaginary component), and press y [i] (constant).

real component(

+

or

N

)imaginary componenti

Polar-Complex

Mode

Polar-complex mode recognizes and displays a complex number in the form re^ log, q q

i, where r is the magnitude, e is the base of the natural

is the angle, and i is a constant equal to

-1

.

To enter a complex number in polar form, enter the value of r

(magnitude), press y [ e value of q

x

] (exponential function), enter the

(angle), press y [i] (constant), and then press ¤.

magnitude

e^(

anglei

)

Math, Angle, and Test Operations 2.17

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MATH CPX (Complex) Operations

MATH CPX Menu

To display the

MATH CPX

menu, press  ~ ~.

MATH NU

M

1: conj(

2: real(

3: imag(

4: angle(

5: abs(

6: 4Rect

7: 4Polar

CPX PRB

Returns the complex conjugate.

Returns the real part.

Returns the imaginary part.

Returns the polar angle.

Returns the magnitude (modulus).

Displays the result in rectangular form.

Displays the result in polar form.

conj( conj(

(conjugate) returns the complex conjugate of a complex number or list of complex numbers.

conj(

a

+

bi

)

returns aNbi in

a+b

i mode.

conj(

r

e^(

q

i

))

returns r

e^(

Lq

i

)

in

re^q

i mode.

real( imag( real(

(real part) returns the real part of a complex number or list of complex numbers.

real(

a

+

bi

)

returns a.

real(

r

e^(

q

i

))

returns r

ääää

cos( q

).

imag(

(imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers.

imag(

a

+

bi

)

returns b.

imag(

r

e^(

q

i

))

returns r ääää

sin(

q

).

2.18 Math, Angle, and Test Operations

angle( abs(

4Rect

4Polar angle(

returns the polar angle of a complex number or list of complex numbers, calculated as tan

L1

(b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant.

angle(

a

+

bi

)

returns tan L

1

(b/a).

angle(

r

e^(

q

i

))

returns q

, where Lp< q

<p.

abs(

(absolute value) returns the magnitude (modulus),

(real2+imag2) , of a complex number or list of complex numbers.

abs(

a

+

bi

)

returns (a2+b2) .

abs(

r

e^(

q

i

))

returns r (magnitude).

4Rect

(display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real.

complex result

8Rect

returns a+bi.

4Polar

(display as polar) displays a complex result in polar form.

It is valid only at the end of an expression. It is not valid if the result is real.

complex result

8Polar

returns r

e^(

q

i

)

.

Math, Angle, and Test Operations 2.19

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MATH PRB (Probability) Operations

MATH PRB Menu

To display the

MATH PRB

menu, press  |.

MATH NUM CPXPRB

1: rand

2: nPr

3: nCr

4: !

5: randInt(

6: randNorm(

7: randBin(

Random-number generator

Number of permutations

Number of combinations

Factorial

Random-integer generator

Random # from Normal distribution

Random # from Binomial distribution

rand rand

(random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of randomnumbers, specify an integer > 1 for numtrials (number of trials).

The default for numtrials is 1.

rand

[

(

numtrials

)

]

Tip: To generate random numbers beyond the range of 0 to 1, you can include

rand in an expression. For example, rand

ääää5 generates a random number > 0 and < 5.

With each

rand

execution, the TI-82 STATS generates the same random-number sequence for a given seed value. The

TI-82 STATS factory-set seed value for

rand

is

0

. To generate a different random-number sequence, store any nonzero seed value to

rand

. To restore the factory-set seed value, store

0

to

rand

or reset the defaults (Chapter 18).

Note: The seed value also affects randInt(, randNorm(, and

randBin( instructions (page 2.22).

2.20 Math, Angle, and Test Operations

nPr, nCr nPr

(number of permutations) returns the number of permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists.

items

nPr

number

nCr

(number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists.

items

nCr

number

! (Factorial)

!

(factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be ‚L.5 and 69.

value

!

Note: The factorial is computed recursively using the relationship

(n+1)! = n

än!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence: n!=n

ä(nN1)ä(nN2)ä ... ä2ä1, if n is an integer ‚0 n!= n

ä(nN1)ä(nN2)ä ... ä1à2ä‡p, if n+1à2 is an integer ‚0 n! is an error, if neither n nor n+1à2 is an integer ‚0.

(The variable n equals value in the syntax description above.)

Math, Angle, and Test Operations 2.21

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MATH PRB (Probability) Operations

(continued) randInt( randInt(

(random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1.

randInt(

lower

,

upper[

,

numtrials]

) randNorm( randNorm(

(random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1.

randNorm(

m

,

s [

,

numtrials]

) randBin( randBin(

(random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials

(number of trials) must be ‚ 1. prob (probability of success) must be ‚ 0 and  1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1.

randBin(

numtrials

,

prob[

,

numsimulations]

)

Note: The seed value stored to

rand also affects randInt(,

randNorm(, and randBin( instructions (page 2-20).

2.22 Math, Angle, and Test Operations

ANGLE Operations

ANGLE Menu

DMS Entry

Notation

To display the

ANGLE

menu, press y [

ANGLE

]. The

ANGLE menu displays angle indicators and instructions. The

Radian

/

Degree

mode setting affects the TI-82 STATS interpretation of

ANGLE

menu entries.

ANGLE

1: ¡

2: '

3: r

4: 8DMS

5: R8Pr(

6: R8Pq(

7: P8Rx(

8: P8Ry(

Degree notation

DMS minute notation

Radian notation

Displays as degree/minute/second

Returns

Returns

Returns

Returns r q x y

, given

, given

, given

, given

X

X

R

R and and and and

Y

Y q q

DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (

¡

), the minute symbol (

'

), and the second symbol

(

"

). degrees must be a real number; minutes and seconds must be real numbers ‚ 0.

degrees

¡

minutes

'

seconds

"

For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to

Degree

, you must use

¡

so that the

TI-82 STATS can interpret the argument as degrees, minutes, and seconds.

Degree

mode

Radian

mode

¡ (Degree)

¡

(degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In

Radian

mode, you can use

¡

to convert degrees to radians.

value

¡

{

value1

,

value2

,

value3

,

value4

,

...

,

value n

¡

also designates degrees (D) in DMS format.

'

(minutes) designates minutes (M) in DMS format.

"

(seconds) designates seconds (S) in DMS format.

Note: " is not on the ANGLE menu. To enter ", press ƒ [

ã

].

Math, Angle, and Test Operations 2.23

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ANGLE Operations

(continued) r

(Radians) r

(radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In

Degree

mode, you can use

r

to convert radians to degrees.

value

r

Degree

mode

8DMS

8DMS

(degree/minute/second) displays answer in DMS format

(page 2.23). The mode setting must be

Degree

for answer to be interpreted as degrees, minutes, and seconds.

8DMS

is valid only at the end of a line.

answer

8DMS

R8Pr (,

R8Pq ( ,

P8Rx(,

P8Ry(

R8Pr(

converts rectangular coordinates to polar coordinates and returns

r

.

R8Pq(

converts rectangular coordinates to polar coordinates and returns

q

. x and y can be lists.

R8Pr(

x

,

y

), R8Pq(

x

,

y

)

Note: Radian mode is set.

P8Rx(

converts polar coordinates to rectangular coordinates and returns

x

.

P8Ry(

converts polar coordinates to rectangular coordinates and returns

y

. r and q

can be lists.

P8Rx(

r

,

q

), P8Ry(

r

,

q

)

Note: Radian mode is set.

2.24 Math, Angle, and Test Operations

TEST (Relational) Operations

TEST Menu

=, ƒ,

>, ‚,

<, 

To display the

TEST

menu, press y [

TEST

].

This operator...

TEST LOGIC

1: =

2: ƒ

3: >

4: ‚

5: <

6: 

Returns 1 (true) if...

Equal

Not equal to

Greater than

Greater than or equal to

Less than

Less than or equal to

Relational operators compare valueA and valueB and return

1

if the test is true or

0

if the test is false. valueA and valueB can be real numbers, expressions, or lists. For

=

and

ƒ

only, valueA and

valueB also can be matrices or complex numbers. If valueA and

valueB are matrices, both must have the same dimensions.

Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.

valueA

=

valueB valueA

>

valueB valueA

<

valueB valueA

ƒ

valueB valueA

valueB valueA

valueB

Using Tests

Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1).

The expression

2+2=2+3

returns

0

. The TI-82 STATS performs the addition first because of EOS rules, and then it compares 4 to 5.

The expression

2+(2=2)+3

returns

6

. The TI-82 STATS performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.

Math, Angle, and Test Operations 2.25

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TEST LOGIC (Boolean) Operations

TEST LOGIC

Menu

Boolean

Operators and, or, xor not(

Using Boolean

Operations

To display the

TEST LOGIC

menu, press y ã

TEST

ä ~.

This operator...

TEST LOGIC

1: and

2: or

3: xor

4: not(

Returns a 1 (true) if...

Both values are nonzero (true).

At least one value is nonzero (true).

Only one value is zero (false).

The value is zero (false).

Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero

(false) or nonzero (true).

and

,

or

, and

xor

(exclusive or) return a value of

1

if an expression is true or

0

if an expression is false, according to the table below. valueA and valueB can be real numbers, expressions, or lists.

valueA

and

valueB valueA

or

valueB valueA

xor

valueB

valueA valueB

ƒ0

ƒ0

0

0

ƒ0

0

ƒ0

0 returns returns returns returns

and

1

0

0

0 or

1

1

1

0 xor

0

1

1

0 not(

returns

1

if value (which can be an expression) is

0

.

not(

value

)

Boolean logic is often used with relational tests. In the following program, the instructions store

4

into

C

.

2.26 Math, Angle, and Test Operations

Contents

3

Function

Graphing

Getting Started: Graphing a Circle

..............................................................

Defining Graphs

......................................................................................................

Setting the Graph Modes

...................................................................................

Defining Functions

................................................................................................

Selecting and Deselecting Functions

..........................................................

Setting Graph Styles for Functions

..............................................................

Setting the Viewing Window Variables

...................................................

11

Setting the Graph Format

..................................................................................

13

7

9

4

5

2

3

Displaying Graphs

..................................................................................................

15

Exploring Graphs with the Free-Moving Cursor

................................

17

Exploring Graphs with

TRACE

.....................................................................

18

Exploring Graphs with the

ZOOM

Instructions

..................................

20

Using

ZOOM MEMORY

....................................................................................

23

Using the

CALC

(Calculate) Operations

..................................................

25

Function Graphing 3.1

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Getting Started: Graphing a Circle

Getting Started is a fast-paced introduction. Read the chapter for details.

Graph a circle of radius 10, centered on the origin in the standard viewing window.

To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use

ZSquare

(zoom square) to adjust the display and make the functions appear as a circle.

1. In

Func

mode, press o to display the

Y= editor. Press y ã

ä

100

¹ „ ¡ ¤

Í to enter the expression Y=‡(100NX

2

), which defines the top half of the circle.

The expression Y=L‡(100NX

2

) defines the bottom half of the circle. On the TI-82 STATS, you can define one function in terms of another.

To define

Y

2

=LY

1

, press Ì to enter the negation sign. Press  ~ to display the

VARS Y.VARS

menu. Then press Í to select

1:Function

. The

FUNCTION secondary menu is displayed. Press

1

to select

1:Y

1

.

2. Press q

6

to select

6:ZStandard

. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s.

Notice that the functions appear as an ellipse in the standard viewing window.

3. To adjust the display so that each pixel represents an equal width and height, press q

5

to select

5:ZSquare

. The functions are replotted and now appear as a circle on the display.

4. To see the

ZSquare

window variables, press p and notice the new values for

Xmin

,

Xmax

,

Ymin

, and

Ymax

.

3.2 Function Graphing

Defining Graphs

TI-82 STATS—

Graphing Mode

Similarities

Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-82 STATS graphing mode.

Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing.

Defining a Graph

To define a graph in any graphing mode, follow these steps.

Some steps are not always necessary.

1. Press z and set the appropriate graph mode (page 3.4).

2. Press o and enter, edit, or select one or more functions in the

Y=

editor (page 3.5 and 3.7).

3. Deselect stat plots, if necessary (page 3.7).

4. Set the graph style for each function (page 3.9).

5. Press p and define the viewing window variables

(page 3.11).

6. Press y [

FORMAT

] and select the graph format settings

(page 3.13).

Displaying and

Exploring a

Graph

Saving a Graph for Later Use

After you have defined a graph, press s to display it.

Explore the behavior of the function or functions using the

TI-82 STATS tools described in this chapter.

You can store the elements that define the current graph to any of 10 graph database variables (

GDB1

through

GDB9

, and

GDB0

; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph.

These types of information are stored in a

GDB

.

Y=

functions

Graph style settings

Window settings

Format settings

You can store a picture of the current graph display to any of 10 graph picture variables (

Pic1

through

Pic9

, and

Pic0

; Chapter

8). Then you can superimpose one or more stored pictures onto the current graph.

Function Graphing 3.3

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Setting the Graph Modes

Checking and

Changing the

Graphing Mode

To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select

Func

mode before you enter values for the window variables and before you enter the functions.

Setting Modes from a Program

The TI-82 STATS has four graphing modes.

Func

(function graphing)

Par

(parametric graphing; Chapter 4)

Pol

(polar graphing; Chapter 5)

Seq

(sequence graphing; Chapter 6)

Other mode settings affect graphing results. Chapter 1 describes each mode setting.

Float

or

0123456789

(fixed) decimal mode affects displayed graph coordinates.

Radian

or

Degree

angle mode affects interpretation of some functions.

Connected

or

Dot

plotting mode affects plotting of selected functions.

Sequential

or

Simul

graphing-order mode affects function plotting when more than one function is selected.

To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps.

1. Press z to display the mode settings.

2. Press †, ~, |, and } to place the cursor on the mode that you want to select.

3. Press Í to paste the mode name to the cursor location.

The mode is changed when the program is executed.

3.4 Function Graphing

Defining Functions

Displaying

Functions in the

Y= Editor

To display the

Y=

editor, press o. You can store up to 10 functions to the function variables

Y

1

through

Y

9

, and

Y

0

. You can graph one or more defined functions at once. In this example, functions

Y

1

and

Y

2

are defined and selected.

Defining or

Editing a

Function

To define or edit a function, follow these steps.

1. Press o to display the

Y=

editor.

2. Press † to move the cursor to the function you want to define or edit. To erase a function, press ‘.

3. Enter or edit the expression to define the function.

You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.

The independent variable in the function is

X

.

Func

mode defines „ as

X

. To enter

X

, press „ or press

ƒ [

X

].

When you enter the first character, the

=

is highlighted, indicating that the function is selected.

As you enter the expression, it is stored to the variable

Yn

as a user-defined function in the

Y=

editor.

4. Press Í or † to move the cursor to the next function.

Function Graphing 3.5

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Defining Functions

(continued)

Defining a

Function from the Home Screen or a Program

To define a function from the home screen or a program, begin on a blank line and follow these steps.

1. Press ƒ [

ã

], enter the expression, and then press ƒ

[

ã

] again.

2. Press ¿.

3. Press  ~

1

to select

1:Function

from the

VARS Y.VARS

menu.

4. Select the function name, which pastes the name to the cursor location on the home screen or program editor.

5. Press Í to complete the instruction.

"

expression

"

!

n

Evaluating Y=

Functions in

Expressions

When the instruction is executed, the TI-82 STATS stores the expression to the designated variable

Y

n, selects the function, and displays the message

Done

.

You can calculate the value of a

Y=

function

Y

n at a specified

value of

X

. A list of values returns a list.

Y

n

(

value

)

Y

n

({

value1

,

value2

,

value3

,

. . .

,

value n

})

3.6 Function Graphing

Selecting and Deselecting Functions

Selecting and

Deselecting a

Function

You can select and deselect (turn on and turn off) a function in the

Y=

editor. A function is selected when the

=

sign is highlighted. The TI-82 STATS graphs only the selected functions. You can select any or all functions

Y

1

through

Y

9

, and

Y

0

.

To select or deselect a function in the

Y=

editor, follow these steps.

1. Press o to display the

Y=

editor.

2. Move the cursor to the function you want to select or deselect.

3. Press | to place the cursor on the function’s

=

sign.

4. Press Í to change the selection status.

When you enter or edit a function, it is selected automatically.

When you clear a function, it is deselected.

Turning On or

Turning Off a Stat

Plot in the Y=

Editor

To view and change the on/off status of a stat plot in the

Y=

editor, use

Plot1 Plot2 Plot3

(the top line of the

Y=

editor).

When a plot is on, its name is highlighted on this line.

To change the on/off status of a stat plot from the

Y= editor, press } and ~ to place the cursor on

Plot1

,

Plot2

, or

Plot3

, and then press Í.

Plot1

is turned on.

Plot2

and

Plot3

are turned off.

Function Graphing 3.7

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Selecting and Deselecting Functions

(continued)

Selecting and

Deselecting

Functions from the Home Screen or a Program

To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps.

1. Press  ~ to display the

VARS Y.VARS

menu.

2. Select

4:On/Off

to display the

ON/OFF

secondary menu.

3. Select

1:FnOn

to turn on one or more functions or

2:FnOff

to turn off one or more functions. The instruction you select is copied to the cursor location.

4. Enter the number (

1

through

9

, or

0

; not the variable

Y

n) of each function you want to turn on or turn off.

If you enter two or more numbers, separate them with commas.

To turn on or turn off all functions, do not enter a number after

FnOn

or

FnOff

.

FnOn

[function#

,

function#

,

. . .

,

function n]

FnOff

[function#

,

function#

,

. . .

,

function n]

5. Press Í. When the instruction is executed, the status of each function in the current mode is set and

Done

is displayed.

For example, in

Func

mode,

FnOff :FnOn 1,3

turns off all functions in the

Y=

editor, and then turns on

Y

1

and

Y

3

.

3.8 Function Graphing

Setting Graph Styles for Functions

Graph Style

Icons in the Y=

Editor

This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set

Y

1

as a solid line,

Y

2

as a dotted line, and

Y

3

as a thick line.

Icon Style

ì

ç

è

é

ê

ë

í

Line

Thick

Above

Below

Path

Description

A solid line connects plotted points; this is the default in

Connected

mode

A thick solid line connects plotted points

Shading covers the area a*bove the graph

Shading covers the area below the graph

A circular cursor traces the leading edge of the graph and draws a path

Animate A circular cursor traces the leading edge of the graph without drawing a path

Dot A small dot represents each plotted point; this is the default in

Dot

mode

Note: Some graph styles are not available in all graphing modes.

Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.

Setting the Graph

Style

To set the graph style for a function, follow these steps.

1. Press o to display the

Y=

editor.

2. Press † and } to move the cursor to the function.

3. Press | | to move the cursor left, past the

=

sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)

4. Press Í repeatedly to rotate through the graph styles.

The seven styles rotate in the same order in which they are listed in the table above.

5. Press ~, }, or † when you have selected a style.

Function Graphing 3.9

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Setting Graph Styles for Functions

(continued)

Shading Above and Below

When you select é or ê for two or more functions, the

TI-82 STATS rotates through four shading patterns.

Vertical lines shade the first function with a é or ê graph style.

Horizontal lines shade the second.

Negatively sloping diagonal lines shade the third.

Positively sloping diagonal lines shade the fourth.

The rotation returns to vertical lines for the fifth é or ê function, repeating the order described above.

When shaded areas intersect, the patterns overlap.

Setting a Graph

Style from a

Program

Note: When

é or ê is selected for a Y= function that graphs a family of curves, such as

Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves.

To set the graph style from a program, select

H:GraphStyle(

from the

PRGM CTL

menu. To display this menu, press  while in the program editor. function# is the number of the

Y= function name in the current graphing mode. graphstyle# is an integer from

1

to

7

that corresponds to the graph style, as shown below.

1

= ç (line)

4

= ê (below)

2

= è (thick)

5

= ë (path)

3

= é (above)

6

= ì (animate)

GraphStyle(

function#

,

graphstyle#

)

For example, when this program is executed in

Func

mode,

GraphStyle(1,3)

sets

Y

1

to é (above).

7

= í (dot)

3.10 Function Graphing

Setting the Viewing Window Variables

The TI-82 STATS

Viewing Window

The viewing window is the portion of the coordinate plane defined by

Xmin

,

Xmax

,

Ymin

, and

Ymax

.

Xscl

(X scale) defines the distance between tick marks on the x-axis.

Yscl

(Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set

Xscl=0

and

Yscl=0

.

Ymax

Xmin

Xscl

Yscl

Xmax

Ymin

Displaying the

Window

Variables

To display the current window variable values, press p.

The window editor above and to the right shows the default values in

Func

graphing mode and

Radian

angle mode. The window variables differ from one graphing mode to another.

Xres

sets pixel resolution (

1

through

8

) for function graphs only.

The default is

1

.

At

Xres=1

, functions are evaluated and graphed at each pixel on the x-axis.

At

Xres=8

, functions are evaluated and graphed at every eighth pixel along the x-axis.

Tip: Small Xres values improve graph resolution but may cause the

TI-82 STATS to draw graphs more slowly.

Changing a

Window Variable

Value

To change a window variable value from the window editor, follow these steps.

1. Press † or } to move the cursor to the window variable you want to change.

2. Edit the value, which can be an expression.

Enter a new value, which clears the original value.

Move the cursor to a specific digit, and then edit it.

3. Press Í, †, or }. If you entered an expression, the

TI-82 STATS evaluates it. The new value is stored.

Note:

Xmin<Xmax and Ymin<Ymax must be true in order to graph.

Function Graphing 3.11

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Setting the Viewing Window Variables

(continued)

Storing to a

Window Variable from the Home

Screen or a

Program

To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps.

1. Enter the value you want to store.

2. Press ¿.

3. Press  to display the

VARS

menu.

4. Select

1:Window

to display the

Func

window variables (

X/Y secondary menu).

Press ~ to display the

Par

and

Pol

window variables (

T/q secondary menu).

Press ~ ~ to display the

Seq

window variables (

U/V/W secondary menu).

5. Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location.

6. Press Í to complete the instruction.

When the instruction is executed, the TI-82 STATS stores the value to the window variable and displays the value.

@X and @Y

The variables

@X

and

@Y

(items

8

and

9

on the

VARS

(

1:Window

)

X/Y

secondary menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph

(graphing accuracy).

@

X

and

@

Y

are calculated from

Xmin

,

Xmax

,

Ymin

, and

Ymax

when you display a graph.

@X

=

(Xmax N Xmin)

94

@Y

=

(Ymax N Ymin)

62

You can store values to

@X

and

@Y

. If you do,

Xmax

and

Ymax

are calculated from

@X

,

Xmin

,

@Y

, and

Ymin

.

3.12 Function Graphing

Setting the Graph Format

Displaying the

Format Settings

To display the format settings, press y [

FORMAT

]. The default settings are highlighted below.

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

Sets cursor coordinates.

Sets coordinates display on or off.

Sets grid off or on.

Sets axes on or off.

Sets axes label off or on.

Sets expression display on or off.

Format settings define a graph’s appearance on the display.

Format settings apply to all graphing modes.

Seq

graphing mode has an additional mode setting (Chapter 6).

Changing a

Format Setting

To change a format setting, follow these steps.

1. Press †, ~, }, and | as necessary to move the cursor to the setting you want to select.

2. Press Í to select the highlighted setting.

RectGC, PolarGC RectGC

(rectangular graphing coordinates) displays the cursor location as rectangular coordinates

X

and

Y

.

PolarGC

(polar graphing coordinates) displays the cursor location as polar coordinates

R

and

q

.

The

RectGC

/

PolarGC

setting determines which variables are updated when you plot the graph, move the free-moving cursor, or trace.

RectGC

updates

X

and

Y

; if

CoordOn

format is selected,

X

and

Y

are displayed.

PolarGC

updates

X

,

Y

,

R

, and

q

; if

CoordOn

format is selected,

R

and

q

are displayed.

Function Graphing 3.13

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Setting the Graph Format

(continued)

CoordOn,

CoordOff

CoordOn

(coordinates on) displays the cursor coordinates at the bottom of the graph. If

ExprOff

format is selected, the function number is displayed in the top-right corner.

CoordOff

(coordinates off) does not display the function number or coordinates.

GridOff, GridOn

Grid points cover the viewing window in rows that correspond to the tick marks (page 3.11) on each axis.

GridOff

does not display grid points.

GridOn

displays grid points.

AxesOn, AxesOff

AxesOn

displays the axes.

AxesOff

does not display the axes.

This overrides the

LabelOff

/

LabelOn

format setting.

LabelOff,

LabelOn

LabelOff

and

LabelOn

determine whether to display labels for the axes (

X

and

Y

), if

AxesOn

format is also selected.

ExprOn, ExprOff

ExprOn

and

ExprOff

determine whether to display the

Y=

expression when the trace cursor is active. This format setting also applies to stat plots.

When

ExprOn

is selected, the expression is displayed in the topleft corner of the graph screen.

When

ExprOff

and

CoordOn

both are selected, the number in the top-right corner specifies which function is being traced.

3.14 Function Graphing

Displaying Graphs

Displaying a New

Graph

To display the graph of the selected function or functions, press s.

TRACE

,

ZOOM

instructions, and

CALC

operations display the graph automatically. As the TI-82 STATS plots the graph, the busy indicator is on. As the graph is plotted,

X

and

Y

are updated.

Pausing or

Stopping a Graph

While plotting a graph, you can pause or stop graphing.

Press Í to pause; then press Í to resume.

Press É to stop; then press s to redraw.

Smart Graph

Smart Graph is a TI-82 STATS feature that redisplays the last graph immediately when you press s, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.

If you performed any of these actions since the graph was last displayed, the TI-82 STATS will replot the graph based on new values when you press s.

Changed a mode setting that affects graphs

Changed a function in the current picture

Selected or deselected a function or stat plot

Changed the value of a variable in a selected function

Changed a window variable or graph format setting

Cleared drawings by selecting

ClrDraw

Changed a stat plot definition

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Displaying Graphs

(continued)

Overlaying

Functions on a

Graph

On the TI-82 STATS, you can graph one or more new functions without replotting existing functions. For example, store

sin(X)

to

Y

1

in the

Y=

editor and press s. Then store

cos(X)

to

Y

2

and press s again. The function

Y

2

is graphed on top of

Y

1

, the original function.

Graphing a

Family of Curves

If you enter a list (Chapter 11) as an element in an expression, the TI-82 STATS plots the function for each value in the list, thereby graphing a family of curves. In

Simul

graphing-order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.

{2,4,6}sin(X)

graphs three functions:

2 sin(X)

,

4 sin(X)

, and

6 sin(X)

.

{2,4,6}sin({1,2,3}X)

graphs

2 sin(X)

,

4 sin(2X)

, and

6 sin(3X)

.

Note: When using more than one list, the lists must have the same dimensions.

3.16 Function Graphing

Exploring Graphs with the Free-Moving Cursor

Free-Moving

Cursor

Graphing

Accuracy

When a graph is displayed, press |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or †, the cursor moves from the center of the viewing window.

As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if

CoordOn

format is selected. The

Float

/

Fix

decimal mode setting determines the number of decimal digits displayed for the coordinate values.

To display the graph with no cursor and no coordinate values, press ‘ or Í. When you press |, ~, }, or †, the cursor moves from the same position.

The free-moving cursor moves from pixel to pixel on the screen.

When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function. The coordinate value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r (page 3.18).

The coordinate values displayed as you move the cursor approximate actual math coordinates, *accurate to within the width and height of the pixel. As

Xmin

,

Xmax

,

Ymin

, and

Ymax

get closer together (as in a

ZoomIn

) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.

Free-moving cursor “on” the curve

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Exploring Graphs with TRACE

Beginning a

Trace

Use

TRACE

to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the

Y= editor, at the middle

X

value on the screen. The cursor coordinates are displayed at the bottom of the screen if

CoordOn

format is selected. The

Y= expression is displayed in the top-left corner of the screen, if

ExprOn

format is selected.

Moving the Trace

Cursor

To move the TRACE cursor . . .

do this:

. . . to the previous or next plotted point, press | or ~.

. . . five plotted points on a function (

Xres

affects this), press y | or y

~.

. . . to any valid

X

value on a function, enter a value, and then press Í.

. . . from one function to another, press } or †.

When the trace cursor moves along a function, the

Y

value is calculated from the

X

value; that is,

Y

=

Y

n

(X)

. If the function is undefined at an

X

value, the

Y

value is blank.

Trace cursor on the curve

If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

Moving the Trace

Cursor from

Function to

Function

To move the trace cursor from function to function, press † and

}. The cursor follows the order of the selected functions in the

Y=

editor. The trace cursor moves to each function at the same

X

value. If

ExprOn

format is selected, the expression is updated.

3.18 Function Graphing

Moving the Trace

Cursor to Any

Valid X Value

To move the trace cursor to any valid

X

value on the current function, enter the value. When you enter the first digit, an

X=

prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the

X=

prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor.

Panning to the

Left or Right

Note: This feature does not apply to stat plots.

If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right.

Xmin

and

Xmax

are updated to correspond to the new viewing window.

Quick Zoom

Leaving and

Returning to

TRACE

While tracing, you can press Í to adjust the viewing window so that the cursor location becomes the center of the new viewing window, even if the cursor is above or below the display. This allows panning up and down. After Quick Zoom, the cursor remains in

TRACE

.

When you leave and return to

TRACE

, the trace cursor is displayed in the same location it was in when you left

TRACE unless Smart Graph has replotted the graph (page 3.15).

,

Using TRACE in a Program

On a blank line in the program editor, press r. The instruction

Trace

is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function.

As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press Í to resume program execution.

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Exploring Graphs with the ZOOM Instructions

ZOOM Menu

Zoom Cursor

ZBox

To display the

ZOOM

menu, press q. You can adjust the viewing window of the graph quickly in several ways. All

ZOOM

instructions are accessible from programs.

ZOO

M

MEMORY

1: ZBox

2: Zoom In

3: Zoom Out

4: ZDecimal

5: ZSquare

6: ZStandard

7: ZTrig

8: ZInteger

9: ZoomStat

0: ZoomFit

Draws a box to define the viewing window.

Magnifies the graph around the cursor.

Views more of a graph around the cursor.

Sets

@

X

and

@

Y

to 0.1.

Sets equal-size pixels on the

X

and

Y

axes.

Sets the standard window variables.

Sets the built-in trig window variables.

Sets integer values on the

X

and

Y

axes.

Sets the values for current stat lists.

Fits

YMin

and

YMax

between

XMin

and

XMax

.

When you select

1:ZBox

,

2:Zoom In

, or

3:Zoom Out

, the cursor on the graph becomes the zoom cursor (

+

), a smaller version of the free-moving cursor (

+

).

To define a new viewing window using

ZBox

, follow these steps.

1. Select

1:ZBox

from the

ZOOM

menu. The zoom cursor is displayed at the center of the screen.

2. Move the zoom cursor to any spot you want to define as a corner of the box, and then press Í. When you move the cursor away from the first defined corner, a small, square dot indicates the spot.

3. Press |, }, ~, or †. As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen.

Note: To cancel ZBox before you press Í, press ‘.

4. When you have defined the box, press Í to replot the graph.

To use

ZBox

to define another box within the new graph, repeat steps 2 through 4. To cancel

ZBox

, press ‘.

3.20 Function Graphing

Zoom In,

Zoom Out

ZDecimal

ZSquare

Zoom In

magnifies the part of the graph that surrounds the cursor location.

Zoom Out

displays a greater portion of the graph, centered on the cursor location. The

XFact

and

YFact

settings determine the extent of the zoom.

To zoom in on a graph, follow these steps.

1. Check

XFact

and

YFact

(page 3.24); change as needed.

2. Select

2:Zoom In

from the

ZOOM

menu. The zoom cursor is displayed.

3. Move the zoom cursor to the point that is to be the center of the new viewing window.

4. Press Í. The TI-82 STATS adjusts the viewing window by

XFact

and

YFact

; updates the window variables; and replots the selected functions, centered on the cursor location.

5. Zoom in on the graph again in either of two ways.

To zoom in at the same point, press Í.

To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press Í.

To zoom out on a graph, select

3:Zoom Out

and repeat steps 3 through 5.

To cancel

Zoom In

or

Zoom Out

, press ‘.

ZDecimal

replots the functions immediately. It updates the window variables to preset values, as shown below. These values set

@

X

and

@

Y

equal to

0.1

and set the

X

and

Y

value of each pixel to one decimal place.

Xmin=L4.7

Xmax=4.7

Xscl=1

Ymin=L3.1

Ymax=3.1

Yscl=1

ZSquare

replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that

@[email protected]

, which makes the graph of a circle look like a circle.

Xscl

and

Yscl

remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.

Function Graphing 3.21

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Exploring Graphs with the ZOOM Instructions

(cont.)

ZStandard

ZTrig

ZInteger

ZoomStat

ZoomFit

ZStandard

replots the functions immediately. It updates the window variables to the standard values shown below.

Xmin=L10

Xmax=10

Xscl=1

Ymin=L10

Ymax=10

Yscl=1

Xres=1

ZTrig

replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in

Radian

mode are shown below.

Xmin=L(47à24)p

Xmax=(47à24)p

Xscl=p/2

Ymin=L4

Ymax=4

Yscl=1

ZInteger

redefines the viewing window to the dimensions shown below. To use

ZInteger

, move the cursor to the point that you want to be the center of the new window, and then press

Í;

ZInteger

replots the functions.

@X=1

@Y=1

Xscl=10

Yscl=10

ZoomStat

redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only

Xmin

and

Xmax

are adjusted.

ZoomFit

replots the functions immediately.

ZoomFit

recalculates

YMin

and

YMax

to include the minimum and maximum

Y

values of the selected functions between the current

XMin

and

XMax

.

XMin

and

XMax

are not changed.

3.22 Function Graphing

Using ZOOM MEMORY

ZOOM MEMORY

Menu

To display the

ZOOM MEMORY

menu, press q ~.

ZOOMMEMOR

Y

1: ZPrevious

2: ZoomSto

3: ZoomRcl

4: SetFactors...

Uses the previous viewing window.

Stores the user-defined window.

Recalls the user-defined window.

Changes

Zoom In

and

Zoom Out

factors.

ZPrevious

ZoomSto

ZoomRcl

ZPrevious

replots the graph using the window variables of the graph that was displayed before you executed the last

ZOOM instruction.

ZoomSto

immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the user-defined

ZOOM

variables

ZXmin

,

ZXmax

,

ZXscl

,

ZYmin

,

ZYmax

,

ZYscl

, and

ZXres

.

These variables apply to all graphing modes. For example, changing the value of

ZXmin

in

Func

mode also changes it in

Par

mode.

ZoomRcl

graphs the selected functions in a user-defined viewing window. The user-defined viewing window is determined by the values stored with the

ZoomSto

instruction.

The window variables are updated with the user-defined values, and the graph is plotted.

Function Graphing 3.23

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Using ZOOM MEMORY

(continued)

ZOOM FACTORS

The zoom factors,

XFact

and

YFact

, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to

Zoom In

or

Zoom Out

around a point.

Checking XFact and YFact

To display the

ZOOM FACTORS

screen, where you can review the current values for

XFact

and

YFact

, select

4:SetFactors

from the

ZOOM MEMORY

menu. The values shown are the defaults.

Changing XFact and YFact

Using ZOOM

MEMORY Menu

Items from the

Home Screen or a Program

You can change

XFact

and

YFact

in either of two ways.

Enter a new value. The original value is cleared automatically when you enter the first digit.

Place the cursor on the digit you want to change, and then enter a value or press { to delete it.

From the home screen or a program, you can store directly to any of the user-defined

ZOOM

variables.

From a program, you can select the

ZoomSto

and

ZoomRcl

instructions from the

ZOOM MEMORY

menu.

3.24 Function Graphing

Using the CALC (Calculate) Operations

CALCULATE

Menu value

To display the

CALCULATE

menu, press y ã

CALC

ä. Use the items on this menu to analyze the current graph functions.

CALCULAT

E

1: value

2: zero

3: minimum

4: maximum

5: intersect

6: dy/dx

7: ‰f(x)dx

Calculates a function

Y

value for a given

Finds a zero (x-intercept) of a function.

Finds a minimum of a function.

Finds a maximum of a function.

Finds an intersection of two functions.

Finds a numeric derivative of a function.

Finds a numeric integral of a function.

X

.

value

evaluates one or more currently selected functions for a specified value of

X

.

Note: When a value is displayed for

X, press ‘ to clear the value. When no value is displayed, press

‘ to cancel the value operation.

To evaluate a selected function at

X

, follow these steps.

1. Select

1:value

from the

CALCULATE

menu. The graph is displayed with

X=

in the bottom-left corner.

2. Enter a real value, which can be an expression, for

X

between

Xmin

and

Xmax

.

3. Press Í.

The cursor is on the first selected function in the

Y= editor at the

X

value you entered, and the coordinates are displayed, even if

CoordOff

format is selected.

To move the cursor from function to function at the entered

X

value, press } or †. To restore the free-moving cursor, press

| or ~.

Function Graphing 3.25

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Using the CALC (Calculate) Operations

(continued) zero zero

finds a zero (x-intercept or root) of a function using

solve(

.

Functions can have more than one x-intercept value;

zero

finds the zero closest to your guess.

The time

zero

spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess.

To find a zero of a function, follow these steps.

1. Select

2:zero

from the

CALCULATE

menu. The current graph is displayed with

Left Bound?

in the bottom-left corner.

2. Press } or † to move the cursor onto the function for which you want to find a zero.

3. Press | or ~ (or enter a value) to select the x-value for the left bound of the interval, and then press Í. A

4

indicator on the graph screen shows the left bound.

Right

Bound?

is displayed in the bottom-left corner. Press | or ~

(or enter a value) to select the x-value for the right bound, and then press Í. A

3

indicator on the graph screen shows the right bound.

Guess?

is then displayed in the bottom-left corner.

4. Press | or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press

Í.

The cursor is on the solution and the coordinates are displayed, even if

CoordOff

format is selected. To move to the same x-value for other selected functions, press } or †. To restore the free-moving cursor, press | or ~.

3.26 Function Graphing

minimum, maximum intersect minimum

and

maximum

find a minimum or maximum of a function within a specified interval to a tolerance of 1âL5.

To find a minimum or maximum, follow these steps.

1. Select

3:minimum

or

4:maximum

from the

CALCULATE menu. The current graph is displayed.

2. Select the function and set left bound, right bound, and guess as described for

zero

(steps 2 through 4; page 3.26).

The cursor is on the solution, and the coordinates are displayed, even if you have selected

CoordOff

format;

Minimum

or

Maximum

is displayed in the bottom-left corner.

To move to the same x-value for other selected functions, press

} or †. To restore the free-moving cursor, press | or ~.

intersect

finds the coordinates of a point at which two or more functions intersect using

solve(

. The intersection must appear on the display to use

intersect

.

To find an intersection, follow these steps.

1. Select

5:intersect

from the

CALCULATE

menu. The current graph is displayed with

First curve?

in the bottom-left corner.

2. Press † or }, if necessary, to move the cursor to the first function, and then press Í.

Second curve?

is displayed in the bottom-left corner.

3. Press † or }, if necessary, to move the cursor to the second function, and then press Í.

4. Press ~ or | to move the cursor to the point that is your guess as to location of the intersection, and then press Í.

The cursor is on the solution and the coordinates are displayed, even if

CoordOff

format is selected.

Intersection

is displayed in the bottom-left corner. To restore the free-moving cursor, press

|, }, ~, or †.

Function Graphing 3.27

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Using the CALC (Calculate) Operations

(continued) dy/dx

‰f(x)dx dy/dx

(numerical derivative) finds the numerical derivative

(slope) of a function at a point, with H=1âL3.

To find a function’s slope at a point, follow these steps.

1. Select

6:dy/dx

from the

CALCULATE

menu. The current graph is displayed.

2. Press } or † to select the function for which you want to find the numerical derivative.

3. Press | or ~ (or enter a value) to select the

X

value at which to calculate the derivative, and then press Í.

The cursor is on the solution and the numerical derivative is displayed.

To move to the same x-value for other selected functions, press

} or †. To restore the free-moving cursor, press | or ~.

‰f(x)dx

(numerical integral) finds the numerical integral of a function in a specified interval. It uses the

fnInt(

function, with a tolerance of H=1âL3.

To find the numerical derivative of a function, follow these steps.

1. Select

7:‰f(x)dx

from the

CALCULATE

menu. The current graph is displayed with

Lower Limit?

in the bottom-left corner.

2. Press } or † to move the cursor to the function for which you want to calculate the integral.

3. Set lower and upper limits as you would set left and right bounds for

zero

(step 3; page 3.26). The integral value is displayed, and the integrated area is shaded.

Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area.

3.28 Function Graphing

Contents

4

Parametric

Graphing

Getting Started: Path of a Ball

........................................................................

4-2

Defining and Displaying Parametric Graphs

........................................

4-4

Exploring Parametric Graphs

..........................................................................

4-7

Parametric Graphing 4-1

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Getting Started: Path of a Ball

Getting Started is a fast-paced introduction. Read the chapter for details.

Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.

For initial velocity v

0

and angle q, the position of the ball as a function of time has horizontal and vertical components.

Horizontal: X1(t)=tv

Vertical: Y1(t)=tv

0

0 cos(q) sin(q)N

1

2

gt 2

The vertical and horizontal vectors of the ball’s motion also will be graphed.

Vertical vector: X2(t)=0

Horizontal vector: X3(t)=X1(t)

Gravity constant: g=9.8 m/sec 2

Y2(t)=Y1(t)

Y3(t)=0

1. Press z. Press † † † ~ Í to select

Par

mode. Press † † ~ Í to select

Simul

for simultaneous graphing of all three parametric equations in this example.

2. Press o. Press

30

„ ™

25

y

[

ANGLE

]

1

(to select ¡) ¤ Í to define

X

1T

in terms of

T

.

3. Press

30

„ ˜

25

y [

ANGLE

]

1

¤ ¹

9.8

¥

2

„ ¡ Í to define

Y

1T

.

The vertical component vector is defined by

X

2T

and

Y

2T

.

4. Press

0

Í to define

X

2T

.

5. Press  ~ to display the

VARS Y.VARS

menu. Press

2

to display the

PARAMETRIC secondary menu. Press

2

Í to define

Y

2T

.

4-2 Parametric Graphing

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The horizontal component vector is defined by

X

3T

and

Y

3T

.

6. Press  ~

2

, and then press

1

Í to define

X

3T

. Press

0

Í to define

Y

3T

.

7. Press | | } Í to change the graph style to è for

X

3T

and

Y

3T

. Press } Í

Í to change the graph style to ë for

X

2T

and

Y

2T

. Press } Í Í to change the graph style to ë for

X

1T

and

Y

1T

. (These keystrokes assume that all graph styles were set to ç originally.)

8. Press p. Enter these values for the window variables.

Tmin=0

Tmax=5

Tstep=.1

Xmin=L10

Xmax=100

Xscl=50

Ymin=L5

Ymax=15

Yscl=10

9. Press y [

FORMAT

] † † † ~ Í to set

AxesOff

, which turns off the axes.

10. Press s. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion.

Tip: To simulate the ball flying through the air, set graph style to

ì (animate) for X

1T

and

Y

1T

.

11. Press r to obtain numerical results and answer the questions at the beginning of this section.

Tracing begins at

Tmin

on the first parametric equation (

X

1T

and

Y

1T

). As you press ~ to trace the curve, the cursor follows the path of the ball over time. The values for

X

(distance),

Y

(height), and

T

(time) are displayed at the bottom of the screen.

Parametric Graphing 4-3

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Defining and Displaying Parametric Graphs

TI-82 STATS

Graphing Mode

Similarities

Setting

Parametric

Graphing Mode

Displaying the

Parametric Y=

Editor

The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing.

To display the mode screen, press z. To graph parametric equations, you must select

Par

graphing mode before you enter window variables and before you enter the components of parametric equations.

After selecting

Par

graphing mode, press o to display the parametric

Y=

editor.

Selecting a

Graph Style

In this editor, you can display and enter both the

X

and

Y

components of up to six equations,

X

1T

and

Y

1T

through

X

6T

and

Y

6T

. Each is defined in terms of the independent variable

T

. A common application of parametric graphs is graphing equations over time.

The icons to the left of

X

1T

through

X

6T

represent the graph style of each parametric equation (Chapter 3). The default in

Par

mode is ç (line), which connects plotted points. Line, è (thick),

ë (path), ì (animate), and í (dot) styles are available for parametric graphing.

4-4 Parametric Graphing

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Defining and

Editing

Parametric

Equations

Selecting and

Deselecting

Parametric

Equations

To define or edit a parametric equation, follow the steps in

Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is

T

. In

Par

graphing mode, you can enter the parametric variable

T

in either of two ways.

Press „.

Press ƒ ã

T

ä.

Two components,

X

and

Y

, define a single parametric equation.

You must define both of them.

The TI-82 STATS graphs only the selected parametric equations. In the

Y=

editor, a parametric equation is selected when the

=

signs of both the

X

and

Y

components are highlighted. You may select any or all of the equations

X

1T

and

Y

1T

through

X

6T

and

Y

6T

.

To change the selection status, move the cursor onto the = sign of either the

X

or

Y

component and press Í. The status of both the

X

and

Y

components is changed.

Setting Window

Variables

To display the window variable values, press p. These variables define the viewing window. The values below are defaults for

Par

graphing in

Radian

angle mode.

Tmin=0

Tmax=6.2831853...

Tstep=.1308996...

Xmin=L10

Xmax=10

Xscl=1

Ymin=L10

Ymax=10

Yscl=1

Smallest

T

value to evaluate

Largest

T

value to evaluate (2p)

T

value increment (pà24)

Smallest

X

value to be displayed

Largest

X

value to be displayed

Spacing between the

X

tick marks

Smallest

Y

value to be displayed

Largest

Y

value to be displayed

Spacing between the

Y

tick marks

Note: To ensure that sufficient points are plotted, you may want to change the

T window variables.

Parametric Graphing 4-5

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Defining and Displaying Parametric Graphs

(continued)

Setting the Graph

Format

To display the current graph format settings, press y

[

FORMAT

]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings;

Seq

graphing mode has an additional axes format setting.

Displaying a

Graph

When you press s, the TI-82 STATS plots the selected parametric equations. It evaluates the

X

and

Y

components for each value of

T

(from

Tmin

to

Tmax

in intervals of

Tstep

), and then plots each point defined by

X

and

Y

. The window variables define the viewing window.

As the graph is plotted,

X

,

Y

, and

T

are updated.

Smart Graph applies to parametric graphs (Chapter 3).

Window

Variables and

Y.VARS Menus

You can perform these actions from the home screen or a program.

Access functions by using the name of the

X

or

Y

component of the equation as a variable.

Store parametric equations.

Select or deselect parametric equations.

Store values directly to window variables.

4-6 Parametric Graphing

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Exploring Parametric Graphs

Free-Moving

Cursor

TRACE

The free-moving cursor in

Par

graphing works the same as in

Func

graphing.

In

RectGC

format, moving the cursor updates the values of

X

and

Y

; if

CoordOn

format is selected,

X

and

Y

are displayed.

In

PolarGC

format,

X

,

Y

,

R

, and

q

are updated; if

CoordOn

format is selected,

R

and

q

are displayed.

To activate

TRACE

, press r. When

TRACE

is active, you can move the trace cursor along the graph of the equation one

Tstep

at a time. When you begin a trace, the trace cursor is on the first selected function at

Tmin

. If

ExprOn

is selected, then the function is displayed.

In

RectGC

format,

TRACE

updates and displays the values of

X

,

Y

, and

T

if

CoordOn

format is on.

In

PolarGC

format,

X

,

Y

,

R

,

q

and

T

are updated; if

CoordOn

format is selected,

R

,

q

, and

T

are displayed. The

X

and

Y

(or

R

and

q

) values are calculated from

T

.

To move five plotted points at a time on a function, press y

| or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

Quick Zoom is available in

Par

graphing; panning is not

(Chapter 3).

Parametric Graphing 4-7

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Exploring Parametric Graphs

(continued)

Moving the Trace

Cursor to Any

Valid T Value

To move the trace cursor to any valid

T

value on the current function, enter the number. When you enter the first digit, a

T=

prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the

T=

prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor.

ZOOM

CALC

ZOOM

operations in

Par

graphing work the same as in

Func

graphing. Only the

X

(

Xmin

,

Xmax

, and

Xscl

) and

Y

(

Ymin

,

Ymax

, and

Yscl

) window variables are affected.

The

T

window variables (

Tmin

,

Tmax

, and

Tstep

) are only affected when you select

ZStandard

. The

VARS ZOOM secondary menu

ZT/Zq

items

1:ZTmin

,

2:ZTmax

, and

3:ZTstep

are the zoom memory variables for

Par

graphing.

CALC

operations in

Par

graphing work the same as in

Func

graphing. The

CALCULATE

menu items available in

Par

graphing are

1:value

,

2:dy/dx

,

3:dy/dt

, and

4:dx/dt

.

4-8 Parametric Graphing

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Contents

5

Polar

Graphing

Getting Started: Polar Rose

..............................................................................

Defining and Displaying Polar Graphs

.....................................................

Exploring Polar Graphs

......................................................................................

2

3

6

Polar Graphing 5–1

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Getting Started: Polar Rose

Getting Started is a fast-paced introduction. Read the chapter for details.

The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B.

1. Press z to display the mode screen. Press

† † † ~ ~ Í to select

Pol

graphing mode. Select the defaults (the options on the left) for the other mode settings.

2. Press o to display the polar

Y= editor. Press

8

˜

2.5

„ ¤ Í to define

r

1

.

3. Press q

6

to select

6:ZStandard

and graph the equation in the standard viewing window.

The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets

qmax=2p

and defines the window, rather than the pixels, as square.

4. Press p to display the window variables. Press †

4

y [ p

] to increase the value of

qmax

to 4p.

5. Press q

5

to select

5:ZSquare

and plot the graph.

6. Repeat steps 2 through 5 with new values for the variables

A

and

B

in the polar equation

r

1

=Asin(Bq)

. Observe how the new values affect the graph.

5–2 Polar Graphing

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Defining and Displaying Polar Graphs

TI-82 STATS

Graphing Mode

Similarities

Setting Polar

Graphing Mode

Displaying the

Polar Y= Editor

The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing.

To display the mode screen, press z. To graph polar equations, you must select

Pol

graphing mode before you enter values for the window variables and before you enter polar equations.

After selecting

Pol

graphing mode, press o to display the polar

Y=

editor.

In this editor, you can enter and display up to six polar equations,

r

1

through

r

6

. Each is defined in terms of the independent variable

q

(page 5.4).

Selecting Graph

Styles

The icons to the left of

r

1

through

r

6

represent the graph style of each polar equation (Chapter 3). The default in

Pol

graphing mode is ç (line), which connects plotted points. Line, è (thick),

ë (path), ì (animate), and í (dot) styles are available for polar graphing.

Polar Graphing 5–3

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Defining and Displaying Polar Graphs

(continued)

Defining and

Editing Polar

Equations

To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is

q

. In

Pol

graphing mode, you can enter the polar variable

q

in either of two ways.

Press „.

Press ƒ ãqä.

Selecting and

Deselecting Polar

Equations

The TI-82 STATS graphs only the selected polar equations. In the

Y=

editor, a polar equation is selected when the

=

sign is highlighted. You may select any or all of the equations.

To change the selection status, move the cursor onto the

=

sign, and then press Í.

Setting Window

Variables

To display the window variable values, press p. These variables define the viewing window. The values below are defaults for

Pol

graphing in

Radian

angle mode.

qmin=0 qmax=6.2831853... qstep=.1308996...

Xmin=L10

Xmax=10

Xscl=1

Ymin=L10

Ymax=10

Yscl=1

Smallest

q

value to evaluate

Largest

q

value to evaluate (2p)

Increment between

q

values (pà24)

Smallest

X

value to be displayed

Largest

X

value to be displayed

Spacing between the

X

tick marks

Smallest

Y

value to be displayed

Largest

Y

value to be displayed

Spacing between the

Y

tick marks

Note: To ensure that sufficient points are plotted, you may want to change the q window variables.

5–4 Polar Graphing

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Setting the Graph

Format

To display the current graph format settings, press y

[

FORMAT

]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings.

Displaying a

Graph

Window

Variables and

Y.VARS Menus

When you press s, the TI-82 STATS plots the selected polar equations. It evaluates

R

for each value of

q

(from

qmin

to

qmax

in intervals of

qstep

) and then plots each point. The window variables define the viewing window.

As the graph is plotted,

X

,

Y

,

R

, and

q

are updated.

Smart Graph applies to polar graphs (Chapter 3).

You can perform these actions from the home screen or a program.

Access functions by using the name of the equation as a variable.

Store polar equations.

Select or deselect polar equations.

Store values directly to window variables.

Polar Graphing 5–5

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Exploring Polar Graphs

Free-Moving

Cursor

TRACE

The free-moving cursor in

Pol

graphing works the same as in

Func

graphing. In

RectGC

format, moving the cursor updates the values of

X

and

Y

; if

CoordOn

format is selected,

X

and

Y

are displayed. In

PolarGC

format,

X

,

Y

,

R

, and

q

are updated; if

CoordOn

format is selected,

R

and

q

are displayed.

To activate

TRACE

, press r. When

TRACE

is active, you can move the trace cursor along the graph of the equation one

qstep

at a time. When you begin a trace, the trace cursor is on the first selected function at

qmin

. If

ExprOn

format is selected, then the equation is displayed.

In

RectGC

format,

TRACE

updates the values of

X

,

Y

, and

q

; if

CoordOn

format is selected,

X

,

Y

, and

q

are displayed. In

PolarGC

format,

TRACE

updates

X

,

Y

,

R

, and

q

; if

CoordOn

format is selected,

R

and

q

are displayed.

To move five plotted points at a time on a function, press y

| or y ~. If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

Quick Zoom is available in

Pol

graphing mode; panning is not

(Chapter 3).

Moving the Trace

Cursor to Any

Valid q Value

To move the trace cursor to any valid

q

value on the current function, enter the number. When you enter the first digit, a

q=

prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the

q=

prompt. The value must be valid for the current viewing window. When you complete the entry, press Í to move the cursor.

ZOOM

CALC

ZOOM

operations in

Pol

graphing work the same as in

Func

graphing. Only the

X

(

Xmin

,

Xmax

, and

Xscl

) and

Y

(

Ymin

,

Ymax

, and

Yscl

) window variables are affected.

The

q

window variables (

qmin

,

qmax

, and

qstep

) are not affected, except when you select

ZStandard

. The

VARS ZOOM

secondary menu

ZT/Zq

items

4:Zqmin

,

5:Zqmax

, and

6:Zqstep

are zoom memory variables for

Pol

graphing.

CALC

operations in

Pol

graphing work the same as in

Func

graphing. The

CALCULATE

menu items available in

Pol

graphing are

1:value

,

2:dy/dx

, and

3:dr/dq

.

5–6 Polar Graphing

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Contents

6

Sequence

Graphing

Getting Started: Forest and Trees

.................................................................

Defining and Displaying Sequence Graphs

...........................................

Selecting Axes Combinations

.........................................................................

Exploring Sequence Graphs

.............................................................................

Graphing Web Plots

..............................................................................................

11

Using Web Plots to Illustrate Convergence

...........................................

12

Graphing Phase Plots

...........................................................................................

13

Comparing TI-82 STATS and TI.82 Sequence Variables

...........

15

Keystroke Differences Between TI-82 STATS and TI-82

..........

16

8

9

2

3

Sequence Graphing 6–1

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Getting Started: Forest and Trees

Getting Started is a fast-paced introduction. Read the chapter for details.

A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees?

1. Press z. Press † † † ~ ~ ~ Í to select

Seq

graphing mode.

2. Press y [

FORMAT

] and select

Time

axes format and

ExprOn

format if necessary.

3. Press o. If the graph-style icon is not

íííí

(dot), press | |, press Í until

íííí is displayed, and then press ~ ~.

4. Press  ~

3

to select

iPart(

(integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain. Press Ë

8

y [ u

] £ „ ¹

1

¤ to define the number of trees after each harvest. Press Ã

1000

¤ to define the new trees. Press †

4000

to define the number of trees at the beginning of the program.

5. Press p

0

to set

nMin=0

. Press †

50

to set

nMax=50

.

nMin

and

nMax

evaluate forest size over 50 years. Set the other window variables.

PlotStart=1

PlotStep=1

Xmin=0

Xmax=50

Xscl=10

Ymin=0

Ymax=6000

Yscl=1000

6. Press r. Tracing begins at

nMin

(the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for

n

(number of years),

X

(

X=n

, because

n

is plotted on the x-axis), and

Y

(tree count) are displayed at the bottom. When will the forest stabilize? With how many trees?

6–2 Sequence Graphing

82EAB9~1.DOC TI-83 international English Bob Fedorisko Revised: 10/28/05 9:28 AM Printed: 10/28/05 9:28

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Defining and Displaying Sequence Graphs

TI-82 STATS

Graphing Mode

Similarities

TI-82 STATS

Sequence

Functions u, v, and w

The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing.

Setting Sequence

Graphing Mode

To display the mode screen, press z. To graph sequence functions, you must select

Seq

graphing mode before you enter window variables and before you enter sequence functions.

Sequence graphs automatically plot in

Simul

mode, regardless of the current plotting-order mode setting.

The TI-82 STATS has three sequence functions that you can enter from the keyboard:

u

,

v

, and

w

. They are above the ¬, −, and ® keys.

You can define sequence functions in terms of:

The independent variable

n

The previous term in the sequence function, such as

u(nN1)

The term that precedes the previous term in the sequence function, such as

u(nN2)

The previous term or the term that precedes the previous term in another sequence function, such as

u(nN1)

or

u(nN2)

referenced in the sequence

v(n)

.

Note: Statements in this chapter about u(n) are also true for v(n) and

w(n); statements about

u(nN1) are also true for v(nN1) and w(nN1); statements about u(nN2) are also true for v(nN2) and w(nN2).

Sequence Graphing 6–3

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Defining and Displaying Sequence Graphs

(continued)

Displaying the

Sequence Y=

Editor

After selecting

Seq

mode, press o to display the sequence

Y=

editor.

In this editor, you can display and enter sequences for

u(n)

,

v(n)

, and

w(n)

. Also, you can edit the value for

nMin

, which is the sequence window variable that defines the minimum

n

value to evaluate.

The sequence

Y=

editor displays the

nMin

value because of its relevance to

u(nMin)

,

v(nMin)

, and

w(nMin)

, which are the initial values for the sequence equations

u(n)

,

v(n)

, and

w(n)

, respectively.

nMin

in the

Y=

editor is the same as

nMin

in the window editor.

If you enter a new value for

nMin

in one editor, the new value for

nMin

is updated in both editors.

Note: Use

u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an initial value.

Selecting Graph

Styles

The icons to the left of

u(n)

,

v(n)

, and

w(n)

represent the graph style of each sequence (Chapter 3). The default in

Seq

mode is

í (dot), which shows discrete values. Dot, ç (line), and è (thick) styles are available for sequence graphing. Graph styles are ignored in

Web

format.

Selecting and

Deselecting

Sequence

Functions

The TI-82 STATS graphs only the selected sequence functions.

In the

Y=

editor, a sequence function is selected when the

=

signs of both

u(n)=

and

u(nMin)=

are highlighted.

To change the selection status of a sequence function, move the cursor onto the

=

sign of the function name, and then press

Í. The status is changed for both the sequence function

u(n)

and its initial value

u(nMin)

.

6–4 Sequence Graphing

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Defining and

Editing a

Sequence

Function

Nonrecursive

Sequences

To define or edit a sequence function, follow the steps in

Chapter 3 for defining a function. The independent variable in a sequence is

n

.

In

Seq

graphing mode, you can enter the sequence variable in either of two ways.

Press „.

Press y [

CATALOG

] [

N

].

You can enter the function name from the keyboard.

To enter the function name

u

, press y [ u

] (above ¬).

To enter the function name

v

, press y [ v

] (above −).

To enter the function name

w

, press y [ w

] (above ®).

Generally, sequences are either nonrecursive or recursive.

Sequences are evaluated only at consecutive integer values.

n

is always a series of consecutive integers, starting at zero or any positive integer.

In a nonrecursive sequence, the

n

th term is a function of the independent variable

n

. Each term is independent of all other terms.

For example, in the nonrecursive sequence below, you can calculate

u(5)

directly, without first calculating

u(1)

or any previous term.

The sequence equation above returns the sequence

2

,

4

,

6

,

8

,

10

, . . . for

n

=

1

,

2

,

3

,

4

,

5

,

. . . .

Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences.

Sequence Graphing 6–5

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Defining and Displaying Sequence Graphs

(continued)

Recursive

Sequences

In a recursive sequence, the

n

th term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by

u(nN1)

and

u(nN2)

. A recursive sequence may also be defined in relation to

n

, as in

u(n)=u(nN1)+n.

For example, in the sequence below you cannot calculate

u(5)

without first calculating

u(1)

,

u(2)

,

u(3)

, and

u(4)

.

Using an initial value

u(nMin) = 1

, the sequence above returns

1

,

2

,

4

,

8

,

16

, . . .

Tip: On the TI-82 STATS, you must type each character of the terms.

For example, to enter

u(nN1), press y [ u

]

£ „ ¹ À ¤.

Recursive sequences require an initial value or values, since they reference undefined terms.

If each term in the sequence is defined in relation to the previous term, as in

u(nN1)

, you must specify an initial value for the first term.

If each term in the sequence is defined in relation to the term that precedes the previous term, as in

u(nN2)

, you must specify initial values for the first two terms. Enter the initial values as a list enclosed in braces ({ }) with commas separating the values.

The value of the first term is 0 and the value of the second term is 1 for the sequence

u(n)

.

6–6 Sequence Graphing

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Setting Window

Variables

To display the window variables, press p. These variables define the viewing window. The values below are defaults for

Seq

graphing in both

Radian

and

Degree

angle modes.

nMin=1

nMax=10

PlotStart=1

PlotStep=1

Xmin=L10

Xmax=10

Xscl=1

Ymin=L10

Ymax=10

Yscl=1

Smallest

n

value to evaluate

Largest

n

value to evaluate

First term number to be plotted

Incremental

n

value (for graphing only)

Smallest

X

value to be displayed

Largest

X

value to be displayed

Spacing between the

X

tick marks

Smallest

Y

value to be displayed

Largest

Y

value to be displayed

Spacing between the

Y

tick marks

nMin

must be an integer ‚ 0.

nMax

,

PlotStart

, and

PlotStep

must be integers ‚ 1.

nMin

is the smallest

n

value to evaluate.

nMin

also is displayed in the sequence

Y=

editor.

nMax

is the largest

n

value to evaluate. Sequences are evaluated at

u(nMin)

,

u(nMin+1)

,

u(nMin+2)

, . . . ,

u(nMax)

.

PlotStart

is the first term to be plotted.

PlotStart=1

begins plotting on the first term in the sequence. If you want plotting to begin with the fifth term in a sequence, for example, set

PlotStart=5

. The first four terms are evaluated but are not plotted on the graph.

PlotStep

is the incremental

n

value for graphing only.

PlotStep

does not affect sequence evaluation; it only designates which points are plotted on the graph. If you specify

PlotStep=2

, the sequence is evaluated at each consecutive integer, but it is plotted on the graph only at every other integer.

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Selecting Axes Combinations

Setting the Graph

Format

To display the current graph format settings, press y

[

FORMAT

]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in

Seq

mode.

Time Web uv vw uw

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

Type of sequence plot (axes)

Rectangular or polar output

Cursor coordinate display on/off

Grid display off or on

Axes display on or off

Axes label display off or on

Expression display on or off

Setting Axes

Format

For sequence graphing, you can select from five axes formats.

The table below shows the values that are plotted on the x-axis and y-axis for each axes setting.

Axes Setting

Time

Web uv vw uw x-axis

n

v(n) u(n) y-axis u(n)

,

v(n)

,

w(n) u(nN1)

,

v(nN1)

,

w(nN1) u(n)

,

v(n)

,

w(n) u(n) v(n) w(n) w(n)

See pages 6.11 and 6.12 for more information on

Web

plots.

See page 6.13 for more information on phase plots (

uv

,

vw

, and

uw

axes settings).

Displaying a

Sequence Graph

To plot the selected sequence functions, press s. As a graph is plotted, the TI-82 STATS updates

X

,

Y

, and

n

.

Smart Graph applies to sequence graphs (Chapter 3).

6–8 Sequence Graphing

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Exploring Sequence Graphs

Free-Moving

Cursor

TRACE

The free-moving cursor in

Seq

graphing works the same as in

Func

graphing. In

RectGC

format, moving the cursor updates the values of

X

and

Y

; if

CoordOn

format is selected,

X

and

Y

are displayed. In

PolarGC

format,

X

,

Y

,

R

, and

q

are updated; if

CoordOn

format is selected,

R

and

q

are displayed.

The axes format setting affects

TRACE

.

When

Time

,

uv

,

vw

, or

uw

axes format is selected,

TRACE moves the cursor along the sequence one

PlotStep

increment at a time. To move five plotted points at once, press y ~ or y

|.

When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by

PlotStart

, even if it is outside the viewing window.

Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press Í. The trace cursor returns to

nMin

.

In

Web

format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the first selected function.

Tip: To move the cursor to a specified n during a trace, enter a value for

n, and press Í. For example, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= prompt and press

Í.

Moving the Trace

Cursor to Any

Valid n Value

To move the trace cursor to any valid

n

value on the current function, enter the number. When you enter the first digit, an

n

=

prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the

n =

prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor.

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Exploring Sequence Graphs

(continued)

ZOOM

CALC

Evaluating u, v, and w

ZOOM

operations in

Seq

graphing work the same as in

Func

graphing. Only the

X

(

Xmin

,

Xmax

, and

Xscl

) and

Y

(

Ymin

,

Ymax

, and

Yscl

) window variables are affected.

PlotStart

,

PlotStep

,

nMin

, and

nMax

are only affected when you select

ZStandard

. The

VARS Zoom

secondary menu

ZU items

1

through

7

are the

ZOOM MEMORY

variables for

Seq

graphing.

The only

CALC

operation available in

Seq

graphing is

value

.

When

Time

axes format is selected,

value

displays

Y

(the

u(n)

value) for a specified

n

value.

When

Web

axes format is selected,

value

draws the web and displays

Y

(the

u(n)

value) for a specified

n

value.

When

uv

,

vw

, or

uw

axes format is selected,

value

displays

X

and

Y

according to the axes format setting. For example, for

uv

axes format,

X

represents

u(n)

and

Y

represents

v(n)

.

To enter the sequence names

u

,

v,

or

w

, press y [ u

], [ v

], or

[ w

]. You can evaluate these names in any of three ways.

Calculate the

n

th value in a sequence.

Calculate a list of values in a sequence.

Generate a sequence with optional; default is 1.

u(

nstart

,

nstop

[,

nstep

])

. nstep is

6–10 Sequence Graphing

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Graphing Web Plots

Graphing a Web

Plot

To select

Web

axes format, press y [

FORMAT

] ~ Í. A web plot graphs

u(n)

versus

u(nN1)

, which you can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes.

Valid Functions for Web Plots

Displaying the

Graph Screen

When

Web

axes format is selected, a sequence will not graph properly or will generate an error.

It must be recursive with only one recursion level (

u(nN1)

but not

u(nN2)

).

It cannot reference

n

directly.

It cannot reference any defined sequence except itself.

In

Web

format, press s to display the graph screen. The

TI-82 STATS:

Draws a y=x

reference line in

AxesOn

format.

Plots the selected sequences with

u(nN1)

as the independent variable.

Note: A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequence’s initial value.

Drawing the Web

To activate the trace cursor, press r. The screen displays the sequence and the current

n

,

X

, and

Y

values (

X

represents

u(nN1)

and

Y

represents

u(n)

). Press ~ repeatedly to draw the web step by step, starting at

nMin

. In

Web

format, the trace cursor follows this course.

1. It starts on the x-axis at the initial value

u(nMin)

(when

PlotStart=1

).

2. It moves vertically (up or down) to the sequence.

3. It moves horizontally to the y=x

reference line.

4. It repeats this vertical and horizontal movement as you continue to press ~.

Sequence Graphing 6–11

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Using Web Plots to Illustrate Convergence

Example:

Convergence

1. Press o in

Seq

mode to display the sequence

Y=

editor. Make sure the graph style is set to í (dot), and then define

nMin

,

u(n)

and

u(nMin)

as shown below.

2. Press y [

FORMAT

] Í to set

Time

axes format.

3. Press p and set the variables as shown below.

nMin=1

nMax=25

Xmin=0

Xmax=25

Ymin=L10

Ymax=10

PlotStart=1

PlotStep=1

Xscl=1 Yscl=1

4. Press s to graph the sequence.

5. Press y [

FORMAT

] and select the

Web

axes setting.

6. Press p and change the variables below.

Xmin=L10 Xmax=10

7. Press s to graph the sequence.

8. Press r, and then press ~ to draw the web. The displayed cursor coordinates

n

,

X

(

u(nN1)

), and

Y

(

u(n)

) change accordingly. When you press ~, a new

n

value is displayed, and the trace cursor is on the sequence.

When you press ~ again, the

n

value remains the same, and the cursor moves to the y=x

reference line. This pattern repeats as you trace the web.

6–12 Sequence Graphing

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Graphing Phase Plots

Graphing with uv, vw, and uw

The phase-plot axes settings

uv

,

vw

, and

uw

show relationships between two sequences. To select a phase-plot axes setting, press y [

FORMAT

], press ~ until the cursor is on

uv

,

vw

, or

uw

, and then press Í.

Axes Setting uv vw uw x-axis u(n) v(n) u(n) y-axis v(n) w(n) w(n)

Example:

Predator-Prey

Model

Use the predator-prey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.

This example uses the model to determine the equilibrium populations of wolves and rabbits, with initial populations of

200 rabbits (

u(nMin)

) and 50 wolves (

v(nMin)

).

These are the variables (given values are in parentheses):

R = number of rabbits

M = rabbit population growth rate without wolves

K = rabbit population death rate with wolves

W = number of wolves

G = wolf population growth rate with rabbits

D = wolf population death rate without rabbits

n

R

W

n n

= time (in months)

= R

nN1

= W

nN1

(1+MNKW

nN1

(1+GR

nN1

ND)

)

(.05)

(.001)

(.0002)

(.03)

1. Press o in

Seq

mode to display the sequence

Y=

editor.

Define the sequences and initial values for R shown below. Enter the sequence R sequence W

n

as

v(n)

.

n n

and W

n

as

as

u(n)

and enter the

Sequence Graphing 6–13

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Graphing Phase Plots

(continued)

Example:

Predator-Prey

Model

(continued)

2. Press y [

FORMAT

] Í to select

Time

axes format.

3. Press p and set the variables as shown below.

nMin=0 Xmin=0 Ymin=0

nMax=400

PlotStart=1

PlotStep=1

Xmax=400

Xscl=100

Ymax=300

Yscl=100

4. Press s to graph the sequence.

5. Press r ~ to individually trace the number of rabbits

(

u(n)

) and wolves (

v(n)

) over time (

n

).

Tip: Press a number, and then press

Í to jump to a specific n value (month) while in

TRACE.

6. Press y [

FORMAT

] ~ ~ Í to select

uv

axes format.

7. Press p and change these variables as shown below.

Xmin=84 Ymin=25

Xmax=237

Xscl=50

Ymax=75

Yscl=10

8. Press r. Trace both the number of rabbits (

X

) and the number of wolves (

Y

) through 400 generations.

Note: When you press r, the equation for u is displayed in the top-left corner. Press

} or † to see the equation for v.

6–14 Sequence Graphing

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Comparing TI-82 STATS and TI-82 Sequence Variables

Sequences and

Window

Variables

Refer to the table if you are familiar with the TI-82. It shows

TI-82 STATS sequences and sequence window variables, as well as their TI-82 counterparts.

TI.82

TI-82 STATS

In the

Y=

editor:

u(n) u(nMin) v(n) v(nMin) w(n) w(nMin)

In the window editor:

nMin

nMax

PlotStart

PlotStep

Un

UnStart

(window variable)

Vn

VnStart

(window variable)

not available not available

nStart

nMax

nMin

not available

Sequence Graphing 6–15

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Keystroke Differences Between TI-82 STATS and TI-82

Sequence

Keystroke

Changes

Refer to the table if you are familiar with the TI-82. It compares

TI-82 STATS sequence-name syntax and variable syntax with

TI.82 sequence-name syntax and variable syntax.

On TI.82, press: TI-82 STATS /

TI.82

n / n u(n) / Un v(n) / Vn w(n) u(nN1) / UnN1 v(nN1) / VnN1 w(nN1)

On TI-82 STATS, press:

„ y [ u

]

£ „ ¤ y [ v

]

£ „ ¤ y [ w

]

£ „ ¤ y [ u

]

£ „ ¹ À ¤ y [ v

]

£ „ ¹ À ¤ y [ w

]

£ „ ¹ À ¤ y [ y [ y [

n

]

Y.VARS

Y.VARS

not available y [

U

n

y [

V

n

N

1

]

N

1

] not available

] ¶ À

] ¶ Á

6–16 Sequence Graphing

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Contents

7

Tables

Getting Started: Roots of a Function

..........................................................

Setting Up the Table

.............................................................................................

Defining the Dependent Variables

...............................................................

Displaying the Table

.............................................................................................

4

5

2

3

Tables 7–1

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Getting Started: Roots of a Function

Getting Started is a fast-paced introduction. Read the chapter for details.

Evaluate the function Y = X 3

N 2X at each integer between L10 and 10. How many sign changes occur, and at what

X

values?

1. Press z † † † Í to set

Func

graphing mode.

2. Press o. Press „ 

3

to select

3

.

Then press ¹

2

„ to enter the function

Y

1

=X

3

N2X

.

3. Press y [

TBLSET

] to display the

TABLE

SETUP

screen. Press Ì

10

Í to set

TblStart=L10

. Press

1

Í to set

@Tbl=1

.

Press Í to select

Indpnt: Auto

(automatically generated independent values).

Press † Í to select

Depend: Auto

(automatically generated dependent values).

4. Press y [

TABLE

] to display the table screen.

5. Press † until you see the sign changes in the value of

Y

1

. How many sign changes occur, and at what

X

values?

7–2 Tables

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Setting Up the Table

TABLE SETUP

Screen

To display the

TABLE SETUP

screen, press y [

TBLSET

].

TblStart, @Tbl

TblStart

(table start) defines the initial value for the independent variable.

TblStart

applies only when the independent variable is generated automatically (when

Indpnt: Auto

is selected).

@Tbl

(table step) defines the increment for the independent variable.

Note: In Seq mode, both TblStart and @Tbl must be integers.

Indpnt: Auto,

Indpnt: Ask,

Depend: Auto,

Depend: Ask

Setting Up the

Table from the

Home Screen or a Program

Selections

Indpnt: Auto

Depend: Auto

Indpnt: Ask

Depend: Auto

Indpnt: Auto

Depend: Ask

Indpnt: Ask

Depend: Ask

Table Characteristics

Values are displayed automatically in both the independent-variable column and in all dependent-variable columns.

The table is empty; when you enter a value for the independent variable, all corresponding dependent-variable values are calculated and displayed automatically.

Values are displayed automatically for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press Í.

The table is empty; enter values for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press Í.

To store a value to

TblStart

,

@Tbl

, or

TblZnput

from the home screen or a program, select the variable name from the

VARS

TABLE

secondary menu.

TblZnput

is a list of independentvariable values in the current table.

When you press y [

TBLSET

] in the program editor, you can select

IndpntAuto

,

IndpntAsk

,

DependAuto

, and

DependAsk

.

Tables 7–3

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Defining the Dependent Variables

Defining

Dependent

Variables from the Y= Editor

In the

Y=

editor, enter the functions that define the dependent variables. Only functions that are selected in the

Y=

editor are displayed in the table. The current graphing mode is used. In

Par

mode, you must define both components of each parametric equation (Chapter 4).

Editing

Dependent

Variables from the Table Editor

To edit a selected

Y=

function from the table editor, follow these steps.

1. Press y [

TABLE

] to display the table, then press ~ or | to move the cursor to a dependent-variable column.

2. Press } until the cursor is on the function name at the top of the column. The function is displayed on the bottom line.

3. Press Í. The cursor moves to the bottom line. Edit the function.

4. Press Í or †. The new values are calculated. The table and the

Y=

function are updated automatically.

Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table.

7–4 Tables

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Displaying the Table

The Table

To display the table, press y [

TABLE

].

Current cell

Independentvariable values in the first column

Dependentvariable values in the second and third columns

Current cell’s full value

Note: The table abbreviates the values, if necessary.

Independent and

Dependent

Variables

The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the independent variable

X

and the dependent variables

Y

1

and

Y

2

are displayed because

Func

graphing mode is set.

Graphing Mode

Func

Par

Pol

Seq

(function)

(parametric)

(polar)

(sequence)

q n

Independent

Variable

X

T

Dependent

Variable

Y

1

Y

0

through

Y

9

, and

X

1T

X

6T

/

Y

1T

through

/

Y

6T r

1

through

r

6 u(n)

,

v(n)

, and

w(n)

Clearing the

Table from the

Home Screen or a Program

From the home screen, select the

ClrTable

instruction from the

CATALOG

. To clear the table, press Í.

From a program, select

9:ClrTable

from the

PRGM I/O

menu or from the

CATALOG

. The table is cleared upon execution. If

IndpntAsk

is selected, all independent and dependent variable values on the table are cleared. If

DependAsk

is selected, all dependent variable values on the table are cleared.

Tables 7–5

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Displaying the Table

(continued)

Scrolling

Independent-

Variable Values

If

Indpnt: Auto

is selected, you can press } and † in the independent-variable column to display more values. As you scroll the column, the corresponding dependent-variable values also are displayed. All dependent-variable values may not be displayed if

Depend: Ask

is selected.

Note: You can scroll back from the value entered for

TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above,

TblStart=0 and

@Tbl=1 generates and displays values of X=0, . . . , 6; but you can press

} to scroll back and display the table for X=M1, . . ., 5.

Displaying Other

Dependent

Variables

If you have defined more than two dependent variables, the first two selected

Y=

functions are displayed initially. Press ~ or | to display dependent variables defined by other selected

Y= functions. The independent variable always remains in the left column, except during a trace with

Par

graphing mode and

G.T

split-screen mode set.

Tip: To simultaneously display on the table two dependent variables that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display.

For example, to simultaneously display

Y

4

and

Y

7

on the table, go to the Y= editor and deselect

Y

5

and

Y

6

.

7–6 Tables

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Contents

8

Draw

Instructions

Getting Started: Drawing a Tangent Line

...............................................

Using the DRAW Menu

......................................................................................

Clearing Drawings

.................................................................................................

Drawing Line Segments

.....................................................................................

Drawing Horizontal and Vertical Lines

...................................................

Drawing Tangent Lines

......................................................................................

Drawing Functions and Inverses

...................................................................

9

Shading Areas on a Graph

................................................................................

10

6

8

4

5

2

3

Drawing Circles

.......................................................................................................

11

Placing Text on a Graph

.....................................................................................

12

Using Pen to Draw on a Graph

......................................................................

13

Drawing Points on a Graph

..............................................................................

14

Drawing Pixels

.........................................................................................................

16

Storing Graph Pictures (

Pic s)

.........................................................................

17

Recalling Graph Pictures (

Pic s)

....................................................................

18

Storing Graph Databases (

GDB s)

.................................................................

19

Recalling Graph Databases (

GDB s)

............................................................

20

DRAW

Instructions 8–1

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Getting Started: Drawing a Tangent Line

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to find the equation of the tangent line at X = ‡2/2 for the function

Y = sinX.

Before you begin, select

Radian

and

Func

mode from the mode screen, if necessary.

1. Press o to display the

Y= editor. Press ˜

„ ¤ to store

sin(X)

in

Y

1

.

2. Press q

7

to select

7:ZTrig

, which graphs the equation in the Zoom Trig window.

3. Press y [

DRAW

]

5

to select

5:Tangent(

. The tangent instruction is initiated.

4. Press y [

]

2

¤ ¥

2

.

5. Press Í. The tangent line is drawn; the

X

value and the tangent-line equation are displayed on the graph.

8–2

DRAW

Instructions

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Using the DRAW Menu

DRAW Menu

Before Drawing on a Graph

Drawing on a

Graph

To display the

DRAW

menu, press y [

DRAW

]. The

TI-82 STATS interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph.

DRA

W

POINTS STO

1: ClrDraw

2: Line(

3: Horizontal

4: Vertical

5: Tangent(

6: DrawF

7: Shade(

8: DrawInv

9: Circle(

0: Text(

A: Pen

Clears all drawn elements.

Draws a line segment between 2 points.

Draws a horizontal line.

Draws a vertical line.

Draws a line segment tangent to a function.

Draws a function.

Shades an area between two functions.

Draws the inverse of a function.

Draws a circle.

Draws text on a graph screen.

Activates the free-form drawing tool.

The

DRAW

instructions draw on top of graphs. Therefore, before you use the

DRAW

instructions, consider whether you want to perform one or more of the following actions.

Change the mode settings on the mode screen.

Change the format settings on the format screen.

Enter or edit functions in the

Y=

editor.

Select or deselect functions in the

Y=

editor.

Change the window variable values.

Turn stat plots on or off.

Clear existing drawings with

ClrDraw

(page 8.4).

Note: If you draw on a graph and then perform any of the actions listed above, the graph is replotted without the drawings when you display the graph again.

You can use any

DRAW

menu instructions except

DrawInv

to draw on

Func

,

Par

,

Pol

, and

Seq

graphs.

DrawInv

is valid only in

Func

graphing. The coordinates for all

DRAW

instructions are the display’s x-coordinate and y-coordinate values.

You can use most

DRAW

menu and

DRAW POINTS

menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a

DRAW

menu instruction, the home screen is displayed.

DRAW

Instructions 8–3

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Clearing Drawings

Clearing

Drawings When a Graph Is

Displayed

All points, lines, and shading drawn on a graph with

DRAW instructions are temporary.

To clear drawings from the currently displayed graph, select

1:ClrDraw

from the

DRAW

menu. The current graph is replotted and displayed with no drawn elements.

Clearing

Drawings from the Home Screen or a Program

To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select

1:ClrDraw

from the

DRAW

menu. The instruction is copied to the cursor location. Press Í.

When

ClrDraw

is executed, it clears all drawings from the current graph and displays the message

Done

. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone.

Note: Before you clear drawings, you can store them with

StorePic

(page 8.17).

8–4

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Instructions

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Drawing Line Segments

Drawing a Line

Segment Directly on a Graph

To draw a line segment when a graph is displayed, follow these steps.

1. Select

2:Line(

from the

DRAW

menu.

2. Place the cursor on the point where you want the line segment to begin, and then press Í.

3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press Í.

To continue drawing line segments, repeat steps 2 and 3. To cancel

Line(

, press ‘.

Drawing a Line

Segment from the Home Screen or a Program

Line(

also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions.

Line(

X1

,

Y1

,

X2

,

Y2

)

To erase a line segment, enter

Line(

X1

,

Y1

,

X2

,

Y2

,0)

DRAW

Instructions 8–5

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Drawing Horizontal and Vertical Lines

Drawing a Line

Directly on a

Graph

To draw a horizontal or vertical line when a graph is displayed, follow these steps.

1. Select

3:Horizontal

or

4:Vertical

from the

DRAW

menu. A line is displayed that moves as you move the cursor.

2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass.

3. Press Í to draw the line on the graph.

To continue drawing lines, repeat steps 2 and 3.

To cancel

Horizontal

or

Vertical

, press ‘.

8–6

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Drawing a Line from the Home

Screen or a

Program

Horizontal

(horizontal line) draws a horizontal line at

Y

=y. y can be an expression but not a list.

Horizontal

y

Vertical

(vertical line) draws a vertical line at

X

=x. x can be an expression but not a list.

Vertical

x

To instruct the TI-82 STATS to draw more than one horizontal or vertical line, separate each instruction with a colon (

:

).

DRAW

Instructions 8–7

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Drawing Tangent Lines

Drawing a Tangent Line

Directly on a Graph

To draw a tangent line when a graph is displayed, follow these steps.

1. Select

5:Tangent(

from the

DRAW

menu.

2. Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph’s

Y= function is displayed in the top-left corner, if

ExprOn

is selected.

3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line.

4. Press Í. In

Func

mode, the

X

value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the

dy/dx

value is displayed.

Drawing a Tangent Line from the Home

Screen or a Program

Tip: Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for

X and the equation for Y.

Tangent(

(tangent line) draws a line tangent to expression in terms of

X

, such as

Y

1

or

X

2

, at point

X

=value.

X

can be an expression. expression is interpreted as being in

Func

mode.

Tangent(

expression

,

value

)

8–8

DRAW

Instructions

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Drawing Functions and Inverses

Drawing a

Function

DrawF

(draw function) draws expression as a function in terms of

X

on the current graph. When you select

6:DrawF

from the

DRAW

menu, the TI-82 STATS returns to the home screen or the program editor.

DrawF

is not interactive.

DrawF

expression

Drawing an

Inverse of a

Function

Note: You cannot use a list in expression to draw a family of curves.

DrawInv

(draw inverse) draws the inverse of expression by plotting

X

values on the y-axis and

Y

values on the x-axis. When you select

8:DrawInv

from the

DRAW

menu, the TI-82 STATS returns to the home screen or the program editor.

DrawInv

is not interactive.

DrawInv

works in

Func

mode only.

DrawInv

expression

Note: You cannot use a list in expression to draw a family of curves.

DRAW

Instructions 8–9

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Shading Areas on a Graph

Shading a Graph

To shade an area on a graph, select

7:Shade(

from the

DRAW menu. The instruction is pasted to the home screen or to the program editor.

Shade(

draws lowerfunc and upperfunc in terms of

X

on the current graph and shades the area that is specifically above

lowerfunc and below upperfunc. Only the areas where lowerfunc

< upperfunc are shaded.

Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and Xright must be numbers between

Xmin

and

Xmax

, which are the defaults.

pattern specifies one of four shading patterns.

pattern=

1

pattern=

2

pattern=

3

pattern=

4

vertical (default) horizontal negative—slope 45¡ positive—slope 45¡

patres specifies one of eight shading resolutions.

patres=

1

patres=

2

patres=

3

patres=

4

patres=

5

patres=

6

patres=

7

patres=

8

shades every pixel (default) shades every second pixel shades every third pixel shades every fourth pixel shades every fifth pixel shades every sixth pixel shades every seventh pixel shades every eighth pixel

Shade(

lowerfunc

,

upperfunc[

,

Xleft

,

Xright

,

pattern

,

patres]

)

8–10

DRAW

Instructions

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Drawing Circles

Drawing a Circle

Directly on a

Graph

To draw a circle directly on a displayed graph using the cursor, follow these steps.

1. Select

9:Circle(

from the

DRAW

menu.

2. Place the cursor at the center of the circle you want to draw.

Press Í.

3. Move the cursor to a point on the circumference. Press

Í to draw the circle on the graph.

Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the

Circle( instruction from the home screen or a program, the current window variables may distort the shape.

To continue drawing circles, repeat steps 2 and 3. To cancel

Circle(

, press ‘.

Drawing a Circle from the Home

Screen or a

Program

Circle(

draws a circle with center (X,Y ) and radius. These values can be expressions.

Circle(

X

,

Y

,

radius

)

Tip: When you use

Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use

ZSquare

(Chapter 3) before drawing the circle to adjust the window variables and make the circle circular.

DRAW

Instructions 8–11

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Placing Text on a Graph

Placing Text

Directly on a

Graph

To place text on a graph when the graph is displayed, follow these steps.

1. Select

0:Text(

from the

DRAW

menu.

2. Place the cursor where you want the text to begin.

3. Enter the characters. Press ƒ or y [

A.LOCK

] to enter letters and q. You may enter TI-82 STATS functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.

To cancel

Text(

, press ‘.

Placing Text on a

Graph from the

Home Screen or a Program

Text(

places on the current graph the characters comprising

value, which can include TI-82 STATS functions and instructions. The top-left corner of the first character is at pixel

(row,column), where row is an integer between

0 and 57 and column is an integer between 0 and 94. Both row and column can be expressions.

Text(

row

,

column

,

value

,

value . . .

)

value can be text enclosed in quotation marks (

"

), or it can be an expression. The TI-82 STATS will evaluate an expression and display the result with up to 10 characters.

Split Screen

On a

Horiz

split screen, the maximum value for row is 25. On a

G.T

split screen, the maximum value for row is 45, and the maximum value for column is 46.

8–12

DRAW

Instructions

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Using Pen to Draw on a Graph

Using Pen to

Draw on a Graph

Pen

draws directly on a graph only. You cannot execute

Pen

from the home screen or a program.

To draw on a displayed graph, follow these steps.

1. Select

A:Pen

from the

DRAW

menu.

2. Place the cursor on the point where you want to begin drawing. Press Í to turn on the pen.

3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time.

4. Press Í to turn off the pen.

For example,

Pen

was used to create the arrow pointing to the local minimum of the selected function.

To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel

Pen

, press ‘.

DRAW

Instructions 8–13

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Drawing Points on a Graph

DRAW POINTS

Menu

To display the

DRAW POINTS

menu, press y [

DRAW

] ~. The

TI-82 STATS interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph.

DRAW POINTS STO

1: Pt-On(

2: Pt-Off(

3: Pt-Change(

4: Pxl-On(

5: Pxl-Off(

6: Pxl-Change(

7: pxl-Test(

Turns on a point.

Turns off a point.

Toggles a point on or off.

Turns on a pixel.

Turns off a pixel.

Toggles a pixel on or off.

Returns 1 if pixel on, 0 if pixel off.

Drawing Points

Directly on a

Graph with

Pt

.

On(

To draw a point on a graph, follow these steps.

1. Select

1:Pt.On(

from the

DRAW POINTS

menu.

2. Move the cursor to the position where you want to draw the point.

3. Press Í to draw the point.

To continue drawing points, repeat steps 2 and 3. To cancel

Pt.On(

, press ‘.

8–14

DRAW

Instructions

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Erasing Points with Pt.Off(

Changing Points with Pt.Change(

To change (toggle on or off) a point on a graph, follow these steps.

1. Select

3:Pt.Change(

(point change) from the

DRAW POINTS menu.

2. Move the cursor to the point you want to change.

3. Press Í to change the point’s on/off status.

To continue changing points, repeat steps 2 and 3. To cancel

Pt.Change(

, press ‘.

Drawing Points from the Home

Screen or a

Program

To erase (turn off) a drawn point on a graph, follow these steps.

1. Select

2:Pt.Off(

(point off) from the

DRAW POINTS

menu.

2. Move the cursor to the point you want to erase.

3. Press Í to erase the point.

To continue erasing points, repeat steps 2 and 3. To cancel

Pt.Off(

, press ‘.

Pt.On(

(point on) turns on the point at (

X

=x,

Y

=y).

Pt.Off(

turns the point off.

Pt.Change(

toggles the point on or off. mark is optional; it determines the point’s appearance; specify

1

,

2

, or

3

, where:

1

=

¦

(dot; default)

2

=

(box)

3

=

+

(cross)

Pt.On(

x

,

y[

,

mark]

)

Pt.Off(

x

,

y[

,

mark]

)

Pt.Change(

x

,

y

)

Note: If you specified mark to turn on a point with Pt.On(, you must specify mark when you turn off the point with

Pt.Off(. Pt.Change( does not have the mark option.

DRAW

Instructions 8–15

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Drawing Pixels

TI-82 STATS

Pixels

A pixel is a square dot on the TI-82 STATS display. The

Pxl.

(pixel) instructions let you turn on, turn off, or reverse a pixel

(dot) on the graph using the cursor. When you select a pixel instruction from the

DRAW POINTS

menu, the TI-82 STATS returns to the home screen or the program editor. The pixel instructions are not interactive.

Turning On and

Off Pixels with

Pxl.On( and

Pxl.Off(

Pxl.On(

(pixel on) turns on the pixel at (row,column), where

row is an integer between 0 and 62 and column is an integer between 0 and 94.

Pxl.Off(

turns the pixel off.

Pxl.Change(

toggles the pixel on and off.

Pxl.On(

row

,

column

)

Pxl.Off(

row

,

column

)

Pxl.Change(

row

,

column

)

Using pxl.Test(

Split Screen pxl.Test(

(pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph. row must be an integer between 0 and 62. column must be an integer between 0 and 94.

pxl.Test(

row

,

column

)

On a

Horiz

split screen, the maximum value for row is 30 for

Pxl.On(

,

Pxl.Off(

,

Pxl.Change(

, and

pxl.Test(

.

On a

G.T

split screen, the maximum value for row is 50 and the maximum value for column is 46 for

Pxl.On(

,

Pxl.Off(

,

Pxl.Change(

, and

pxl.Test(

.

8–16

DRAW

Instructions

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Storing Graph Pictures (Pics)

DRAW STO Menu

To display the

DRAW STO

menu, press y [

DRAW

] |. When you select an instruction from the

DRAW STO menu, the

TI-82 STATS returns to the home screen or the program editor.

The picture and graph database instructions are not interactive.

DRAW POINTS STO

1: StorePic

2: RecallPic

3: StoreGDB

4: RecallGDB

Stores the current picture.

Recalls a saved picture.

Stores the current graph database.

Recalls a saved graph database.

Storing a Graph

Picture

You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables

Pic1

through

Pic9

, or

Pic0

. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program.

A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture.

To store a graph picture, follow these steps.

1. Select

1:StorePic

from the

DRAW STO

menu.

StorePic

is pasted to the current cursor location.

2. Enter the number (from

1

to

9

, or

0

) of the picture variable to which you want to store the picture. For example, if you enter

3

, the TI-82 STATS will store the picture to

Pic3

.

Note: You also can select a variable from the PICTURE secondary menu (

4). The variable is pasted next to

StorePic.

3. Press Í to display the current graph and store the picture.

DRAW

Instructions 8–17

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Recalling Graph Pictures (Pics)

Recalling a

Graph Picture

To recall a graph picture, follow these steps.

1. Select

2:RecallPic

from the

DRAW STO

menu.

RecallPic

is pasted to the current cursor location.

2. Enter the number (from

1

to

9

, or

0

) of the picture variable from which you want to recall a picture. For example, if you enter

3

, the TI-82 STATS will recall the picture stored to

Pic3

.

Note: You also can select a variable from the

PICTURE secondary menu (

4). The variable is pasted next to

RecallPic.

3. Press Í to display the current graph with the picture superimposed on it.

Note: Pictures are drawings. You cannot trace a curve that is part of a picture.

Deleting a Graph

Picture

To delete graph pictures from memory, use the

MEMORY DELETE FROM

menu (Chapter 18).

8–18

DRAW

Instructions

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Storing Graph Databases (GDBs)

What Is a Graph

Database?

A graph database (

GDB

) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10

GDB s in variables

GDB1

through

GDB9

, or

GDB0

and recall them to recreate graphs.

A

GDB

stores five elements of a graph.

Graphing mode

Window variables

Format settings

All functions in the

Y=

editor and the selection status of each

Graph style for each

Y= function

GDB s do not contain drawn items or stat plot definitions.

Storing a Graph

Database

To store a graph database, follow these steps.

1. Select

3:StoreGDB

from the

DRAW STO

menu.

StoreGDB

is pasted to the current cursor location.

2. Enter the number (from

1

to

9

, or

0

) of the

GDB

variable to which you want to store the graph database. For example, if you enter

7

, the TI-82 STATS will store the

GDB

to

GDB7

.

Note: You also can select a variable from the

GDB secondary menu (

3). The variable is pasted next to StoreGDB.

3. Press Í to store the current database to the specified

GDB

variable.

DRAW

Instructions 8–19

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Recalling Graph Databases (GDBs)

Recalling a

Graph Database

CAUTION: When you recall a

GDB

, it replaces all existing

Y= functions. Consider storing the current

Y=

functions to another database before recalling a stored

GDB

.

To recall a graph database, follow these steps.

1. Select

4:RecallGDB

from the

DRAW STO

menu.

RecallGDB

is pasted to the current cursor location.

2. Enter the number (from

1

to

9

, or

0

) of the

GDB

variable from which you want to recall a

GDB

. For example, if you enter

7

, the TI-82 STATS will recall the

GDB

stored to

GDB7

.

Note: You also can select a variable from the

GDB secondary menu (

3). The variable is pasted next to RecallGDB.

3. Press Í to replace the current

GDB

with the recalled

GDB

. The new graph is not plotted. The TI-82 STATS changes the graphing mode automatically, if necessary.

Deleting a Graph

Database

To delete a

GDB

from memory, use the

MEMORY DELETE

FROM

menu (Chapter 18).

8–20

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Instructions

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Contents

9

Split

Screen

Getting Started: Exploring the Unit Circle

.............................................

Using Split Screen

..................................................................................................

Horiz

(Horizontal) Split Screen

.....................................................................

G.T

(Graph-Table) Split Screen

....................................................................

TI-82 STATS Pixels in

Horiz

and

G.T

Mode

......................................

4

5

2

3

6

Split Screen 9–1

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Getting Started: Exploring the Unit Circle

Getting Started is a fast-paced introduction. Read the chapter for details.

Use

G.T

(graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0

°

, 30

°

, 45

°

,

60

°

, 90

°

, and so on.

1. Press z to display the mode screen. Press

† † ~ Í to select

Degree

mode. Press

† ~ Í to select

Par

(parametric) graphing mode.

Press † † † † ~ ~ Í to select

G.T

(graph-table) split-screen mode.

2. Press y [

FORMAT

] to display the format screen. Press † † † † † ~ Í to select

ExprOff

.

3. Press o to display the

Y= editor for

Par

graphing mode. Press ™ „ ¤ Í to store

cos(T)

to

X

1T

. Press ˜ „ ¤

Í to store

sin(T)

to

Y

1T

.

4. Press p to display the window editor.

Enter these values for the window variables.

Tmin=0 Xmin=L2.3

Tmax=360 Xmax=2.3

Tstep=15 Xscl=1

Ymin=L2.5

Ymax=2.5

Yscl=1

5. Press r. On the left, the unit circle is graphed parametrically in

Degree

mode and the trace cursor is activated. When

T=0

(from the graph trace coordinates), you can see from the table on the right that the value of

X

1T

(

cos(T)

) is

1

and

Y

1T

(

sin(T)

) is

0

. Press ~ to move the cursor to the next 15

° angle increment. As you trace around the circle in steps of 15

°

, an approximation of the standard value for each angle is highlighted in the table.

9–2 Split Screen

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Using Split Screen

Setting a Split-

Screen Mode

To set a split-screen mode, press z, and then move the cursor to the bottom line of the mode screen.

Select

Horiz

(horizontal) to display the graph screen and another screen split horizontally.

Select

G.T

(graph-table) to display the graph screen and table screen split vertically.

$ $

The split screen is activated when you press any key that applies to either half of the split screen.

Some screens are never displayed as split screens. For example, if you press z in

Horiz

or

G.T

mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns.

When you press a key or key combination in either

Horiz

or

G.T

mode, the cursor is placed in the half of the display for which that key applies. For example, if you press r, the cursor is placed in the half in which the graph is displayed. If you press y [

TABLE

], the cursor is placed in the half in which the table is displayed.

The TI-82 STATS will remain in split-screen mode until you change back to

Full

screen mode.

Split Screen 9–3

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Horiz (Horizontal) Split Screen

Horiz Mode

In

Horiz

(horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves.

The top half displays the graph.

The bottom half displays any of these editors.

Home screen (four lines)

Y=

editor (four lines)

Stat list editor (two rows)

Window editor (three settings)

Table editor (two rows)

Moving from Half to Half in Horiz

Mode

To use the top half of the split screen:

Press s or r.

Select a

ZOOM

or

CALC

operation.

To use the bottom half of the split screen:

Press any key or key combination that displays the home screen.

Press o (

Y=

editor).

Press … Í (stat list editor).

Press p (window editor).

Press y [

TABLE

] (table editor).

Full Screens in

Horiz Mode

All other screens are displayed as full screens in

Horiz

split-screen mode.

To return to the

Horiz

split screen from a full screen when in

Horiz

mode, press any key or key combination that displays the graph, home screen,

Y=

editor, stat list editor, window editor, or table editor.

9–4 Split Screen

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G.T (Graph-Table) Split Screen

G.T Mode

In

G.T

(graph-table) split-screen mode, a vertical line splits the screen into left and right halves.

The left half displays the graph.

The right half displays the table.

Moving from Half to Half in G.T

Mode

To use the left half of the split screen:

Press s or r.

Select a

ZOOM

or

CALC

operation.

To use the right half of the split screen, press y [

TABLE

].

Using

r

G.T Mode

As you move the trace cursor along a graph in the split screen’s left half in

G.T

mode, the table on the right half automatically scrolls to match the current cursor values.

Full Screens in

G.T Mode

Note: When you trace in Par graphing mode, both components of an equation (

Xn

T

and

Yn

T

) are displayed in the two columns of the table.

As you trace, the current value of the independent variable T is displayed on the graph.

All screens other than the graph and the table are displayed as full screens in

G.T

split-screen mode.

To return to the

G.T

split screen from a full screen when in

G.T

mode, press any key or key combination that displays the graph or the table.

Split Screen 9–5

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TI-82 STATS Pixels in Horiz and G.T Modes

TI-82 STATS

Pixels in Horiz and G.T Modes

DRAW POINTS

Menu Pixel

Instructions

Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.

For

Pxl.On(

,

Pxl.Off(

,

Pxl.Change(

, and

pxl.Test(

:

In

Horiz

mode, row must be {30; column must be {94.

In

G.T

mode, row must be {50; column must be {46.

Pxl.On(

row

,

column

)

DRAW Menu

Text( Instruction

For the

Text(

instruction:

In

Horiz

mode, row must be {25; column must be {94.

In

G.T

mode, row must be {45; column must be {46.

Text(

row

,

column

,"

text

")

PRGM I/O Menu

Output(

Instruction

For the

Output(

instruction:

In

Horiz

mode, row must be {4; column must be {16.

In

G.T

mode, row must be {8; column must be {16.

Output(

row

,

column

,"

text

")

Setting a

Split-Screen

Mode from the

Home Screen or a Program

To set

Horiz

or

G.T

from a program, follow these steps.

1. Press z while the cursor is on a blank line in the program editor.

2. Select

Horiz

or

G.T

.

The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution.

It remains in effect after execution.

Note: You also can paste

Horiz or G.T to the home screen or program editor from the

CATALOG (Chapter 15).

9–6 Split Screen

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10

Matrices

Contents

Getting Started: Systems of Linear Equations

.....................................

Defining a Matrix

...................................................................................................

Viewing and Editing Matrix Elements

......................................................

Using Matrices with Expressions

.................................................................

Displaying and Copying Matrices

................................................................

Using Math Functions with Matrices

.........................................................

Using the

MATRX MATH

Operations

.......................................................

12

8

9

4

7

2

2

Matrices 10–1

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Getting Started: Systems of Linear Equations

Getting Started is a fast-paced introduction. Read the chapter for details.

Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-82 STATS, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using

rref(

to obtain the reduced row-echelon form.

1. Press . Press ~ ~ to display the

MATRX EDIT

menu. Press

1

to select

1: [A]

¸

2. Press

2

Í

4

Í to define a 2×4 matrix.

The rectangular cursor indicates the current element. Ellipses (

...

) indicate additional columns beyond the screen.

3. Press

1

Í to enter the first element. The rectangular cursor moves to the second column of the first row.

4. Press

2

Í

3

Í

3

Í to complete the first row for X + 2Y + 3Z = 3.

5. Press

2

Í

3

Í

4

Í

3

Í to enter the second row for 2X + 3Y + 4Z = 3.

6. Press y [

QUIT

] to return to the home screen.

If necessary, press ‘ to clear the home screen. Press  ~ to display the

MATRX

MATH

menu. Press } to wrap to the end of the menu. Select

B:rref(

to copy

rref(

to the home screen.

7. Press 

1

to select

1: [A]

from the

MATRX NAMES

menu. Press ¤ Í. The reduced row-echelon form of the matrix is displayed and stored in

Ans

.

1X N 1Z = L3 so X = L3 + Z

1Y + 2Z = 3 so Y = 3 N 2Z

10–2 Matrices

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Defining a Matrix

What Is a Matrix?

A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. The TI-82 STATS has 10 matrix variables,

[A]

through

[J]

. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-82 STATS matrices.

Selecting a

Matrix

Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps.

1. Press  | to display the

MATRX EDIT

menu. The dimensions of any previously defined matrices are displayed.

2. Select the matrix you want to define. The

MATRX EDIT screen is displayed.

Accepting or

Changing Matrix

Dimensions

The dimensions of the matrix (row × column) are displayed on the top line. The dimensions of a new matrix are

1 ×1

. You must accept or change the dimensions each time you edit a matrix.

When you select a matrix to define, the cursor highlights the row dimension.

To accept the row dimension, press Í.

To change the row dimension, enter the number of rows (up to

99

), and then press Í.

The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press Í, the rectangular cursor moves to the first matrix element.

Matrices 10–3

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Viewing and Editing Matrix Elements

Displaying Matrix

Elements

After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero.

Select the matrix from the

MATRX EDIT

menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line.

This is an 8 × 4 matrix. Ellipses in the left or right column indicate additional columns.

#

or

$

in the right column indicate additional rows.

Deleting a Matrix

To delete matrices from memory, use the

MEMORY DELETE

FROM

secondary menu (Chapter 18).

10–4 Matrices

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Viewing a Matrix

The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line.

Select the matrix from the

MATRX EDIT

menu, and then enter or accept the dimensions.

Viewing-Context

Keys

Key

| or ~

† or }

Í

Any entry character y [

INS

]

{

Function

Moves the rectangular cursor within the current row.

Moves the rectangular cursor within the current column; on the top row, } moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimension.

Switches to editing context; activates the edit cursor on the bottom line.

Switches to editing context; clears the value on the bottom line.

Switches to editing context; clears the value on the bottom line; copies the character to the bottom line.

Nothing

Nothing

Matrices 10–5

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Viewing and Editing Matrix Elements

(continued)

Editing a Matrix

Element

In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps.

1. Select the matrix from the

MATRX EDIT

menu, and then enter or accept the dimensions.

2. Press |, }, ~, and † to move the cursor to the matrix element you want to change.

3. Switch to editing context by pressing Í, ‘, or an entry key.

4. Change the value of the matrix element using the editingcontext keys described below. You may enter an expression, which is evaluated when you leave editing context.

Note: You can press

‘ Í to restore the value at the rectangular cursor if you make a mistake.

5. Press Í, }, or † to move to another element.

Editing-Context

Keys

Key

| or ~

† or }

Í

Any entry character y [

INS

]

{

Function

Moves the edit cursor within the value.

Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor within the column.

Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor to the next row element.

Clears the value on the bottom line.

Copies the character to the location of the edit cursor on the bottom line.

Activates the insert cursor.

Deletes the character under the edit cursor on the bottom line.

10–6 Matrices

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Using Matrices with Expressions

Using a Matrix in an Expression

To use a matrix in an expression, you can do any of the following.

Copy the name from the

MATRX NAMES

menu.

Recall the contents of the matrix into the expression with y [

RCL

] (Chapter 1).

Enter the matrix directly (see below).

Entering a Matrix in an Expression

You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression.

To enter a matrix in an expression, follow these steps.

1. Press y [

[

] to indicate the beginning of the matrix.

2. Press y [

[

] to indicate the beginning of a row.

3. Enter a value, which can be an expression, for each element in the row. Separate the values with commas.

4. Press y [

]

] to indicate the end of a row.

5. Repeat steps 2 through 4 to enter all of the rows.

6. Press y [

]

] to indicate the end of the matrix.

Note: The closing

]] are not necessary at the end of an expression or preceding

!

The resulting matrix is displayed in the form:

[[

element

1,1

,

...

,

element

1,n

],

...

,[

element m,1

,

...

,

element m,n

]]

Any expressions are evaluated when the entry is executed.

Note: The commas that you must enter to separate elements are not displayed on output.

Matrices 10–7

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Displaying and Copying Matrices

Displaying a

Matrix

To display the contents of a matrix on the home screen, select the matrix from the

MATRX NAMES

menu, and then press

Í.

Ellipses in the left or right column indicate additional columns.

#

or

$

in the right column indicate additional rows. Press ~, |,

†, and } to scroll the matrix.

Copying One

Matrix to Another

To copy a matrix, follow these steps.

1. Press  to display the

MATRX NAMES

menu.

2. Select the name of the matrix you want to copy.

3. Press ¿.

4. Press  again and select the name of the new matrix to which you want to copy the existing matrix.

5. Press Í to copy the matrix to the new matrix name.

Accessing a

Matrix Element

On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select

matrix from the

MATRX NAMES

menu.

[

matrix

](

row

,

column

)

10–8 Matrices

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Using Math Functions with Matrices

Using Math

Functions with

Matrices

+ (Add), –

(Subtract),

ääää

(Multiply)

You can use many of the math functions on the TI-82 STATS keyboard, the

MATH

menu, the

MATH NUM

menu, and the

MATH

TEST

menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same.

To add (Ã) or subtract (¹) matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements.

matrixA

+

matrixB matrixA

N

matrixB

To multiply (¯) two matrices together, the column dimension of matrixA must match the row dimension of matrixB.

matrixA

ääää

matrixB

Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value.

matrix

ääää

value value

ääää

matrix

L (Negation)

Negating a matrix (Ì) returns a matrix in which the sign of every element is changed (reversed).

L

matrix

Matrices 10–9

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Using Math Functions with Matrices

(continued) abs( abs(

(absolute value,

MATH NUM

menu) returns a matrix containing the absolute value of each element of matrix.

abs(

matrix

) round( round(

(

MATH NUM

menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits.

round(

matrix[

,

#decimals]

)

M1 (Inverse)

Use the

L1

function (—) to invert a matrix (

^L1

is not valid).

matrix must be square. The determinant cannot equal zero.

matrix

L1

Powers

To raise a matrix to a power, matrix must be square. You can use

2

(¡),

3

(

MATH

menu), or

^

power (›) for integer power between

0

and

255

.

matrix

2

matrix

3

matrix

^

power

10–10 Matrices

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Relational

Operations

To compare two matrices using the relational operations

=

and

ƒ

(

TEST

menu), they must have the same dimensions.

=

and

ƒ

compare matrixA and matrixB on an element-by-element basis.

The other relational operations are not valid with matrices.

matrixA

=

matrixB returns

1

if every comparison is true; it returns

0

if any comparison is false.

matrixA

ƒ

matrixB returns

1

if at least one comparison is false; it returns

0

if no comparison is false.

iPart(, fPart(, int( iPart(

(integer part),

fPart(

(fractional part), and

int(

(greatest integer) are on the

MATH NUM

menu.

iPart(

returns a matrix containing the integer part of each element of matrix.

fPart(

returns a matrix containing the fractional part of each element of matrix.

int(

returns a matrix containing the greatest integer of each element of matrix.

iPart(

matrix

) fPart(

matrix

) int(

matrix

)

Matrices 10–11

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Using the MATRX MATH Operations

MATRX MATH

Menu det(

T

(Transpose)

To display the

MATRX MATH

menu, press  ~.

NAMES MAT

H

1: det(

2:

T

3: dim(

4: Fill(

5: identity(

6: randM(

7: augment(

8: Matr4list(

9: List4matr(

0: cumSum(

A: ref(

B: rref(

C: rowSwap(

D: row+(

E: ärow(

F: ärow+(

EDIT

Calculates the determinant.

Transposes the matrix.

Returns the matrix dimensions.

Fills all elements with a constant.

Returns the identity matrix.

Returns a random matrix.

Appends two matrices.

Stores a matrix to a list.

Stores a list to a matrix.

Returns the cumulative sums of a matrix.

Returns the row-echelon form of a matrix.

Returns the reduced row-echelon form.

Swaps two rows of a matrix.

Adds two rows; stores in the second row.

Multiplies the row by a number.

Multiplies the row, adds to the second row.

det(

(determinant) returns the determinant (a real number) of a square matrix.

det(

matrix

)

T

(transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix.

matrix

T

Accessing Matrix

Dimensions with dim( dim(

(dimension) returns a list containing the dimensions

(

{

rows columns

}

) of matrix.

dim(

matrix

)

Note:

dim(matrix)

!

dim(matrix)

!

10–12 Matrices

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Creating a Matrix with dim(

Use

dim(

with ¿ to create a new matrixname of dimensions

rows × columns with

0

as each element.

{

rows

,

columns

}

!

matrixname

)

Redimensioning a

Matrix with dim(

Use

dim(

with ¿ to redimension an existing matrixname to dimensions rows × columns. The elements in the old

matrixname that are within the new dimensions are not changed.

Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.

{

rows

,

columns

}

!

matrixname

)

Fill(

Fill(

stores value to every element in matrixname.

Fill(

value

,

matrixname

) identity( randM( identity(

returns the identity matrix of dimension rows ×

dimension columns.

identity(

dimension

) randM(

(create random matrix) returns a rows × columns random matrix of integers ‚ L9 and  9. The seed value stored to the

rand

function controls the values (Chapter 2).

randM(

rows

,

columns

)

Matrices 10–13

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Using the MATRX MATH Operations

(continued) augment( augment(

appends matrixA to matrixB as new columns. matrixA and matrixB both must have the same number of rows.

augment(

matrixA

,

matrixB

)

Matr4list(

List4matr(

Matr4list(

(matrix stored to list) fills each listname with elements from each column in matrix.

Matr4list(

ignores extra listname arguments. Likewise,

Matr4list(

ignores extra matrix columns.

Matr4list(

matrix

,

listnameA

,

...,listname n

)

&

Matr4list(

also fills a listname with elements from a specified

column# in matrix. To fill a list with a specific column from matrix, you must enter column# after matrix.

Matr4list(

matrix

,

column#

,

listname

)

&

List4matr(

(lists stored to matrix) fills matrixname column by column with the elements from each list. If dimensions of all lists are not equal,

List4matr(

fills each extra matrixname row with

0

.

Complex lists are not valid.

List4matr(

listA

,

...,list n

,

matrixname

)

&

10–14 Matrices

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cumSum( cumSum(

returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom.

cumSum(

matrix

)

Row Operations

MATRX MATH

menu items

A

through

F

are row operations. You can use a row operation in an expression. Row operations do not change matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the

MATRX NAMES

menu.

ref(, rref( ref(

(row-echelon form) returns the row-echelon form of a real

matrix. The number of columns must be greater than or equal to the number of rows.

ref(

matrix

) rref(

(reduced row-echelon form) returns the reduced row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows.

rref(

matrix

)

Matrices 10–15

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Using the MATRX MATH Operations

(continued) rowSwap( rowSwap(

returns a matrix. It swaps rowA and rowB of matrix.

rowSwap(

matrix

,

rowA

,

rowB

) row+( row+(

(row addition) returns a matrix. It adds rowA and rowB of

matrix and stores the results in rowB.

row+(

matrix

,

rowA

,

rowB

)

äääärow(

äääärow+(

äääärow(

(row multiplication) returns a matrix. It multiplies row of

matrix by value and stores the results in row.

äääärow(

value

,

matrix

,

row

)

äääärow+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB.

äääärow+(

value

,

matrix

,

rowA

,

rowB

)

10–16 Matrices

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11

Lists

Contents

Getting Started: Generating a Sequence

..................................................

Naming Lists

..............................................................................................................

Storing and Displaying Lists

...........................................................................

Entering List Names

.............................................................................................

Attaching Formulas to List Names

..............................................................

Using Lists in Expressions

................................................................................

LIST OPS

Menu

......................................................................................................

10

LIST MATH

Menu

..................................................................................................

17

7

9

4

6

2

3

Lists 11–1

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Getting Started: Generating a Sequence

Getting Started is a fast-paced introduction. Read the chapter for details.

Calculate the first eight terms of the sequence 1/A 2 . Store the results to a user-created list. Then display the results in fraction form. Begin this example on a blank line on the home screen.

1. Press y [

LIST

] ~ to display the

LIST OPS menu.

2. Press

5

to select

5:seq(

, which pastes

seq(

to the current cursor location.

3. Press

1

¥ ƒ [

A

] ¡ ¢ ƒ [

A

] ¢

1

¢

8

¢

1

¤ to enter the sequence.

4. Press ¿, and then press y ƒ to turn on alpha-lock. Press [

S

] [

E

] [

Q

], and then press

ƒ to turn off alpha-lock. Press

1

to complete the list name.

5. Press Í to generate the list and store it in

SEQ1

. The list is displayed on the home screen.

An ellipsis (

...

) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

6. Press y [

LIST

] to display the

LIST NAMES menu. Press Í to paste

ÙÙÙÙSEQ1 to the current cursor location. (If

SEQ1

is not item

1

on your

LIST NAMES

menu, move the cursor to

SEQ1

before you press Í.)

7. Press  to display the

MATH menu. Press

1

to select

1:4Frac

, which pastes

4Frac

to the current cursor location.

8. Press Í to show the sequence in fraction form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

11–2 Lists

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Naming Lists

Using

TI-82 STATS List

Names L

1 through L

6

The TI-82 STATS has six list names in memory:

L

1

,

L

2

,

L

3

,

L

4

,

L

5

, and

L

6

. The list names

L

1

through

L

6

are on the keyboard above the numeric keys À through ¸. To paste one of these names to a valid screen, press y, and then press the appropriate key.

L

1

through

L

6

are stored in stat list editor columns

1

through

6

when you reset memory.

Creating a List

Name on the

Home Screen

To create a list name on the home screen, follow these steps.

1. Press y [

{

], enter one or more list elements, and then press y [

}

]. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions.

2. Press ¿.

3. Press ƒ [letter from A to Z or of the name.

q ] to enter the first letter

4. Enter zero to four letters, q, or numbers to complete the name.

5. Press Í. The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the

LIST NAMES

menu.

Note: If you want to view a user-created list in the stat list editor, you must store it in the stat list editor (Chapter 12).

You also can create a list name in these four places.

At the

Name=

prompt in the stat list editor

At an

Xlist:

,

Ylist:

, or

Data List:

prompt in the stat plot editor

At a

List:

,

List1:

,

List2:

,

Freq:

,

Freq1:

,

Freq2:

,

XList:

, or

YList:

prompt in the inferential stat editors

On the home screen using

SetUpEditor

You can create as many list names as your TI-82 STATS memory has space to store.

Lists 11–3

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Storing and Displaying Lists

Storing Elements to a List

You can store list elements in either of two ways.

Use braces and ¿ on the home screen.

Use the stat list editor (Chapter 12).

The maximum dimension of a list is 999 elements.

Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter

real(listname)

!

Displaying a List on the Home

Screen

To display the elements of a list on the home screen, enter the name of the list (preceded by Ù if necessary; see page 11.16), and then press Í. An ellipsis indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

11–4 Lists

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Copying One List to Another

To copy a list, store it to another list.

Accessing a List

Element

You can store a value to or recall a value from a specific list

element. You can store to any element within the current list dimension or one element beyond.

listname

(

element

)

Deleting a List from Memory

Using Lists in

Graphing

To delete lists from memory, including

L

1

through

L

6

, use the

MEMORY DELETE FROM

secondary menu (Chapter 18).

Resetting memory restores

L

1

through

L

6

. Removing a list from the stat list editor does not delete it from memory.

You can use lists to graph a family of curves (Chapter 3).

Lists 11–5

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Entering List Names

Using the

LIST NAMES

Menu

To display the

LIST NAMES

menu, press y [

LIST

]. Each item is a user-created list name.

LIST NAMES

menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using

1

through

9

, then

0

. To jump to the first list name that begins with a particular alpha character or q, press ƒ

[letter from A to Z or q

].

Tip: From the top of a menu, press

} to move to the bottom. From the bottom, press

† to move to the top.

Note: The LIST NAMES menu omits list names L

1

through

L

6

. Enter

L1

through

L

6

directly from the keyboard (page 11.3).

When you select a list name from the

LIST NAMES

menu, the list name is pasted to the current cursor location.

The list name symbol ÙÙÙÙ precedes a list name when the name is pasted where non-list name data also is valid, such as the home screen.

The

ÙÙÙÙ

symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor’s

Name=

prompt or the stat plot editor’s

XList:

and

YList:

prompts.

Entering a User-

Created List

Name Directly

To enter an existing list name directly, follow these steps.

1. Press y [

LIST

] ~ to display the

LIST OPS

menu.

2. Select

B:

ÙÙÙÙ , which pastes ÙÙÙÙ to the current cursor location. ÙÙÙÙ is not always necessary (page 11.16).

Note: You also can paste

ÙÙÙÙ to the current cursor location from the

CATALOG (Chapter 15).

3. Enter the characters that comprise the list name.

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Attaching Formulas to List Names

Attaching a

Formula to a List

Name

You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list.

When anything in the attached formula changes, the list to which the formula is attached is updated automatically.

When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated.

When you edit the formula itself, all elements in the list to which the formula is attached are updated.

For example, the first screen below shows that elements are stored to

L

3

, and the formula

L

3

+10

is attached to the list name

ÙÙÙÙADD10 . The quotation marks designate the formula to be attached to ÙÙÙÙADD10 . Each element of ÙÙÙÙADD10 is the sum of an element in

L

3

and 10.

The next screen shows another list,

L

4

. The elements of

L

4

are the sum of the same formula that is attached to

L

3

. However, quotation marks are not entered, so the formula is not attached to

L

4

.

On the next line,

L6

L6!

3

(1):L

, and then redisplays

L

3

.

3

changes the first element in

L

3

to

The last screen shows that editing

L

3

updated ÙÙÙÙADD10 , but did not change

L

4

. This is because the formula

L

3

+10

is attached to

ÙÙÙÙADD10 , but it is not attached to

L

4

.

Note: To view a formula that is attached to a list name, use the stat list editor (Chapter 12).

Lists 11–7

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Attaching Formulas to List Names

(continued)

Attaching a

Formula to a List on the Home

Screen or in a

Program

To attach a formula to a list name from a blank line on the home screen or from a program, follow these steps.

1. Press ƒ [

ã

], enter the formula (which must resolve to a list), and press ƒ [

ã

] again.

Note: When you include more than one list name in a formula, each list must have the same dimension.

2. Press ¿.

3. Enter the name of the list to which you want to attach the formula.

Press y, and then enter a TI-82 STATS list name

L

1

through

L

6

.

Press y [

LIST

] and select a user.created list name from the

LIST NAMES

menu.

Enter a user.created list name directly using ÙÙÙÙ (page

11.16).

4. Press Í.

Detaching a

Formula from a

List

Note: The stat list editor displays a formula-lock symbol next to each list name that has an attached formula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, edit attached formulas, and detach formulas from lists.

You can detach (clear) an attached formula from a list in any of three ways.

Enter

""

!

listname on the home screen.

Edit any element of a list to which a formula is attached.

Use the stat list editor (Chapter 12).

Note: You also can use ClrList or ClrAllList to detach a formula from a list (Chapter 18).

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Using Lists in Expressions

Using a List in an

Expression

You can use lists in an expression in any of three ways. When you press Í, any expression is evaluated for each list element, and a list is displayed.

Use

L

1

L

6

or any user-created list name in an expression.

Enter the list elements directly (step 1 on page 11.3).

Use y [

RCL

] to recall the contents of the list into an expression at the cursor location (Chapter 1).

&

Note: You must paste user-created list names to the

Rcl prompt by selecting them from the LIST NAMES menu. You cannot enter them directly using

ÙÙÙÙ.

Using Lists with

Math Functions

You can use a list to input several values for some math functions. Other chapters and Appendix A specify whether a list is valid. The function is evaluated for each list element, and a list is displayed.

When you use a list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as

L1

in

‡({1,0,L1})

, is ignored.

This returns an error.

This graphs

X

ääää‡(1) and Xääää‡(0), but skips

X

ääää‡(L1).

When you use two lists with a two-argument function, the dimension of each list must be the same. The function is evaluated for corresponding elements.

When you use a list and a value with a two-argument function, the value is used with each element in the list.

Lists 11–9

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LIST OPS Menu

LIST OPS Menu

To display the

LIST OPS

menu, press y [

LIST

] ~.

NAMESOPS MATH

1: SortA(

2: SortD(

3: dim(

4: Fill(

5: seq(

6: cumSum(

7:

@

List(

8: Select(

9: augment(

0: List4matr(

A: Matr4list(

Sorts lists in ascending order.

Sorts lists in descending order.

Sets the list dimension.

Fills all elements with a constant.

Creates a sequence.

Returns a list of cumulative sums.

Returns difference of successive elements.

Selects specific data points.

Concatenates two lists.

Stores a list to a matrix.

Stores a matrix to a list.

Designates the list-name data type.

SortA(, SortD(

SortA(

(sort ascending) sorts list elements from low to high values.

SortD(

(sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude

(modulus).

With one list,

SortA(

and

SortD(

sort the elements of listname and update the list in memory.

SortA(

listname

) SortD(

listname

)

With two or more lists,

SortA(

and

SortD(

sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. All lists must have the same dimension.

SortA(

keylistname

,

dependlist1[

,

dependlist2

,

...

,

dependlist n]

)

SortD(

keylistname

,

dependlist1[

,

dependlist2

,

...

,

dependlist n]

)

Note: In the example, 5 is the first element in L

4

, and 1 is the first element in

L

5

. After

SortA(L

4

,L

5

), 5 becomes the second element of

L

4

, and likewise, 1 becomes the second element of L

5

.

Note:

SortA( and SortD( are the same as SortA( and SortD( on the

STAT EDIT menu (Chapter 12).

11–10 Lists

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Using dim( to

Find List

Dimensions dim(

(dimension) returns the length (number of elements) of list.

dim(

list

)

Using dim( to

Create a List

You can use

dim(

with ¿ to create a new listname with dimension length from 1 to 999. The elements are zeros.

length

!

listname

)

Using dim( to

Redimension a

List

You can use

dim

with ¿ to redimension an existing listname to dimension length from 1 to 999.

The elements in the old listname that are within the new dimension are not changed.

Extra list elements are filled by

0

.

Elements in the old list that are outside the new dimension are deleted.

length

!

listname

)

Fill(

Fill(

replaces each element in listname with value.

Fill(

value

,

listname

)

Note:

dim( and Fill( are the same as dim( and Fill( on the MATRX

MATH menu (Chapter 10).

Lists 11–11

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LIST OPS Menu

(continued) seq( seq(

(sequence) returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment. variable need not be defined in memory. increment can be negative; the default value for increment is 1.

seq(

is not valid within

expression.

seq(

expression

,

variable

,

begin

,

end[

,

increment]

) cumSum( cumSum(

(cumulative sum) returns the cumulative sums of the elements in list, starting with the first element. list elements can be real or complex numbers.

cumSum(

list

)

@List(

@List(

returns a list containing the differences between consecutive elements in list.

@List

subtracts the first element in

list from the second element, subtracts the second element from the third, and so on. The list of differences is always one element shorter than the original list. list elements can be a real or complex numbers.

@List(

list

)

Select(

Select(

selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, xlistname and ylistname. For example, you can use

Select(

to select and then analyze a portion of plotted CBL or CBR data.

Select(

xlistname

,

ylistname

)

Note: Before you use

Select(, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window (page 11.13).

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Before Using

Select(

Before using

Select(

, follow these steps.

1. Create two list names and enter the data.

2. Turn on a stat plot, select " (scatter plot) or Ó (xyLine), and enter the two list names for

Xlist:

and

Ylist:

(Chapter 12).

3. Use

ZoomStat

to plot the data (Chapter 3).

Using Select( to

Select Data

Points from a

Plot

To select data points from a scatter plot or xyLine plot, follow these steps.

1. Press y [

LIST

] ~

8

to select

8:Select(

from the

LIST OPS menu.

Select(

is pasted to the home screen.

2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names into which you want the selected data to be stored.

3. Press Í. The graph screen is displayed with

Left Bound?

in the bottom-left corner.

4. Press } or † (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points.

5. Press | and ~ to move the cursor to the stat plot data point that you want as the left bound.

Lists 11–13

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LIST OPS Menu

(continued)

Using Select( to

Select Data

Points from a

Plot (continued)

6. Press Í. A

4

indicator on the graph screen shows the left bound.

Right Bound?

is displayed in the bottom-left corner.

7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í.

The x-values and y-values of the selected points are stored in

xlistname and ylistname. A new stat plot of xlistname and

ylistname replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor.

Note: The two new lists (xlistname and ylistname) will include the points you select as left bound and right bound. Also, left-bound

x-valueright-bound x-value must be true.

11–14 Lists

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augment( augment(

concatenates the elements of listA and listB. The list elements can be real or complex numbers.

augment(

listA

,

listB

)

List4matr(

List4matr(

(lists stored to matrix) fills matrixname column by column with the elements from each list. If the dimensions of all lists are not equal, then

List4matr(

fills each extra matrixname row with

0

. Complex lists are not valid.

List4matr(

list1

,

list2

,

. . .

,

list n

,

matrixname

)

&

Lists 11–15

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LIST OPS Menu

(continued)

Matr4list( Matr4list(

(matrix stored to lists) fills each listname with elements from each column in matrix. If the number of listname arguments exceeds the number of columns in matrix, then

Matr4list(

ignores extra listname arguments. Likewise, if the number of columns in matrix exceeds the number of listname arguments, then

Matr4list(

ignores extra matrix columns.

Matr4list(

matrix

,

listname1

,

listname2

,

. . .

,

listname n

)

&

Matr4list(

also fills a listname with elements from a specified

column# in matrix. To fill a list with a specific column from

matrix, you must enter a column# after matrix.

Matr4list(

matrix

,

column#

,

listname

)

&

ÙÙÙÙ

preceding one to five characters identifies those characters as a user-created listname. listname may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q.

ÙÙÙÙ

listname

Generally,

ÙÙÙÙ

must precede a user-created list name when you enter a user-created list name where other input is valid, for example, on the home screen. Without the

ÙÙÙÙ

, the TI-82 STATS may misinterpret a user-created list name as implied multiplication of two or more characters.

ÙÙÙÙ

need not precede a user-created list name where a list name is the only valid input, for example, at the

Name=

prompt in the stat list editor or the

Xlist:

and

Ylist:

prompts in the stat plot editor. If you enter

ÙÙÙÙ

where it is not necessary, the TI-82 STATS will ignore the entry.

11–16 Lists

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LIST MATH Menu

LIST MATH Menu

To display the

LIST MATH

menu, press y [

LIST

] |.

NAMES

OPS

1: min(

2: max(

3: mean(

4: median(

5: sum(

6: prod(

7: stdDev(

8: variance(

MAT

H

Returns minimum element of a list.

Returns maximum element of a list.

Returns mean of a list.

Returns median of a list.

Returns sum of elements in a list.

Returns product of elements in list.

Returns standard deviation of a list.

Returns the variance of a list.

min(, max( min(

(minimum) and

max(

(maximum) return the smallest or

largest element of listA. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB.

For a complex list, the element with smallest or largest magnitude

(modulus) is returned.

min(

listA[

,

listB]

) max(

listA[

,

listB]

) mean(, median(

Note:

min( and max( are the same as min( and max( on the MATH

NUM menu.

mean(

returns the mean value of list.

median(

returns the median value of list. The default value for freqlist is 1. Each

freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid.

mean(

list[

,

freqlist]

) median(

list[

,

freqlist]

)

Lists 11–17

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LIST MATH Menu

(continued) sum(, prod( sum(

(summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or complex numbers.

prod(

returns the product of all elements of list. start and end elements are optional; they specify a range of list elements. list elements can be real or complex numbers.

sum(

list[

,

start

,

end]

) prod(

list[

,

start

,

end]

)

Sums and

Products of

Numeric

Sequences

You can combine

sum(

or

prod(

with

seq(

to obtain:

upper

G

expression(x)

x=lower upper

expression(x) x=lower

To evaluate G 2 (N–1) from N=1 to 4:

stdDev(, variance( stdDev(

returns the standard deviation of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in

list. Complex lists are not valid.

variance(

returns the variance of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list.

Complex lists are not valid.

stdDev(

list[

,

freqlist]

) variance(

list[

,

freqlist]

)

11–18 Lists

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12

Statistics

Contents

Getting Started: Pendulum Lengths and Periods

................................

2

Setting Up Statistical Analyses

......................................................................

10

Using the Stat List Editor

..................................................................................

11

Attaching Formulas to List Names

..............................................................

14

Detaching Formulas from List Names

......................................................

16

Switching Stat List Editor Contexts

............................................................

17

Stat List Editor Contexts

....................................................................................

18

STAT EDIT

Menu

..................................................................................................

20

Regression Model Features

..............................................................................

22

STAT CALC

Menu

................................................................................................

24

Statistical Variables

...............................................................................................

29

Statistical Analysis in a Program

..................................................................

30

Statistical Plotting

...................................................................................................

31

Statistical Plotting in a Program

....................................................................

37

Statistics 12–1

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Getting Started: Pendulum Lengths and Periods

Getting Started is a fast-paced introduction. Read the chapter for details.

A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling. They record the pendulum’s period for each of 12 string lengths.*

Length (cm)

6.5

11.0

13.2

15.0

18.0

23.1

24.4

26.6

30.5

34.3

37.6

41.5

1. Press z † † † Í to set

Func

graphing mode.

2. Press …

5

to select

5:SetUpEditor

.

SetUpEditor

is pasted to the home screen.

Press Í. This removes lists from stat list editor columns

1

through

20

, and then stores lists

L

1

through

L

6

in columns

1

through

6

.

Note: Removing lists from the stat list editor does not delete them from memory.

3. Press …

1

to select

1:Edit

from the

STAT

EDIT

menu. The stat list editor is displayed.

If elements are stored in

L

1

and

L

2

, press } to move the cursor onto

L

1

, and then press

‘ Í ~ } ‘ Í to clear both lists. Press | to move the rectangular cursor back to the first row in

L

1

.

Time (sec)

0.51

0.68

0.73

0.79

0.88

0.99

1.01

1.08

1.13

1.26

1.28

1.32

*This example is quoted and adapted from Contemporary Precalculus Through Applications, by the North Carolina School of Science and Mathematics, by permission of Janson

Publications, Inc., Dedham, MA. 1-800-322-MATH. © 1992. All rights reserved.

12–2 Statistics

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4. Press

6

Ë

5

Í to store the first pendulum string length (6.5 cm) in

L

1

. The rectangular cursor moves to the next row.

Repeat this step to enter each of the 12 string length values in the table on page

12.2.

5. Press ~ to move the rectangular cursor to the first row in

L

2

.

Press Ë

51

Í to store the first time measurement (.51 sec) in

L

2

. The rectangular cursor moves to the next row.

Repeat this step to enter each of the 12 time values in the table on page 12.2.

6. Press o to display the

Y=

editor.

If necessary, press ‘ to clear the function

Y

1

. As necessary, press }, Í, and ~ to turn off

Plot1

,

Plot2

, and

Plot3

from the top line of the

Y=

editor (Chapter 3). As necessary, press †, |, and Í to deselect functions.

7. Press y [

STAT PLOT

]

1

to select

1:Plot1

from the

STAT PLOTS

menu. The stat plot editor is displayed for plot 1.

8. Press Í to select

On

, which turns on plot 1. Press † Í to select " (scatter plot). Press † y [

L1

] to specify

Xlist:L

1

for plot 1. Press † y [

L2

] to specify

Ylist:L

2

for plot 1. Press † ~ Í to select

+

as the

Mark

for each data point on the scatter plot.

9. Press q

9

to select

9:ZoomStat

from the

ZOOM

menu. The window variables are adjusted automatically, and plot 1 is displayed. This is a scatter plot of the timeversus-length data.

Statistics 12–3

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Getting Started: Pendulum Lengths and Periods

(cont.)

Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to the data.

10. Press … ~

4

to select

4:LinReg(ax+b)

(linear regression model) from the

STAT

CALC menu.

LinReg(ax+b)

is pasted to the home screen.

11. Press y [

L1

] ¢ y [

L2

] ¢. Press 

~

1

to display the

VARS Y.VARS

FUNCTION

secondary menu, and then press

1

to select

1:Y

1

.

L

1

,

L

2

, and

Y

1

are pasted to the home screen as arguments to

LinReg(ax+b)

.

12. Press Í to execute

LinReg(ax+b)

. The linear regression for the data in

L

1

and

L

2

is calculated. Values for

a

and

b

are displayed on the home screen. The linear regression equation is stored in

Y

1

. Residuals are calculated and stored automatically in the list name

RESID

, which becomes an item on the

LIST NAMES

menu.

13. Press s. The regression line and the scatter plot are displayed.

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The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit.

14. Press …

1

to select

1:Edit

. The stat list editor is displayed.

Press ~ and } to move the cursor onto

L

3

.

Press y [

INS

]. An unnamed column is displayed in column

3

;

L

3

,

L

4

,

L

5

, and

L

6

shift right one column. The

Name=

prompt is displayed in the entry line, and alpha-lock is on.

15. Press y [

LIST

] to display the

LIST NAMES menu.

If necessary, press † to move the cursor onto the list name

RESID

.

16. Press Í to select

RESID

and paste it to the stat list editor’s

Name=

prompt.

17. Press Í.

RESID

is stored in column

3

of the stat list editor.

Press † repeatedly to examine the residuals.

Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in

L

1

. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in

L

1

. Plotting the residuals will show this pattern more clearly.

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Getting Started: Pendulum Lengths and Periods

(cont.)

18. Press y [

STAT PLOT

]

2

to select

2:Plot2

from the

STAT PLOTS

menu. The stat plot editor is displayed for plot 2.

19. Press Í to select

On

, which turns on plot 2.

Press † Í to select " (scatter plot).

Press † y [

L1

] to specify

Xlist:L

1

for plot

2. Press † [

R

] [

E

] [

S

] [

I

] [

D

] (alpha-lock is on) to specify

Ylist:RESID

for plot 2. Press

† Í to select

as the mark for each data point on the scatter plot.

20. Press o to display the

Y=

editor.

Press | to move the cursor onto the = sign, and then press Í to deselect

Y

1

. Press

} Í to turn off plot 1.

21. Press q

9

to select

9:ZoomStat

from the

ZOOM

menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.

Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals.

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The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves down with the data would be more accurate. Perhaps a function such as square root would fit. Try a power regression to fit a function of the form y = a ä x b .

22. Press o to display the

Y=

editor.

Press ‘ to clear the linear regression equation from

Y

1

. Press } Í to turn on plot 1. Press ~ Í to turn off plot 2.

23. Press q

9

to select

9:ZoomStat

from the

ZOOM

menu. The window variables are adjusted automatically, and the original scatter plot of time-versus-length data (plot

1) is displayed.

24. Press … ~ ƒ [

A

] to select

A:PwrReg

from the

STAT CALC menu.

PwrReg

is pasted to the home screen.

Press y [

L1

] ¢ y [

L2

] ¢. Press 

~

1

to display the

VARS Y.VARS

FUNCTION

secondary menu, and then press

1

to select

1:Y

1

.

L

1

,

L

2

, and

Y

1

are pasted to the home screen as arguments to

PwrReg

.

25. Press Í to calculate the power regression. Values for

a

and

b

are displayed on the home screen. The power regression equation is stored in

Y

1

. Residuals are calculated and stored automatically in the list name

RESID

.

26. Press s. The regression line and the scatter plot are displayed.

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Getting Started: Pendulum Lengths and Periods

(cont.)

The new function y=.192x

.522 appears to fit the data well. To get more information, examine a residual plot.

27. Press o to display the

Y=

editor.

Press | Í to deselect

Y

1

.

Press } Í to turn off plot 1. Press ~

Í to turn on plot 2.

Note: Step 19 defined plot 2 to plot residuals (

RESID) versus string length (

L

1

).

28. Press q

9

to select

9:ZoomStat

from the

ZOOM

menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.

The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases.

To see the magnitudes of the residuals, continue with these steps.

29. Press r.

Press ~ and | to trace the data. Observe the values for

Y

at each point.

With this model, the largest positive residual is about 0.041 and the smallest negative residual is about L0.027. All other residuals are less than 0.02 in magnitude.

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Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length. To predict the periods for a pendulum with string lengths of 20 cm and 50 cm, continue with these steps.

30. Press  ~

1

to display the

VARS

Y.VARS FUNCTION

secondary menu, and then press

1

to select

1:Y

1

.

Y

1

is pasted to the home screen.

31. Press £

20

¤ to enter a string length of 20 cm.

Press Í to calculate the predicted time of about 0.92 seconds.

Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value.

32. Press y [

ENTRY

] to recall the Last Entry.

Press | | |

5

to change the string length to 50 cm.

33. Press Í to calculate the predicted time of about 1.48 seconds.

Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate.

Note: You also can make predictions using the table with the

TABLE SETUP settings Indpnt:Ask and

Depend:Auto (Chapter 7).

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Setting Up Statistical Analyses

Using Lists to

Store Data

Setting Up a

Statistical

Analysis

Displaying the

Stat List Editor

Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI-82 STATS has six list variables in memory,

L

1

through

L

6

, to which you can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11).

To set up a statistical analysis, follow these steps. Read the chapter for details.

1. Enter the statistical data into one or more lists.

2. Plot the data.

3. Calculate the statistical variables or fit a model to the data.

4. Graph the regression equation for the plotted data.

5. Graph the residuals list for the given regression model.

The stat list editor is a table where you can store, edit, and view up to 20 lists that are in memory. Also, you can create list names from the stat list editor.

To display the stat list editor, press …, and then select

1:Edit

from the

STAT EDIT

menu.

The top line displays list names.

L

1

through

L

6

are stored in columns

1

through

6

after a memory reset. The number of the current column is displayed in the top-right corner.

The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to the current context (page 12.17).

The center area displays up to seven elements of up to three lists; it abbreviates values when necessary. The entry line displays the full value of the current element.

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Using the Stat List Editor

Entering a List

Name in the Stat

List Editor

To enter a list name in the stat list editor, follow these steps.

1. Display the

Name=

prompt in the entry line in either of two ways.

Move the cursor onto the list name in the column where you want to insert a list, and then press y [

INS

]. An unnamed column is displayed and the remaining lists shift right one column.

Press } until the cursor is on the top line, and then press

~ until you reach the unnamed column.

Note: If list names are stored to all 20 columns, you must remove a list name to make room for an unnamed column.

The

Name=

prompt is displayed and alpha-lock is on.

2. Enter a valid list name in any of four ways.

Select a name from the

LIST NAMES

menu (Chapter 11).

Enter

L

1

,

L

2

,

L

3

,

L

4

,

L

5

, or

L

6

from the keyboard.

Enter an existing user-created list name directly from the keyboard.

Enter a new user-created list name (page 12.12).

3. Press Í or † to store the list name and its elements, if any, in the current column of the stat list editor.

To begin entering, scrolling, or editing list elements, press †.

The rectangular cursor is displayed.

Note: If the list name you entered in step 2 already was stored in another stat list editor column, then the list and its elements, if any, move to the current column from the previous column. Remaining list names shift accordingly.

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Using the Stat List Editor

(continued)

Creating a Name in the Stat List

Editor

To create a name in the stat list editor, follow these steps.

1. Follow step 1 on page 12.11 to display the

Name=

prompt.

2. Press [letter from A to Z or q

] to enter the first letter of the name. The first character cannot be a number.

3. Enter zero to four letters, q, or numbers to complete the new user-created list name. List names can be one to five characters long.

4. Press Í or † to store the list name in the current column of the stat list editor. The list name becomes an item on the

LIST NAMES

menu (Chapter 11).

Removing a List from the Stat List

Editor

To remove a list from the stat list editor, move the cursor onto the list name and then press {. The list is not deleted from memory; it is only removed from the stat list editor.

Note: To delete a list name from memory, use the

MEMORY

DELETE:List selection screen (Chapter 18).

Removing All

Lists and

Restoring L

1 through L

6

You can remove all user-created lists from the stat list editor and restore list names

L

1

through

L

6

to columns

1

through

6

in either of two ways.

Use

SetUpEditor

with no arguments (page 12.21).

Reset all memory (Chapter 18).

Clearing All

Elements from a

List

You can clear all elements from a list in any of five ways.

Use

ClrList

to clear specified lists (page 12.20).

In the stat list editor, press } to move the cursor onto a list name, and then press ‘ Í.

In the stat list editor, move the cursor onto each element, and then press { one by one.

On the home screen or in the program editor, enter

0

!dim(

listname

(Chapter 11).

)

to set the dimension of listname to 0

Use

ClrAllLists

to clear all lists in memory (Chapter 18).

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Editing a List

Element

To edit a list element, follow these steps.

1. Move the rectangular cursor onto the element you want to edit.

2. Press Í to move the cursor to the entry line.

Note: If you want to replace the current value, you can enter a new value without first pressing

Í. When you enter the first character, the current value is cleared automatically.

3. Edit the element in the entry line.

Press one or more keys to enter the new value. When you enter the first character, the current value is cleared automatically.

Press ~ to move the cursor to the character before which you want to insert, press y [

INS

], and then enter one or more characters.

Press ~ to move the cursor to a character you want to delete, and then press { to delete the character.

To cancel any editing and restore the original element at the rectangular cursor, press ‘ Í.

Note: You can enter expressions and variables for elements.

4. Press Í, }, or † to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element.

When you edit a list element in the stat list editor, the list is updated in memory immediately.

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Attaching Formulas to List Names

Attaching a

Formula to a List

Name in Stat List

Editor

You can attach a formula to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list. Chapter 11 describes in detail the concept of attaching formulas to list names.

To attach a formula to a list name that is stored in the stat list editor, follow these steps.

1. Press … Í to display the stat list editor.

2. Press } to move the cursor to the top line.

3. Press | or ~, if necessary, to move the cursor onto the list name to which you want to attach the formula.

Note: If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press

Í, and then edit the formula.

4. Press ƒ [

ã

], enter the formula, and press ƒ [

ã

].

Note: If you do not use quotation marks, the TI-82 STATS calculates and displays the same initial list of answers, but does not attach the formula for future calculations.

Note: Any user-created list name referenced in a formula must be preceded by an

ÙÙÙÙ symbol (Chapter 11).

5. Press Í. The TI-82 STATS calculates each list element and stores it to the list name to which the formula is attached.

A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached.

lock symbol

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Using the Stat

List Editor When

Formula-

Generated Lists

Are Displayed

When you edit an element of a list referenced in an attached formula, the TI-82 STATS updates the corresponding element in the list to which the formula is attached (Chapter 11).

When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-82 STATS takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.

Tip: To speed editing time, scroll horizontally until no lists with formulas are displayed, or rearrange the stat list editor so that no lists with formulas are displayed.

Handling Errors

Resulting from

Attached

Formulas

On the home screen, you can attach to a list a formula that references another list with dimension 0 (Chapter 11). However, you cannot display the formula-generated list in the stat list editor or on the home screen until you enter at least one element to the list that the formula references.

All elements of a list referenced by an attached formula must be valid for the attached formula. For example, if

Real

number mode is set and the attached formula is

log(L

1

)

, then each element of

L

1

must be greater than 0, since the logarithm of a negative number returns a complex result.

Tip: If an error menu is returned when you attempt to display a formula-generated list in the stat list editor, you can select 2:Goto, write down the formula that is attached to the list, and then press

‘ Í to detach (clear) the formula. You then can use the stat list editor to find the source of the error. After making the appropriate changes, you can reattach the formula to a list.

If you do not want to clear the formula, you can select

1:Quit, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to listname (element#) (Chapter 11).

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Detaching Formulas from List Names

Detaching a

Formula from a

List Name

Editing an

Element of a

Formula-

Generated List

You can detach (clear) a formula from a list name in any of four ways.

In the stat list editor, move the cursor onto the name of the list to which a formula is attached. Press Í

‘ Í. All list elements remain, but the formula is detached and the lock symbol disappears.

In the stat list editor, move the cursor onto an element of the list to which a formula is attached. Press Í, edit the element, and then press Í. The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain.

Use

ClrList

(page 12.20). All elements of one or more specified lists are cleared, each formula is detached, and each lock symbol disappears. All list names remain.

Use

ClrAllLists

(Chapter 18). All elements of all lists in memory are cleared, all formulas are detached from all list names, and all lock symbols disappear. All list names remain.

As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI-82 STATS protects against inadvertently detaching the formula from the list name by editing an element of the formula-generated list.

Because of the protection feature, you must press Í before you can edit an element of a formula-generated list.

The protection feature does not allow you to delete an element of a list to which a formula is attached. To delete an element of a list to which a formula is attached, you must first detach the formula in any of the ways described above.

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Switching Stat List Editor Contexts

Stat List Editor

Contexts

The stat list editor has four contexts.

View-elements context

View-names context

Edit-elements context

Enter-name context

The stat list editor is first displayed in view-elements context.

To switch through the four contexts, select

1:Edit

from the

STAT EDIT

menu and follow these steps.

1. Press } to move the cursor onto a list name. You are now in view-names context. Press ~ and | to view list names stored in other stat list editor columns.

2. Press Í. You are now in edit-elements context. You may edit any element in a list. All elements of the current list are displayed in braces (

{ }

)in the entry line. Press ~ and

| to view more list elements.

3. Press Í again. You are now in view-elements context.

Press ~, |, †, and } to view other list elements. The current element’s full value is displayed in the entry line.

4. Press Í again. You are now in edit-elements context.

You may edit the current element in the entry line.

5. Press } until the cursor is on a list name, then press y

[

INS

]. You are now in enter-name context.

6.

Press ‘. You are now in view-names context.

7.

Press †. You are now back in view-elements context.

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Stat List Editor Contexts

View-Elements

Context

In view-elements context, the entry line displays the list name, the current element’s place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis (

...

) indicates that the element continues beyond 12 characters.

Edit-Elements

Context

To page down the list six elements, press ƒ †. To page up six elements, press ƒ }. To delete a list element, press

{. Remaining elements shift up one row. To insert a new element, press y [

INS

].

0

is the default value for a new element.

In edit-elements context, the data displayed in the entry line depends on the previous context.

When you switch to edit-elements context from viewelements context, the full value of the current element is displayed. You can edit the value of this element, and then press † and } to edit other list elements.

&

When you switch to edit-elements context from view-names context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list.

&

Note: In edit-elements context, you can attach a formula to a list name only if you switched to it from view-names context.

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View-Names

Context

In view-names context, the entry line displays the list name and the list elements.

Enter-Name

Context

To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory.

To insert a name in the current column, press y [

INS

].

Remaining columns shift to the right one column.

In enter-name context, the

Name=

prompt is displayed in the entry line, and alpha-lock is on.

At the

Name=

prompt, you can create a new list name, paste a list name from

L

1

to

L

6

from the keyboard, or paste an existing list name from the

LIST NAMES

menu (Chapter 11). The ÙÙÙÙ symbol is not required at the

Name=

prompt.

To leave enter-name context without entering a list name, press

‘. The stat list editor switches to view-names context.

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STAT EDIT Menu

STAT EDIT Menu

To display the

STAT EDIT

menu, press ….

EDIT CALC TESTS

1: Edit...

2: SortA(

3: SortD(

4: ClrList

5: SetUpEditor

Displays the stat list editor.

Sorts a list in ascending order.

Sorts a list in descending order.

Deletes all elements of a list.

Stores lists in the stat list editor.

Note: Chapter 13: Inferential Statistics describes the

STAT TESTS menu items.

SortA(, SortD( SortA(

(sort ascending) sorts list elements from low to high values.

SortD(

(sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude

(modulus).

SortA(

and

SortD(

each can sort in either of two ways.

With one listname,

SortA(

and

SortD(

sort the elements in

listname and update the list in memory.

With two or more lists,

SortA(

and

SortD(

sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname.

This lets you sort two-variable data on

X

and keep the data pairs together. All lists must have the same dimension.

The sorted lists are updated in memory.

SortA(

listname

)

SortD(

listname

)

SortA(

keylistname

,

dependlist1[

,

dependlist2

,

...

,

dependlist n]

)

SortD(

keylistname

,

dependlist1[

,

dependlist2

,

...

,

dependlist n]

)

ClrList

Note: SortA( and SortD( are the same as SortA( and SortD( on the

LIST OPS menu.

ClrList

clears (deletes) from memory the elements of one or more listnames.

ClrList

also detaches any formula attached to a

listname.

ClrList

listname1

,

listname2

,

...

,

listname n

Note: To clear from memory all elements of all list names, use

ClrAllLists (Chapter 18).

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SetUpEditor

With

SetUpEditor

you can set up the stat list editor to display one or more listnames in the order that you specify. You can specify zero to 20 listnames.

SetUpEditor

[listname1

,

listname2

,

...

,

listname n]

SetUpEditor

with one to 20 listnames removes all list names from the stat list editor and then stores listnames in the stat list editor columns in the specified order, beginning in column

1

.

If you enter a listname that is not stored in memory already, then listname is created and stored in memory; it becomes an item on the

LIST NAMES

menu.

Restoring L

1 through L

6

to the

Stat List Editor

SetUpEditor

with no listnames removes all list names from the stat list editor and restores list names

L

1

through

L

6

in the stat list editor columns

1

through

6

.

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Regression Model Features

Regression

Model Features

Automatic

Residual List

STAT CALC

menu items

3

through

C

are regression models

(page 12.24). The automatic residual list and automatic regression equation features apply to all regression models.

Diagnostics display mode applies to some regression models.

When you execute a regression model, the automatic residual list feature computes and stores the residuals to the list name

RESID

.

RESID

becomes an item on the

LIST NAMES

menu

(Chapter 11).

Automatic

Regression

Equation

The TI-82 STATS uses the formula below to compute

RESID

list elements. The next section describes the variable

RegEQ

.

RESID

= Ylistname N

RegEQ

(Xlistname)

Each regression model has an optional argument, regequ, for which you can specify a

Y=

variable such as

Y

1

. Upon execution, the regression equation is stored automatically to the specified

Y= variable and the

Y=

function is selected.

Regardless of whether you specify a

Y=

variable for regequ, the regression equation always is stored to the TI-82 STATS variable

RegEQ

, which is item

1

on the

VARS Statistics EQ secondary menu.

Note: For the regression equation, you can use the fixed-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.

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Diagnostics

Display Mode

When you execute some regression models, the TI-82 STATS computes and stores diagnostics values for

r

(correlation coefficient) and

r

2

(coefficient of determination) or for

R

2

(coefficient of determination).

r

and

r

2

are computed and stored for these regression models.

LinReg(ax+b)

LinReg(a+bx)

LnReg

ExpReg

PwrReg

R

2

is computed and stored for these regression models.

QuadReg CubicReg QuartReg

The

r

and

r

2

that are computed for

LnReg

,

ExpReg

, and

PwrReg

are based on the linearly transformed data. For example, for

ExpReg

(y=ab^x),

r

and

r

2

are computed on ln y=ln a+x(ln b).

By default, these values are not displayed with the results of a regression model when you execute it. However, you can set the diagnostics display mode by executing the

DiagnosticOn

or

DiagnosticOff

instruction. Each instruction is in the

CATALOG

(Chapter 15).

Note: To set

DiagnosticOn or DiagnosticOff from the home screen, press y [

CATALOG

], and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press

Í to set the mode.

When

DiagnosticOn

is set, diagnostics are displayed with the results when you execute a regression model.

When

DiagnosticOff

is set, diagnostics are not displayed with the results when you execute a regression model.

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STAT CALC Menu

STAT CALC

Menu

Frequency of

Occurrence for

Data Points

To display the

STAT CALC

menu, press … ~.

EDIT CALC TESTS

1: 1-Var Stats

2: 2-Var Stats

3: Med-Med

4: LinReg(ax+b)

5: QuadReg

6: CubicReg

7: QuartReg

8: LinReg(a+bx)

9: LnReg

0: ExpReg

A: PwrReg

B: Logistic

C: SinReg

Calculates 1-variable statistics.

Calculates 2-variable statistics.

Calculates a median-median line.

Fits a linear model to data.

Fits a quadratic model to data.

Fits a cubic model to data.

Fits a quartic model to data.

Fits a linear model to data.

Fits a logarithmic model to data.

Fits an exponential model to data.

Fits a power model to data.

Fits a logistic model to data.

Fits a sinusoidal model to data.

For each

STAT CALC

menu item, if neither Xlistname nor

Ylistname is specified, then the default list names are

L

1

and

L

2

.

If you do not specify freqlist, then the default is

1

occurrence of each list element.

For most

STAT CALC

menu items, you can specify a list of data occurrences, or frequencies (freqlist).

Each element in freqlist indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing.

For example, if

L

1

={15,12,9,14}

and

ÙÙÙÙFREQ={1,4,1,3}

, then the

TI-82 STATS interprets the instruction

1.Var Stats L

1

,

ÙÙÙÙFREQ to mean that

15

occurs once,

12

occurs four times,

9

occurs once, and

14

occurs three times.

Each element in freqlist must be ‚ 0, and at least one element must be > 0.

Noninteger freqlist elements are valid. This is useful when entering frequencies expressed as percentages or parts that add up to 1. However, if freqlist contains noninteger frequencies,

Sx

and

Sy

are undefined; values are not displayed for

Sx

and

Sy

in the statistical results.

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1.Var Stats 1.Var Stats

(one-variable statistics) analyzes data with one measured variable. Each element in freqlist is the frequency of occurrence for each corresponding data point in Xlistname.

freqlist elements must be real numbers > 0.

1.Var Stats

[Xlistname

,

freqlist]

2.Var Stats

Med.Med

(ax+b)

2.Var Stats

(two-variable statistics) analyzes paired data.

Xlistname is the independent variable. Ylistname is the dependent variable. Each element in freqlist is the frequency of occurrence for each data pair (Xlistname,Ylistname).

2.Var Stats

[Xlistname

,

Ylistname

,

freqlist]

Med.Med

(median-median) fits the model equation y=ax+b to the data using the median-median line (resistant line) technique, calculating the summary points

x

1

,

y

1

,

x

2

,

y

2

,

x

3

, and

y

3

.

Med.Med

displays values for

a

(slope) and

b

(y-intercept).

Med.Med

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

LinReg

(ax+b)

QuadReg

(ax2+bx+c)

LinReg(ax+b)

(linear regression) fits the model equation y=ax+b to the data using a least-squares fit. It displays values for

a

(slope) and

b

(y-intercept); when

DiagnosticOn

is set, it also displays values for

r

2

and

r

.

LinReg(ax+b)

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

QuadReg

(quadratic regression) fits the second-degree polynomial y=ax and

c

; when

DiagnosticOn

is set, it also displays a value for

R

are required.

2

+bx+c to the data. It displays values for

a

,

b

,

For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points

2

.

QuadReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

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STAT CALC Menu

(continued)

CubicReg

(ax

3

+bx

2

+cx+d)

CubicReg

(cubic regression) fits the third-degree polynomial y=ax 3 +bx 2 +cx+d to the data. It displays values for

a

,

b

,

c

, and

d

; when

DiagnosticOn

is set, it also displays a value for

R

2

. For four points, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least four points are required.

CubicReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

QuartReg

(ax

4

+bx

3

+cx

2

+ dx+e)

LinReg

(a+bx)

LnReg

(a+b ln(x))

ExpReg

(ab x

)

QuartReg

(quartic regression) fits the fourth-degree polynomial y=ax 4 +bx 3 +cx 2 +dx+e to the data. It displays values for

a

,

b

,

c

,

d

, and

R

2 e

. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required.

; when

DiagnosticOn

is set, it also displays a value for

QuartReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

LinReg(a+bx)

(linear regression) fits the model equation y=a+bx to the data using a least-squares fit. It displays values for

a

(y-intercept) and

b

(slope); when

DiagnosticOn

is set, it also displays values for

r

2

and

r

.

LinReg(a+bx)

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

LnReg

(logarithmic regression) fits the model equation y=a+b ln(x) to the data using a least-squares fit and transformed values ln(x) and y. It displays values for

a

and

b

; when

DiagnosticOn

is set, it also displays values for

r

2

and

r

.

LnReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

ExpReg

(exponential regression) fits the model equation y=ab x

to the data using a least-squares fit and transformed values x and ln(y). It displays values for

a

and

b

; when

DiagnosticOn

is set, it also displays values for

r

2

and

r

.

ExpReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

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PwrReg

(ax b

)

Logistic c / (1+a

ääääe

Lbx )

SinReg a sin(bx+c)+d

PwrReg

(power regression) fits the model equation y=ax b to the data using a least-squares fit and transformed values ln(x) and ln(y). It displays values for

a

and

b

; when

DiagnosticOn

is set, it also displays values for

r

2

and

r

.

PwrReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

Logistic

fits the model equation y=c / (1+aäe

Lbx

) to the data using an iterative least-squares fit. It displays values for

a

,

b

, and

c

.

Logistic

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

SinReg

(sinusoidal regression) fits the model equation

y=a sin(bx+c)+d to the data using an iterative least-squares fit. It displays values for

a

,

b

,

c

, and

d

. At least four data points are required. At least two data points per cycle are required in order to avoid aliased frequency estimates.

SinReg

[iterations,Xlistname,Ylistname,period,regequ]

iterations is the maximum number of times the algorithm will iterate to find a solution. The value for iterations can be an integer ‚ 1 and  16; if not specified, the default is 3. The algorithm may find a solution before iterations is reached.

Typically, larger values for iterations result in longer execution times and better accuracy for

SinReg

, and vice versa.

A period guess is optional. If you do not specify period, the difference between time values in Xlistname must be equal and the time values must be ordered in ascending sequential order. If you specify period, the algorithm may find a solution more quickly, or it may find a solution when it would not have found one if you had omitted a value for period. If you specify period, the differences between time values in Xlistname can be unequal.

Note: The output of

SinReg is always in radians, regardless of the

Radian/Degree mode setting.

A

SinReg

example is shown on the next page.

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STAT CALC Menu

(continued)

SinReg Example:

Daylight Hours in

Alaska for One

Year

Compute the regression model for the number of hours of daylight in Alaska during one year.

&

&

1 period

With noisy data, you will achieve better convergence results when you specify an accurate estimate for period. You can obtain a period guess in either of two ways.

Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle.

Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles.

Then divide the total distance by N.

After your first attempt to use

SinReg

and the default value for

iterations to fit the data, you may find the fit to be approximately correct, but not optimal. For an optimal fit, execute

SinReg 16,

Xlistname

,

Ylistname

,2p /

b where b is the value obtained from the previous

SinReg

execution.

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Statistical Variables

The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press , and select

5:Statistics

. Then select the

VARS

menu shown in the column below under

VARS

menu. If you edit a list or change the type of analysis, all statistical variables are cleared.

Variables Other

mean of sum of values sum of

x

2

sample standard deviation of

x

population standard deviation of number of data points mean of

y

values sum of

y

values sum of

y

2

values sample standard deviation of

y x

population standard deviation of

y

sum of

x

y

minimum of

x

values maximum of

x

values minimum of

y

values maximum of

y

values

1st quartile median

x x

values

values

3rd quartile regression/fit coefficients polynomial,

Logistic

, and

SinReg

coefficients correlation coefficient coefficient of determination regression equation summary points (

Med.Med

only)

1.Var

Stats v

Gx

Gx

2

Sx sx n minX maxX

Q

1

Med

Q

3 sx n w

Gy

Gy

2

Sy sy

Gxy minX maxX minY maxY

2.Var

Stats v

Gx

Gx

2

Sx

RegEQ x1 y2 a

,

b a

,

b

,

c

,

d

,

e r r

2

,

R

2

,

y1

,

x2

,

,

x3

,

y3

VARS

menu

XY

G

G

XY

XY

XY

XY

G

G

XY

XY

XY

PTS

PTS

PTS

G

XY

XY

XY

EQ

EQ

EQ

EQ

EQ

PTS

Q

1

and Q

3

The first quartile (

Q

1

) is the median of points between

minX

and

Med

(median). The third quartile (

Q

3

) is the median of points between

Med

and

maxX

.

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Statistical Analysis in a Program

Entering Stat

Data

You can enter statistical data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11).

Statistical

Calculations

To perform a statistical calculation from a program, follow these steps.

1. On a blank line in the program editor, select the type of calculation from the

STAT CALC

menu.

2. Enter the names of the lists to use in the calculation. Separate the list names with a comma.

3. Enter a comma and then the name of a

Y=

variable, if you want to store the regression equation to a

Y=

variable.

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Statistical Plotting

Steps for Plotting

Statistical Data in

Lists

You can plot statistical data that is stored in lists. The six types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can define up to three plots.

To plot statistical data in lists, follow these steps.

1. Store the stat data in one or more lists.

2. Select or deselect

Y=

functions as appropriate.

3. Define the stat plot.

4. Turn on the plots you want to display.

5. Define the viewing window.

6. Display and explore the graph.

"

(Scatter)

Scatter

plots plot the data points from

Xlist

and

Ylist

as coordinate pairs, showing each point as a box (

), cross (

+

), or dot (

¦

).

Xlist

and

Ylist

must be the same length. You can use the same list for

Xlist

and

Ylist

.

Ó

(xyLine) xyLine

is a scatter plot in which the data points are plotted and connected in order of appearance in

Xlist

and

Ylist

. You may want to use

SortA(

or

SortD(

to sort the lists before you plot them (page 12.20).

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Statistical Plotting

(continued)

Ò

(Histogram)

Histogram

plots one-variable data. The

Xscl

window variable value determines the width of each bar, beginning at

Xmin

.

ZoomStat

adjusts

Xmin

,

Xmax

,

Ymin

, and

Ymax

to include all values, and also adjusts

Xscl

. The inequality

(

Xmax

N

Xmin

) à

Xscl

 47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right.

Õ

(ModBoxplot)

ModBoxplot

(modified box plot) plots one-variable data, like the regular box plot, except points that are 1.5 ääää Interquartile

Range beyond the quartiles. (The Interquartile Range is defined as the difference between the third quartile

Q

3

and the first quartile

Q

1

.) These points are plotted individually beyond the whisker, using the

Mark

(

or

+

or

¦

) you select. You can trace these points, which are called outliers.

The prompt for outlier points is

x=

, except when the outlier is the maximum point (

maxX

) or the minimum point (

minX

).

When outliers exist, the end of each whisker will display

x=

.

When no outliers exist,

minX

and

maxX

are the prompts for the end of each whisker.

Q

1

,

Med

(median), and

Q

3

define the box

(page 12.29).

Box plots are plotted with respect to

Xmin

and

Xmax

, but ignore

Ymin

and

Ymax

. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.

When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.

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Ö

(Boxplot)

Boxplot

(regular box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set

(

minX

) to the first quartile (

Q

1

) and from the third quartile (

Q

3

) to the maximum point (

maxX

). The box is defined by

Q

1

,

Med

(median), and

Q

3

(page 12.29).

Box plots are plotted with respect to

Xmin

and

Xmax

, but ignore

Ymin

and

Ymax

. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.

When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.

Ô

(NormProbPlot)

NormProbPlot

(normal probability plot) plots each observation

X

in

Data List

versus the corresponding quantile

z

of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal.

Enter a valid list name in the

Data List

field. Select

X

or

Y

for the

Data Axis

setting.

If you select

X

, the TI-82 STATS plots the data on the x-axis and the z-values on the y-axis.

If you select

Y

, the TI-82 STATS plots the data on the y-axis and the z-values on the x-axis.

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Statistical Plotting

(continued)

Defining the

Plots

To define a plot, follow these steps.

1. Press y [

STAT PLOT

]. The

STAT PLOTS

menu is displayed with the current plot definitions.

2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected.

3. Press Í to select

On

if you want to plot the statistical data immediately. The definition is stored whether you select

On

or

Off

.

4. Select the type of plot. Each type prompts for the options checked in this table.

Plot Type

XList YList Mark Freq Data

List

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

Data

Axis

œ

œ

œ

œ

œ

5. Enter list names or select options for the plot type.

Xlist

(list name containing independent data)

Ylist

(list name containing dependent data)

Mark

(

or

+

or

¦

)

Freq

(frequency list for

Xlist

elements; default is

1

)

Data List

(list name for

NormProbPlot

)

Data Axis

(axis on which to plot

Data List

)

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Displaying Other

Stat Plot Editors

Each stat plot has a unique stat plot editor. The name of the current stat plot (

Plot1

,

Plot2

, or

Plot3

) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press }, ~, and | to move the cursor onto the name in the top line, and then press Í. The stat plot editor for the selected plot is displayed, and the selected name remains highlighted.

Turning On and

Turning Off Stat

Plots

PlotsOn

and

PlotsOff

allow you to turn on or turn off stat plots from the home screen or a program. With no plot number,

PlotsOn

turns on all plots and

PlotsOff

turns off all plots. With one or more plot numbers (

1

,

2

, and

3

),

PlotsOn

turns on specified plots, and

PlotsOff

turns off specified plots.

PlotsOff

[

1,2,3

]

PlotsOn

[

1,2,3

]

Note: You also can turn on and turn off stat plots in the top line of the

Y= editor (Chapter 3).

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Statistical Plotting

(continued)

Defining the

Viewing Window

Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables.

ZoomStat

redefines the viewing window to display all statistical data points.

Tracing a Stat

Plot

When you trace a scatter plot or xyLine, tracing begins at the first element in the lists.

When you trace a histogram, the cursor moves from the top center of one column to the top center of the next, starting at the first column.

When you trace a box plot, tracing begins at

Med

(the median).

Press | to trace to

Q

1

and

minX

. Press ~ to trace to

Q

3

and

maxX

.

When you press } or † to move to another plot or to another

Y= function, tracing moves to the current or beginning point on that plot (not the nearest pixel).

The

ExprOn

/

ExprOff

format setting applies to stat plots

(Chapter 3).When

ExprOn

is selected, the plot number and plotted data lists are displayed in the top-left corner.

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Statistical Plotting in a Program

Defining a Stat

Plot in a Program

To display a stat plot from a program, define the plot, and then display the graph.

To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps.

1. Press y [

STAT PLOT

] to display the

STAT PLOTS

menu.

2. Select the plot to define, which pastes

Plot1(

,

Plot2(

, or

Plot3(

to the cursor location.

3. Press y [

STAT PLOT

] ~ to display the

STAT TYPE

menu.

4. Select the type of plot, which pastes the name of the plot type to the cursor location.

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Statistical Plotting in a Program

(continued)

Defining a Stat

Plot in a Program

(continued)

5. Press ¢. Enter the list names, separated by commas.

6. Press ¢ y [

STAT PLOT

] | to display the

STAT PLOT MARK

menu. (This step is not necessary if you selected

3:Histogram

or

5:Boxplot

in step 4.)

Select the type of mark (

or

+

or

¦

) for each data point. The selected mark symbol is pasted to the cursor location.

7. Press ¤ Í to complete the command line.

Displaying a Stat

Plot from a

Program

To display a plot from a program, use the

DispGraph

instruction

(Chapter 16) or any of the

ZOOM

instructions (Chapter 3).

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13

Inferential Statistics and Distributions

Contents

Getting Started: Mean Height of a Population

.....................................

Inferential Stat Editors

.........................................................................................

STAT TESTS Menu

.............................................................................................

9

Inferential Statistics Input Descriptions

...................................................

26

2

6

Test and Interval Output Variables

..............................................................

28

Distribution Functions

.........................................................................................

29

Distribution Shading

.............................................................................................

35

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Getting Started: Mean Height of a Population

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean. The 10 height values below are the first 10 of 90 values, randomly generated from a normally distributed population with an assumed mean of 165.1 cm.

and a standard deviation of 6.35 cm. (

randNorm(165.1,6.35,90)

with a seed of 789).

Height (in cm.) of Each of 10 Women

169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53

1. Press … Í to display the stat list editor.

Press } to move the cursor onto

L

1

, and then press y [

INS

]. The

Name=

prompt is displayed on the bottom line. The

Ø cursor indicates that alpha-lock is on. The existing list name columns shift to the right.

Note: Your stat editor may not look like the one pictured here, depending on the lists you have already stored.

2. Enter [

H

] [

G

] [

H

] [

T

] at the

Name=

prompt, and then press Í. The list to which you will store the women’s height data is created.

Press † to move the cursor onto the first row of the list.

HGHT(1)=

is displayed on the bottom line.

3. Press

169

Ë

43

to enter the first height value.

As you enter it, it is displayed on the bottom line.

Press Í. The value is displayed in the first row, and the rectangular cursor moves to the next row.

Enter the other nine height values the same way.

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4. Press … | to display the

STAT TESTS menu, and then press † until

8:TInterval

is highlighted.

5. Press Í to select

8:TInterval

. The inferential stat editor for

TInterval

is displayed. If

Data

is not selected for

Inpt:

, press | Í to select

Data

.

Press † and [

H

] [

G

] [

H

] [

T

] at the

List:

prompt

(alpha-lock is on).

Press † † Ë

99

to enter a 99 percent confidence level at the

C.Level:

prompt.

6. Press † to move the cursor onto

Calculate

, and then press Í. The confidence interval is calculated, and the

TInterval

results are displayed on the home screen.

Interpret the results.

The first line,

(159.74,173.94)

, shows that the 99 percent confidence interval for the population mean is between about 159.74 cm. and 173.94 cm. This is about a 14.2

cm. spread.

The .99 confidence level indicates that in a very large number of samples, we expect

99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 cm. (introduction; page 13.2), which is in the calculated interval.

The second line gives the mean height of the sample þ used to compute this interval.

The third line gives the sample standard deviation

Sx

. The bottom line gives the sample size

n

.

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Getting Started: Mean Height of a Population

(cont.)

To obtain a more precise bound on the population mean

m

of women’s heights, increase the sample size to 90. Use a sample mean þ of 163.8 and sample standard deviation

Sx

of 7.1 calculated from the larger random sample (introduction; page

13.2). This time, use the

Stats

(summary statistics) input option.

7. Press … |

8

to display the inferential stat editor for

TInterval

.

Press ~ Í to select

Inpt:Stats

. The editor changes so that you can enter summary statistics as input.

8. Press †

163

Ë

8

Í to store 163.8 to þ .

Press

7

Ë

1

Í to store 7.1 to

Sx

.

Press

90

Í to store 90 to

n

.

9. Press † to move the cursor onto

Calculate

, and then press Í to calculate the new 99 percent confidence interval. The results are displayed on the home screen.

If the height distribution among a population of women is normally distributed with a mean

m

of 165.1 cm. and a standard deviation σσσσ of 6.35 cm., what height is exceeded by only 5 percent of the women (the 95th percentile)?

10. Press ‘ to clear the home screen.

Press y [

DISTR

] to display the

DISTR

(distributions) menu.

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11. Press

3

to paste

invNorm(

to the home screen.

Press Ë

95

¢

165

Ë

1

¢

6

Ë

35

¤ Í.

.95

is the area,

165.1

is µµµµ , and

6.35

is σσσσ .

The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 cm.

Now graph and shade the top 5 percent of the population.

12. Press p and set the window variables to these values.

Xmin=145

Xmax=185

Xscl=5

Ymin=L.02

Ymax=.08

Yscl=0

Xres=1

13. Press y [

DISTR

] ~ to display the

DISTR

DRAW

menu.

14. Press Í to paste

ShadeNorm(

to the home screen.

Press y [

ANS

] ¢

1

y [

EE

]

99

¢

165

Ë

1

¢

6

Ë

35

¤.

Ans

(175.5448205 from step 11) is the lower bound. 1å99 is the upper bound. The normal curve is defined by a mean µµµµ of 165.1 and a standard deviation σσσσ of 6.35.

15. Press Í to plot and shade the normal curve.

Area

is the area above the 95th percentile.

low

is the lower bound.

up

is the upper bound.

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Inferential Stat Editors

Displaying the

Inferential Stat

Editors

When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or interval’s input requirements. Below is the inferential stat editor for

T.Test

.

Using an

Inferential Stat

Editor

Note: When you select the

ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen.

To use an inferential stat editor, follow these steps.

1. Select a hypothesis test or confidence interval from the

STAT

TESTS

menu. The appropriate editor is displayed.

2. Select

Data

or

Stats

input, if the selection is available. The appropriate editor is displayed.

3. Enter real numbers, list names, or expressions for each argument in the editor.

4. Select the alternative hypothesis (

ƒ

,

<

, or

>

) against which to test, if the selection is available.

5. Select

No

or

Yes

for the

Pooled

option, if the selection is available.

6. Select

Calculate

or

Draw

(when

Draw

is available) to execute the instruction.

When you select

Calculate

, the results are displayed on the home screen.

When you select

Draw

, the results are displayed in a graph.

This chapter describes the selections in the above steps for each hypothesis test and confidence interval instruction.

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Select

Data

or

Stats

input

Select an alternative hypothesis

Enter values for arguments

Select or

Calculate

Draw

output

Selecting Data or

Stats

Most inferential stat editors prompt you to select one of two types of input. (

1.PropZInt

and

2.PropZTest

,

1.PropZInt

and

2.PropZInt

,

c

2

.Test

, and

LinRegTTest

do not.)

Select

Data

to enter the data lists as input.

Select

Stats

to enter summary statistics, such as

þ

,

Sx

, and

n

, as input.

To select

Data

or

Stats

, move the cursor to either

Data

or

Stats

, and then press Í.

Entering the

Values for

Arguments

Selecting an

Alternative

Hypothesis

(ƒ < >)

Inferential stat editors require a value for every argument. If you do not know what a particular argument symbol represents, see the tables on pages 13.26 and 13.27.

When you enter values in any inferential stat editor, the

TI-82 STATS stores them in memory so that you can run many tests or intervals without having to reenter every value.

Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses.

The first is a

ƒ

alternative hypothesis, such as

mƒm

0

for the

Z.Test

.

The second is a

<

alternative hypothesis, such as

m1<m2

for the

2.SampTTest

.

The third is a

>

alternative hypothesis, such as

p1>p2

for the

2.PropZTest

.

To select an alternative hypothesis, move the cursor to the appropriate alternative, and then press Í.

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Inferential Stat Editors

(continued)

Selecting the

Pooled Option

Pooled

(

2.SampTTest

and

2.SampTInt

only) specifies whether the variances are to be pooled for the calculation.

Select

No

if you do not want the variances pooled.

Population variances can be unequal.

Select

Yes

if you want the variances pooled. Population variances are assumed to be equal.

To select the

Pooled

option, move the cursor to

Yes

, and then press Í.

Selecting

Calculate or

Draw for a

Hypothesis Test

After you have entered all arguments in an inferential stat editor for a hypothesis test, you must select whether you want to see the calculated results on the home screen (

Calculate

) or on the graph screen (

Draw

).

Calculate

calculates the test results and displays the outputs on the home screen.

Draw

draws a graph of the test results and displays the test statistic and p-value with the graph. The window variables are adjusted automatically to fit the graph.

To select

Calculate

or

Draw

, move the cursor to either

Calculate

or

Draw

, and then press Í. The instruction is immediately executed.

Selecting

Calculate for a

Confidence

Interval

Bypassing the

Inferential Stat

Editors

After you have entered all arguments in an inferential stat editor for a confidence interval, select

Calculate

to display the results.

The

Draw

option is not available.

When you press Í,

Calculate

calculates the confidence interval results and displays the outputs on the home screen.

To paste a hypothesis test or confidence interval instruction to the home screen without displaying the corresponding inferential stat editor, select the instruction you want from the

CATALOG

menu. Appendix A describes the input syntax for each hypothesis test and confidence interval instruction.

Note: You can paste a hypothesis test or confidence interval instruction to a command line in a program. From within the program editor, select the instruction from either the

CATALOG (Chapter 15) or the STAT TESTS menu.

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STAT TESTS Menu

STAT TESTS

Menu

Inferential Stat

Editors for the

STAT TESTS

Instructions

To display the

STAT TESTS

menu, press … |. When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed.

Most

STAT TESTS

instructions store some output variables to memory. Most of these output variables are in the

TEST secondary menu (

VARS

menu;

5:Statistics

). For a list of these variables, see page 13.28.

EDIT CALC TESTS

1: Z-Test...

2: T-Test...

3: 2-SampZTest...

4: 2-SampTTest...

5: 1-PropZTest...

6: 2-PropZTest...

7: ZInterval...

8: TInterval...

9: 2-SampZInt...

0: 2-SampTInt...

A: 1-PropZInt...

B: 2-PropZInt...

C: c2-Test...

D: 2-SampÛ

E: LinRegTTest...

F: ANOVA(

Test for 1 m, known s

Test for 1 m, unknown s

Test comparing 2 m’s, known s’s

Test comparing 2 m’s, unknown s’s

Test for 1 proportion

Test comparing 2 proportions

Confidence interval for 1 m, known s

Confidence interval for 1 m, unknown s

Conf. int. for diff. of 2 m’s, known s’s

Conf. int. for diff. of 2 m’s, unknown s’s

Confidence int. for 1 proportion

Confidence int. for diff. of 2 props

Chi-square test for 2-way tables

Test comparing 2 s’s

t test for regression slope and r

One-way analysis of variance

Note: When a new test or interval is computed, all previous output variables are invalidated.

In this chapter, the description of each

STAT TESTS

instruction shows the unique inferential stat editor for that instruction with example arguments.

Descriptions of instructions that offer the

Data

/

Stats

input choice show both types of input screens.

Descriptions of instructions that do not offer the

Data

/

Stats

input choice show only one input screen.

The description then shows the unique output screen for that instruction with the example results.

Descriptions of instructions that offer the

Calculate

/

Draw

output choice show both types of screens: calculated and graphic results.

Descriptions of instructions that offer only the

Calculate

output choice show the calculated results on the home screen.

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STAT TESTS Menu

(continued)

Z.Test

Z.Test

(one-sample z test; item

1

) performs a hypothesis test for a single unknown population mean

m

when the population standard deviation

H s

is known. It tests the null hypothesis

0

: m=m

0

against one of the alternatives below.

H a

: mƒm

0

(

m:ƒm

0

)

H a

: m<m

0

(

m:<m

0

)

H a

: m>m

0

(

m:>m

0

)

In the example:

L

1

={299.4 297.7 301 298.9 300.2 297}

Data Stats

Input:

, ,

Calculated results:

, ,

Drawn results:

Note: All examples on pages13.10 through 13.25 assume a fixeddecimal mode setting of

4 (Chapter 1). If you set the decimal mode to

Float or a different fixed-decimal setting, your output may differ from the output in the examples.

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T.Test

Input:

T.Test

(one-sample t test; item

2

) performs a hypothesis test for a single unknown population mean

m

when the population standard deviation s is unknown. It tests the null hypothesis

H

0

: m=m

0

against one of the alternatives below.

H a

: mƒm

0

(

m:ƒm

0

)

H a

: m<m

0

(

m:<m

0

)

H a

: m>m

0

(

m:>m

0

)

In the example:

TEST={91.9 97.8 111.4 122.3 105.4 95}

Data Stats

, ,

Calculated results:

, ,

Drawn results:

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STAT TESTS Menu

(continued)

2.SampZTest

2.SampZTest

(two-sample z test; item

3

) tests the equality of the means of two populations (m

1

and m

2

0

: m

1

=m

) based on independent samples when both population standard deviations (s are known. The null hypothesis H of the alternatives below.

1

and s

2

)

2

is tested against one

H a

: m

1

ƒm

2

(

m1:ƒm2

)

H a

: m

1

<m

H a

: m

1

>m

2

2

(

m1:<m2

)

(

m1:>m2

)

In the example:

LISTA={154 109 137 115 140}

LISTB={108 115 126 92 146}

Data Stats

Input:

, ,

Calculated results:

, ,

Drawn results:

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2.SampTTest

2.SampTTest

(two-sample t test; item

4

) tests the equality of the means of two populations (m samples when neither population standard deviation (s known. The null hypothesis H the alternatives below.

1

and m

2

) based on independent

0

: m

1

=m

1

or s

2

) is

2

is tested against one of

H a

: m

1

ƒm

2

(

m1:ƒm2

)

H a

: m

1

<m

H a

: m

1

>m

2

2

(

m1:<m2

)

(

m1:>m2

)

In the example:

SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}

SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}

Data Stats

Input:

, ,

Calculated results:

, ,

Drawn results:

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STAT TESTS Menu

(continued)

1.PropZTest

1.PropZTest

(one-proportion z test; item

5

) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n.

1.PropZTest

tests the null hypothesis

H

0

: prop=p

0

against one of the alternatives below.

H a

: propƒp

H a

: prop<p

H a

: prop>p

0

(

prop:ƒp

0

)

0

(

prop:<p

0

)

0

(

prop:>p

0

)

Input:

,

Calculated results:

,

Drawn results:

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2.PropZTest

2.PropZTest

(two-proportion z test; item

6

) computes a test to compare the proportion of successes (p

1

and p

2

) from two populations. It takes as input the count of successes in each sample (x

1 and x

2

(n

1

and n

2

).

) and the count of observations in each sample

2.PropZTest

tests the null hypothesis H

0

: p

1

=p

(using the pooled sample proportion Ç) against one of the alternatives below.

2

H a

: p

1

ƒp

2

(

p1:ƒp2

)

H a

: p

1

<p

H a

: p

1

>p

2

(

p1:<p2

)

2

(

p1:>p2

)

Input:

,

Calculated results:

,

Drawn results:

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STAT TESTS Menu

(continued)

ZInterval ZInterval

(one-sample z confidence interval; item

7

) computes a confidence interval for an unknown population mean m when the population standard deviation s

is known. The computed confidence interval depends on the user-specified confidence level.

In the example:

L

1

={299.4 297.7 301 298.9 300.2 297}

Data Stats

Input:

, ,

Calculated results:

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TInterval

Input:

TInterval

(one-sample t confidence interval; item

8

) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level.

In the example:

L

6

={1.6 1.7 1.8 1.9}

Data Stats

, ,

Calculated results:

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STAT TESTS Menu

(continued)

2.SampZInt

2.SampZInt

(two-sample z confidence interval; item

9

) computes a confidence interval for the difference between two population means (m deviations ( s

1

and s

2

1

Nm

2

) when both population standard

) are known. The computed confidence interval depends on the user-specified confidence level.

In the example:

LISTC={154 109 137 115 140}

LISTD={108 115 126 92 146}

Data Stats

Input:

, ,

Calculated results:

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2.SampTInt

2.SampTInt

(two-sample t confidence interval; item

0

) computes a confidence interval for the difference between two population means (m deviations ( s

1

and s

2

1

Nm

2

) when both population standard

) are unknown. The computed confidence interval depends on the user-specified confidence level.

In the example:

SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}

SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}

Data Stats

Input:

, ,

Calculated results:

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STAT TESTS Menu

(continued)

1.PropZInt

1.PropZInt

(one-proportion z confidence interval; item

A

) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample

x and the count of observations in the sample n. The computed confidence interval depends on the user-specified confidence level.

Input:

,

Calculated results:

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2.PropZInt

2.PropZInt

(two-proportion z confidence interval; item

B

) computes a confidence interval for the difference between the proportion of successes in two populations (p input the count of successes in each sample (x count of observations in each sample (n

1

1

Np

2

). It takes as

and n

1

2

and x

). The computed confidence interval depends on the user-specified confidence level.

2

) and the

Input:

,

Calculated results:

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STAT TESTS Menu

(continued) c

2

.Test

Matrix editor:

c

2

.Test

(chi-square test; item

C

) computes a chi-square test for association on the two-way table of counts in the specified

Observed matrix. The null hypothesis H

0

for a two-way table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related.

Before computing a c 2

.Test, enter the observed counts in a matrix. Enter that matrix variable name at the

Observed:

prompt in the c 2

.Test editor; default=

[A]

. At the

Expected:

prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=

[B]

.

Note: Press

 ~ ~ 1 to select 1:[A] from the MATRX

EDIT menu.

Input:

,

Note: Press

[B] Í to display matrix [B].

Calculated results:

,

Drawn results:

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Input:

(two-sample Û-test; item

D

) computes an Û-test to compare two normal population standard deviations (s

1

and s

2

).

The population means and standard deviations are all unknown.

2.SampÜ

Sx1

2

/Sx2

2

, which uses the ratio of sample variances

, tests the null hypothesis H

0 alternatives below.

: s

1

=s

2

against one of the

H a

: s

1

ƒs

2

(

s1:ƒs2

)

H a

: s

1

<s

2

(

s1:<s2

)

H a

: s

1

>s

2

(

s1:>s2

)

In the example:

SAMP4={ 7 L4 18 17 L3 L5 1 10 11 L2}

SAMP5={ L1 12 L1 L3 3 L5 5 2 L11 L1 L3}

Data Stats

, ,

Calculated results:

, ,

Drawn results:

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STAT TESTS Menu

(continued)

LinRegTTest LinRegTTest

(linear regression t test; item

E

) computes a linear regression on the given data and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H of the alternatives below.

0

: b=0 (equivalently, r

=0) against one

H a

: bƒ0 and rƒ0 (

b & r:ƒ0

)

H a

: b<0 and r<0 (

b & r:<0

)

H a

: b>0 and r>0 (

b & r:>0

)

The regression equation is automatically stored to

RegEQ

(

VARS Statistics EQ

secondary menu). If you enter a

Y=

variable name at the

RegEQ:

prompt, the calculated regression equation is automatically stored to the specified

Y=

equation. In the example below, the regression equation is stored to

Y

1

, which is then selected (turned on).

In the example:

L

3

={38 56 59 64 74}

L

4

={41 63 70 72 84}

Input:

,

Calculated results:

When

LinRegTTest

is executed, the list of residuals is created and stored to the list name

RESID

automatically.

RESID

is placed on the

LIST NAMES

menu.

Note: For the regression equation, you can use the fix -decimal mode setting to control the number of digits stored after the decimal point

(Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.

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ANOVA( ANOVA(

(one-way analysis of variance; item

F

) computes a oneway analysis of variance for comparing the means of two to 20 populations. The

ANOVA

procedure for comparing these means involves analysis of the variation in the sample data. The null hypothesis H not all m

1

...m

0 k

: m

1

=m

2

=...=m are equal.

k

is tested against the alternative H a

:

ANOVA(

list1

,

list2[

,

...

,

list20]

)

In the example:

L

1

={7 4 6 6 5}

L

2

={6 5 5 8 7}

L

3

={4 7 6 7 6}

Input:

,

Calculated results:

Note:

SS is sum of squares and MS is mean square.

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Inferential Statistics Input Descriptions

The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter.

Input m

0 s

List

Freq

Calculate v

,

Sx

,

n s1 s2

List1

Freq1 v1

,

Sx2

/

Draw

,

List2

,

Freq2

Sx1

,

n2

Pooled

,

n1

,

v2

,

Description

Hypothesized value of the population mean that you are testing.

The known population standard deviation; must be a real number > 0.

The name of the list containing the data you are testing.

The name of the list containing the frequency values for the data in

List

. Default=1. All elements must be integers | 0.

Determines the type of output to generate for tests and intervals.

Calculate

displays the output on the home screen. In tests,

Draw

draws a graph of the results.

Summary statistics (mean, standard deviation, and sample size) for the one-sample tests and intervals.

The known population standard deviation from the first population for the two-sample tests and intervals. Must be a real number > 0.

The known population standard deviation from the second population for the two-sample tests and intervals. Must be a real number > 0.

The names of the lists containing the data you are testing for the two-sample tests and intervals. Defaults are

L

1

and

L

2

, respectively.

The names of the lists containing the frequencies for the data in

List1

and

List2

for the two-sample tests and intervals.

Defaults=1. All elements must be integers | 0.

Summary statistics (mean, standard deviation, and sample size) for sample one and sample two in the two-sample tests and intervals.

Specifies whether variances are to be pooled for

2.SampTTest

and

2.SampTInt

.

No

instructs the TI-82 STATS not to pool the variances.

Yes

instructs the TI-82 STATS to pool the variances.

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Input p

0

x n x1 x2 n1 n2

C.Level

Observed (Matrix)

Expected (Matrix)

Xlist

,

Ylist

RegEQ

Description

The expected sample proportion for

1.PropZTest

. Must be a real number, such that 0 < p

0

< 1.

The count of successes in the sample for the

1.PropZTest

and

1.PropZInt

. Must be an integer ‚ 0.

The count of observations in the sample for the

1.PropZTest

and

1.PropZInt

. Must be an integer > 0.

The count of successes from sample one for the

2.PropZTest

and

2.PropZInt

. Must be an integer ‚ 0.

The count of successes from sample two for the

2.PropZTest

and

2.PropZInt

. Must be an integer ‚ 0.

The count of observations in sample one for the

2.PropZTest

and

2.PropZInt

. Must be an integer > 0.

The count of observations in sample two for the

2.PropZTest

and

2.PropZInt

. Must be an integer > 0.

The confidence level for the interval instructions. Must be ‚ 0 and <100. If it is ‚ 1, it is assumed to be given as a percent and is divided by 100. Default=0.95.

The matrix name that represents the columns and rows for the observed values of a two-way table of counts for the

Observed

be at least 2×2.

c

2

.Test

.

must contain all integers ‚ 0. Matrix dimensions must

The matrix name that specifies where the expected values should be stored.

Expected

is created upon successful completion of the c 2

.

Test

.

The names of the lists containing the data for

LinRegTTest

.

Defaults are

L

1

and

L

2

, respectively. The dimensions of

Xlist

and

Ylist

must be the same.

The prompt for the name of the

Y= variable where the calculated regression equation is to be stored. If a

Y= variable is specified, that equation is automatically selected (turned on). The default is to store the regression equation to the

RegEQ

variable only.

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Test and Interval Output Variables

The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press ,

5

(

5:Statistics

), and then select the

VARS

menu listed in the last column below.

Variables

p-value test statistics degrees of freedom sample mean of x values for sample

1 and sample 2 sample standard deviation of x for sample 1 and sample 2 number of data points for sample 1 and sample 2 pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for population 2 confidence interval pair

Tests Intervals p z

,

t

,

c

2

, Ü

df

Sx1,

Sx2

SxP df v1

,

v2 v1

,

v2

Sx1

Sx2

SxP

,

n1

,

n2 n1

,

n2

LinRegTTest,

ANOVA p t

, Ü

df

SxP

TEST

TEST

TEST

TEST

TEST

TEST

TEST mean of x values sample standard deviation of x number of data points standard error about the line regression/fit coefficients correlation coefficient coefficient of determination regression equation

v

Sx n lower upper

,

v

Sx n s a

,

b r r

2

RegEQ

VARS

Menu

TEST

TEST

TEST

TEST

EQ

EQ

EQ

EQ

XY

XY

XY

TEST

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Distribution Functions

DISTR menu normalpdf(

To display the

DISTR

menu, press y [

DISTR

].

DISTR DRAW

1: normalpdf(

2: normalcdf(

3: invNorm(

4: tpdf(

5: tcdf(

6: c

2 pdf(

7: c

2 cdf

8: Üpdf(

9: Ücdf(

0: binompdf(

A: binomcdf(

B: poissonpdf(

C: poissoncdf(

D: geometpdf(

E: geometcdf(

Normal probability density

Normal distribution probability

Inverse cumulative normal distribution

Student-t probability density

Student-t distribution probability

Chi-square probability density

Chi-square distribution probability

Û probability density

Û distribution probability

Binomial probability

Binomial cumulative density

Poisson probability

Poisson cumulative density

Geometric probability

Geometric cumulative density

Note: L1å99 and 1å99 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L1å99.

norwmalpdf(

computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean m

=0 and standard deviation s

=1. To plot the normal distribution, paste

normalpdf(

to the

Y=

editor. The probability density function (pdf) is:

f x

=

1

2

π σ

e

( x

2

σ

µ

2

)

2

,

σ >

0

normalpdf(

x[

,

m

,

s]

)

Note: For this example,

Xmin = 28

Xmax = 42

Ymin = 0

Ymax = .25

Tip: For plotting the normal distribution, you can set window variables

Xmin and Xmax so that the mean m falls between them, and then select 0:ZoomFit from the ZOOM menu.

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Distribution Functions

(continued) normalcdf( normalcdf(

computes the normal distribution probability between lowerbound and upperbound for the specified mean and standard deviation and s

=1.

s

. The defaults are m

=0 m

normalcdf(

lowerbound

,

upperbound[

,

m

,

s

]

) invNorm( invNorm(

computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m

and standard deviation value associated with an area to the left of the x value.

0  area  1 must be true. The defaults are m s

. It calculates the x

=0 and s

=1.

invNorm(

area[

,

m

,

s

]

) tpdf( tpdf(

computes the probability density function (pdf) for the

Student-t distribution at a specified x value. df (degrees of freedom) must be >0. To plot the Student-t distribution, paste

tpdf(

to the

Y=

editor. The probability density function (pdf) is:

=

Γ

[(

df

Γ

(

df

+

/

2 )

/

( 1

+

/

)

(

df

+

π

df

tpdf(

x

,

df

)

Note: For this example,

Xmin = L4.5

Xmax = 4.5

Ymin = 0

Ymax = .4

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tcdf( c

2 pdf( tcdf(

computes the Student-t distribution probability between

lowerbound and upperbound for the specified df (degrees of freedom), which must be > 0.

tcdf(

lowerbound

,

upperbound

,

df

)

c

2 pdf(

computes the probability density function (pdf) for the c 2

(chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c 2 paste c

(pdf) is:

2 pdf(

to the

Y=

distribution,

editor. The probability density function

=

1

Γ

(

df /

2 )

c

2 pdf(

x

,

df

)

(1/2)

df /

2

x df /

2

1

e

x /

2

, x

0

Note: For this example,

Xmin = 0

Xmax = 30

Ymin = L.02

Ymax = .132

c

2 cdf( c

2 cdf(

computes the c 2 (chi-square) distribution probability between lowerbound and upperbound for the specified df

(degrees of freedom), which must be an integer > 0.

c

2 cdf(

lowerbound

,

upperbound

,

df

)

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Distribution Functions

(continued)

computes the probability density function (pdf) for the Û distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the Û distribution, paste Ü density function (pdf) is:

to the

Y=

editor. The probability

=

Γ

[(

Γ

(

n /

2

Γ

d /

2 )



n d

n



/

2

x n /

( 1

+

)

(

n

+

d

)

/

2

, x

0 where n = numerator degrees of freedom

d = denominator degrees of freedom

x

,

numerator df

,

denominator df

)

Note: For this example,

Xmin = 0

Xmax = 5

Ymin = 0

Ymax = 1

computes the Û distribution probability between

lowerbound and upperbound for the specified numerator df

(degrees of freedom) and denominator df. numerator df and

denominator df must be integers >0.

lowerbound

,

upperbound

,

numerator df

,

denominator df

)

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binompdf( binompdf(

computes a probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be an integer or a list of integers.

0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 to numtrials is returned. The probability density function (pdf) is:

=

n

x p x

( 1

p

)

n

x

, x

=

n

where

n = numtrials

binompdf(

numtrials

,

p[

,

x ]

) binomcdf( binomcdf(

computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be a real number or a list of real numbers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of cumulative probabilities is returned.

binomcdf(

numtrials

,

p[

,

x ]

) poissonpdf( poissonpdf(

computes a probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be an integer or a list of integers. The probability density function (pdf) is:

f x

=

e

− µ

µ

x

/ x x

=

poissonpdf(

m

,

x

)

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Distribution Functions

(continued) poissoncdf( poissoncdf(

computes a cumulative probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be a real number or a list of real numbers.

poissoncdf(

m

,

x

) geometpdf( geometpdf(

computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0p1 must be true. x can be an integer or a list of integers. The probability density function (pdf) is:

f x

=

p

( 1

p

)

x

1

, x

=

geometpdf(

p

,

x

) geometcdf( geometcdf(

computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success

p. 0p1 must be true. x can be a real number or a list of real numbers.

geometcdf(

p

,

x

)

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Distribution Shading

DISTR DRAW

Menu

ShadeNorm(

To display the

DISTR DRAW

menu, press y [

DISTR

] ~.

DISTR DRAW

instructions draw various types of density functions, shade the area specified by lowerbound and

upperbound, and display the computed area value.

To clear the drawings, select

1:ClrDraw

from the

DRAW

menu

(Chapter 8).

Note: Before you execute a

DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen.

DISTR DRA

W

1: ShadeNorm(

2: Shade_t(

3: Shadec

4: ShadeÛ

2

(

Shades normal distribution.

Shades Student-t distribution.

Shades c 2 distribution.

Shades Û distribution.

Note: L1å99 and 1å99 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L1å99.

ShadeNorm(

draws the normal density function specified by mean m and standard deviation s and shades the area between

lowerbound and upperbound. The defaults are m =0 and s =1.

ShadeNorm(

lowerbound

,

upperbound[

,

m

,

s]

)

Note: For this example,

Xmin = 55

Xmax = 72

Ymin = L.05

Ymax = .2

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Distribution Shading

(continued)

Shade_t( Shade_t(

draws the density function for the Student-t distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound.

Shade_t(

lowerbound

,

upperbound

,

df

)

Note: For this example,

Xmin = L3

Xmax = 3

Ymin = L.15

Ymax = .5

Shadec

2

( Shadec

2

(

draws the density function for the c 2 (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound.

Shadec

2

(

lowerbound

,

upperbound

,

df

)

Note: For this example,

Xmin = 0

Xmax = 35

Ymin = L.025

Ymax = .1

Shade

Ü(

Shade

Ü( draws the density function for the Û distribution specified by numerator df (degrees of freedom) and

denominator df and shades the area between lowerbound and

upperbound.

Shade

Ü(

lowerbound

,

upperbound

,

numerator df

,

denominator df

)

Note: For this example,

Xmin = 0

Xmax = 5

Ymin = L.25

Ymax = .9

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14

Financial

Functions

Contents

Getting Started: Financing a Car

...................................................................

Getting Started: Computing Compound Interest

................................

Using the TVM Solver

.........................................................................................

Using the Financial Functions

........................................................................

Calculating Time Value of Money ( TVM )

..............................................

Calculating Cash Flows

......................................................................................

Calculating Amortization

...................................................................................

9

Calculating Interest Conversion

....................................................................

12

6

8

Finding Days between Dates/Defining Payment Method

.......................

13

Using the

TVM

Variables

...................................................................................

14

4

5

2

3

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Getting Started: Financing a Car

Getting Started is a fast-paced introduction. Read the chapter for details.

You have found a car you would like to buy. The car costs 9,000. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car?

1. Press z † ~ ~ ~ Í to set the fixed-decimal mode setting to

2

. The

TI-82 STATS will display all numbers with two decimal places.

2. Press y [

FINANCE

] to display the

FINANCE CALC

menu.

3. Press Í to select

1:TVM Solver

. The

TVM

Solver

is displayed.

Press

48

Í to store 48 months to

Ú

. Press

9000

Í to store 9,000 to

PV

. Press Ì

250

Í to store L250 to

PMT

. (Negation indicates cash outflow.) Press

0

Í to store

0 to

FV

. Press

12

Í to store 12 payments per year to

P/Y

and 12 compounding periods per year to

C/Y

. Setting

P/Y

to 12 will compute an annual percentage rate

(compounded monthly) for

æ

. Press † Í to select

PMT:END

, which indicates that payments are due at the end of each period.

4. Press } } } } } } to move the cursor to the for

æ

æ prompt. Press ƒ [

SOLVE

] to solve

. What APR should you look for?

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Getting Started: Computing Compound Interest

At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in

7 years?

Note: Because there are no payments when you solve compound interest problems,

PMT

must be set to 0 and P/Y must be set to 1.

1. Press y [

FINANCE

] to display the

FINANCE

CALC

menu.

2. Press Í to select

1:TVM Solver

. Press

7

to enter the number of periods in years. Press †

† Ì

1250

to enter the present value as a cash outflow (investment). Press †

0

to specify no payments. Press †

2000

to enter the future value as a cash inflow (return). Press †

1

to enter payment periods per year. Press †

12

to set compounding periods per year to

12

.

3. Press } } } } } to place the cursor on the

prompt.

4. Press ƒ [

SOLVE

] to solve for æ, the annual interest rate.

Financial Functions 14–3

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Using the TVM Solver

Using the TVM

Solver

The

TVM Solver

displays the time-value-of-money (

TVM

) variables. Given four variable values, the

TVM Solver

solves for the fifth variable.

The

FINANCE VARS

menu section (page 14.14) describes the five

TVM

variables ( Ú , æ ,

PV

,

PMT

, and

FV

) and

P/Y

and

C/Y

.

PMT: END BEGIN

in the

TVM Solver

corresponds to the

FINANCE CALC

menu items

Pmt_End

(payment at the end of each period) and

Pmt_Bgn

(payment at the beginning of each period).

To solve for an unknown

TVM

variable, follow these steps.

1. Press y [

FINANCE

] Í to display the

TVM Solver

. The screen below shows the default values with the fixeddecimal mode set to two decimal places.

2. Enter the known values for four

TVM

variables.

Note: Enter cash inflows as positive numbers and cash outflows as negative numbers.

3. Enter a value for

P/Y

, which automatically enters the same value for

C/Y

; if

P/Y

ƒ

C/Y

, enter a unique value for

C/Y

.

4. Select

END

or

BEGIN

to specify the payment method.

5. Place the cursor on the

TVM

variable for which you want to solve.

6. Press ƒ [

SOLVE

]. The answer is computed, displayed in the

TVM Solver

, and stored to the appropriate

TVM

variable.

An indicator square in the left column designates the solution variable.

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Using the Financial Functions

Entering Cash

Inflows and Cash

Outflows

When using the TI-82 STATS financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI-82 STATS follows this convention when computing and displaying answers.

FINANCE CALC

Menu

To display the

FINANCE CALC

menu, press y [

FINANCE

].

CAL

C

VARS

1: TVM Solver...

2: tvm_Pmt

4: tvm_PV

6: tvm_FV

7: npv(

8: irr(

9: bal(

0: GPrn(

A: GInt(

B: 4Nom(

C: 4Eff(

D: dbd(

E: Pmt_End

F: Pmt_Bgn

Displays the

TVM Solver.

Computes the amount of each payment.

Computes the interest rate per year.

Computes the present value.

Computes the number of payment periods.

Computes the future value.

Computes the net present value.

Computes the internal rate of return.

Computes the amortization sched. balance.

Computes the amort. sched. principal sum.

Computes the amort. sched. interest sum.

Computes the nominal interest rate.

Computes the effective interest rate.

Calculates the days between two dates.

Selects ordinary annuity (end of period).

Selects annuity due (beginning of period).

Use these functions to set up and perform financial calculations on the home screen.

TVM Solver TVM Solver

displays the

TVM Solver

(page 14.4).

Financial Functions 14–5

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Calculating Time Value of Money (TVM)

Calculating Time

Value of Money

Use time-value-of-money (

TVM

) functions (menu items

2

through

6

) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings.

Each

TVM

function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for these functions are not stored to the

TVM

variables (page 14.14).

Note: To store a value to a

TVM variable, use the TVM Solver (page

14.4) or use ¿ and any TVM variable on the FINANCE VARS menu (page 14.14).

If you enter less than six arguments, the TI-82 STATS substitutes a previously stored

TVM

variable value for each unspecified argument.

If you enter any arguments with a

TVM

function, you must place the argument or arguments in parentheses.

tvm_Pmt tvm_Pmt

computes the amount of each payment.

tvm_Pmt

[

(

Ú

,

æ

,

PV

,

FV

,

P/Y

,

C/Y

)

]

Note: In the example above, the values are stored to the

TVM variables in the

TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen using the values in the

TVM Solver.

Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount.

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tvm_

æ

tvm_

æ computes the annual interest rate.

tvm_

æ [

(

Ú

,

PV

,

PMT

,

FV

,

P/Y

,

C/Y

)

]

tvm_PV tvm_PV

computes the present value.

tvm_PV

[

(

Ú

,

æ

,

PMT

,

FV

,

P/Y

,

C/Y

)

]

tvm_

Ú

tvm_

Ú

computes the number of payment periods.

tvm_

Ú

[

(

æ

,

PV

,

PMT

,

FV

,

P/Y

,

C/Y

)

]

tvm_FV tvm_FV

computes the future value.

tvm_FV

[

(

Ú

,

æ

,

PV

,

PMT

,

P/Y

,

C/Y

)

]

Financial Functions 14–7

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Calculating Cash Flows

Calculating a

Cash Flow

Use the cash flow functions (menu items

7

and

8

) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for

npv( and

irr( use these arguments.

interest rate is the rate by which to discount the cash flows

(the cost of money) over one period.

CF0 is the initial cash flow at time 0; it must be a real number.

CFList is a list of cash flow amounts after the initial cash flow CF0.

CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList.

The default is 1; if you enter values, they must be positive integers < 10,000.

For example, express this uneven cash flow in lists.

2000 2000

2000 4000

4000

npv(, irr(

- 3000

CF0 =

2000

CFList =

{2000,L3000,4000}

CFFreq =

{2,1,2} npv(

(net present value) is the sum of the present values for the cash inflows and outflows. A positive result for

npv

indicates a profitable investment.

npv(

interest rate

,

CF0

,

CFList[

,

CFFreq]

) irr(

(internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero.

irr(

CF0

,

CFList[

,

CFFreq]

)

1000

0 5000

3000

- 2000 - 2500

14–8 Financial Functions

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Calculating Amortization

Calculating an

Amortization

Schedule bal(

Use the amortization functions (menu items

9

,

0

, and

A

) to calculate balance, sum of principal, and sum of interest for an amortization schedule.

bal(

computes the balance for an amortization schedule using stored values for æ ,

PV

, and

PMT

. npmt is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the balance; if you do not specify roundvalue, then the TI-82 STATS uses the current

Float

/

Fix

decimal-mode setting.

bal(

npmt[

,

roundvalue]

)

GPrn(, GInt(

GPrn(

computes the sum of the principal during a specified period for an amortization schedule using stored values for æ ,

PV

, and

PMT

. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000.

roundvalue specifies the internal precision the calculator uses to calculate the principal; if you do not specify roundvalue, the

TI-82 STATS uses the current

Float

/

Fix

decimal-mode setting.

Note: You must enter values for

æ, PV, PMT, and before computing the principal.

GPrn(

pmt1

,

pmt2[

,

roundvalue]

)

GInt(

computes the sum of the interest during a specified period for an amortization schedule using stored values for

æ

,

PV

, and

PMT

. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000.

roundvalue specifies the internal precision the calculator uses to calculate the interest; if you do not specify roundvalue, the

TI-82 STATS uses the current

Float

/

Fix

decimal-mode setting.

GInt(

pmt1

,

pmt2[

,

roundvalue]

)

Financial Functions 14–9

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Calculating Amortization

(continued)

Amortization

Example:

Calculating an

Outstanding

Loan Balance

You want to buy a home with a 30-year mortgage at 8 percent

APR. Monthly payments are 800. Calculate the outstanding loan balance after each payment and display the results in a graph and in the table.

1. Press z. Press † ~ ~ ~ Í to set the fixed-decimal mode setting to

2

. Press † † ~ Í to select

Par

graphing mode.

2. Press y [

FINANCE

] Í to display the

TVM Solver

.

3. Press

360

to enter number of payments. Press †

8

to enter the interest rate. Press † † Ì

800

to enter the payment amount. Press †

0

to enter the future value of the mortgage.

Press †

12

to enter the payments per year, which also sets the compounding periods per year to

12

. Press † † Í to select

PMT:END

.

4. Press } } } } } to place the cursor on the

PV

prompt. Press

ƒ [

SOLVE

] to solve for the present value.

5. Press o to display the parametric

Y=

editor. Turn off all stat plots. Press „ to define

X

1T

as

T

. Press † y

[

FINANCE

]

9

„¤ to define

Y

1T

as

bal(T)

.

14–10 Financial Functions

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Amortization

Example:

Calculating an

Outstanding

Loan Balance

(continued)

6. Press p to display the window variables. Enter the values below.

Tmin=0 Xmin=0 Ymin=0

Tmax=360

Tstep=12

Xmax=360

Xscl=50

Ymax=125000

Yscl=10000

7. Press r to draw the graph and activate the trace cursor.

Press ~ and | to explore the graph of the outstanding balance over time. Press a number and then press Í to view the balance at a specific time

T

.

8. Press y [

TBLSET

] and enter the values below.

TblStart=0

@Tbl=12

9. Press y [

TABLE

] to display the table of outstanding balances (

Y

1T

).

10.Press z † † † † † † † ~ ~ Í to select

G.T

split-screen mode, in which the graph and table are displayed simultaneously.

Press r to display

X

1T

(time) and

Y

1T

(balance) in the table.

Financial Functions 14–11

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Calculating Interest Conversion

Calculating an

Interest

Conversion

4Nom(

Use the interest conversion functions (menu items

B

and

C

) to convert interest rates from an annual effective rate to a nominal rate (

4Nom(

) or from a nominal rate to an annual effective rate

(

4Eff(

).

4Nom(

computes the nominal interest rate. effective rate and

compounding periods must be real numbers. compounding

periods must be >0.

4Nom(

effective rate

,

compounding periods

)

4Eff(

4Eff(

computes the effective interest rate. nominal rate and

compounding periods must be real numbers. compounding

periods must be >0.

4Eff(

nominal rate

,

compounding periods

)

14–12 Financial Functions

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Finding Days between Dates/Defining Payment Method

dbd(

Use the date function

dbd(

(menu item

D

) to calculate the number of days between two dates using the actual-day-count method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar.

Note: Dates must be between the years 1950 through 2049.

dbd(

date1

,

date2

)

You can enter date1 and date2 in either of two formats.

MM.DDYY (United States)

DDMM.YY (Europe)

The decimal placement differentiates the date formats.

Defining the

Payment Method

Pmt_End

and

Pmt_Bgn

(menu items

E

and

F

) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the

TVM Solver

is updated.

Pmt_End

Pmt_Bgn

Pmt_End

(payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category.

Pmt_End

is the default.

Pmt_End

On the

TVM Solver

’s

PMT:END BEGIN

line, select

END

to set

PMT

to ordinary annuity.

Pmt_Bgn

(payment beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category.

Pmt_Bgn

On the

TVM Solver

’s

PMT:END BEGIN

line, select

BEGIN

to set

PMT

to annuity due.

Financial Functions 14–13

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Using the TVM Variables

FINANCE VARS

Menu

To display the

FINANCE VARS

menu, press y [

FINANCE

] ~.

You can use

TVM

variables in

TVM

functions and store values to them on the home screen.

CALC VAR

S

1: Ú

3: PV

4: PMT

5: FV

6: P/Y

7: C/Y

Total number of payment periods

Annual interest rate

Present value

Payment amount

Future value

Number of payment periods per year

Number of compounding periods/year

FV

P/Y and C/Y

, æ ,

PV

,

PMT

, and

FV

are the five

TVM

variables. They represent the elements of common financial transactions, as described in the table above. æ is an annual interest rate that is converted to a per-period rate based on the values of

P/Y

and

C/Y

.

P/Y

is the number of payment periods per year in a financial transaction.

C/Y

is the number of compounding periods per year in the same transaction.

When you store a value to

P/Y

, the value for

C/Y

automatically changes to the same value. To store a unique value to

C/Y

, you must store the value to

C/Y

after you have stored a value to

P/Y

.

14–14 Financial Functions

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15

CATALOG, Strings,

Hyperbolic Functions

Contents

Browsing the TI-82 STATS CATALOG

..................................................

Entering and Using Strings

...............................................................................

Storing Strings to String Variables

..............................................................

String Functions and Instructions in the CATALOG

........................

Hyperbolic Functions in the CATALOG

..................................................

10

2

3

4

6

CATALOG

, Strings, Hyperbolic Functions 15–1

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Browsing the TI-82 STATS CATALOG

What Is the

CATALOG?

The

CATALOG

is an alphabetical list of all functions and instructions on the TI-82 STATS. You also can access each

CATALOG

item from a menu or the keyboard, except:

The six string functions (page 15.6)

The six hyperbolic functions (page 15.10)

The

solve(

instruction without the equation solver editor

(Chapter 2)

The inferential stat functions without the inferential stat editors (Chapter 13)

Note: The only CATALOG programming commands you can execute from the home screen are

GetCalc(, Get(, and Send(.

Selecting an Item from the

CATALOG

To select a

CATALOG

item, follow these steps.

1. Press y ã

CATALOG

ä to display the CATALOG

.

The

4

in the first column is the selection cursor.

2. Press † or } to scroll the

CATALOG

until the selection cursor points to the item you want.

To jump to the first item beginning with a particular letter, press that letter; alpha-lock is on.

Items that begin with a number are in alphabetical order according to the first letter after the number. For example,

2.PropZTest(

is among the items that begin with the letter

P

.

Functions that appear as symbols, such as

+

,

L1

,

<

, and

‡(

, follow the last item that begins with

Z

. To jump to the first symbol,

!

, press [ q

].

3. Press Í to paste the item to the current screen.

Tip: From the top of the

CATALOG menu, press } to move to the bottom. From the bottom, press

† to move to the top.

15–2

CATALOG

, Strings, Hyperbolic Functions

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Entering and Using Strings

What Is a String?

A string is a sequence of characters that you enclose within quotation marks. On the TI-82 STATS, a string has two primary applications.

It defines text to be displayed in a program.

It accepts input from the keyboard in a program.

Characters are the units that you combine to form a string.

Count each number, letter, and space as one character.

Count each instruction or function name, such as

sin(

or

cos(

, as one character; the TI-82 STATS interprets each instruction or function name as one character.

Entering a String

To enter a string on a blank line on the home screen or in a program, follow these steps.

1. Press ƒ [

ã

] to indicate the beginning of the string.

2. Enter the characters that comprise the string.

Use any combination of numbers, letters, function names, or instruction names to create the string.

To enter a blank space, press ƒ [

'

].

To enter several alpha characters in a row, press y

[

A.LOCK

] to activate alpha-lock.

3. Press ƒ [

ã

] to indicate the end of the string.

"

string

"

4. Press Í. On the home screen, the string is displayed on the next line without quotations. An ellipsis (

...

) indicates that the string continues beyond the screen. To scroll the entire string, press ~ and |.

Note: Quotation marks do not count as string characters.

CATALOG

, Strings, Hyperbolic Functions 15–3

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Storing Strings to String Variables

String Variables

The TI-82 STATS has 10 variables to which you can store strings. You can use string variables with string functions and instructions.

To display the

VARS STRING

menu, follow these steps.

1. Press  to display the

VARS

menu. Move the cursor to

7:String

.

2. Press Í to display the

STRING

secondary menu.

15–4

CATALOG

, Strings, Hyperbolic Functions

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Storing a String to a String

Variable

To store a string to a string variable, follow these steps.

1. Press ƒ [

ã

], enter the string, and press ƒ [

ã

].

2. Press ¿.

3. Press 

7

to display the

VARS STRING

menu.

4. Select the string variable (from

Str1

to

Str9

, or

Str0

) to which you want to store the string.

The string variable is pasted to the current cursor location, next to the store symbol ( !

).

5. Press Í to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks.

Displaying the

Contents of a

String Variable

To display the contents of a string variable on the home screen, select the string variable from the

VARS STRING

menu, and then press Í. The string is displayed.

CATALOG

, Strings, Hyperbolic Functions 15–5

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String Functions and Instructions in the CATALOG

Displaying String

Functions and

Instructions in the CATALOG

String functions and instructions are available only from the

CATALOG

. The table below lists the string functions and instructions in the order in which they appear among the other

CATALOG

menu items. The ellipses in the table indicate the presence of additional

CATALOG

items.

CATALOG

...

Equ4String( expr(

...

inString(

...

length(

...

String4Equ( sub(

...

Converts an equation to a string.

Converts a string to an expression.

Returns a character’s place number.

Returns a string’s character length.

Converts a string to an equation.

Returns a string subset as a string.

+ (Concatenation)

To concatenate two or more strings, follow these steps.

1. Enter string1, which can be a string or string name.

2. Press Ã.

3. Enter string2, which can be a string or string name. If necessary, press à and enter string3, and so on.

string1

+

string2

+

string3. . .

4. Press Í to display the strings as a single string.

Selecting a String

Function from the CATALOG

To select a string function or instruction and paste it to the current screen, follow the steps on page 15.2.

15–6

CATALOG

, Strings, Hyperbolic Functions

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Equ4String( Equ4String(

converts to a string an equation that is stored to any

VARS Y.VARS

variable.

Y

n contains the equation.

Str

n (from

Str1

to

Str9

, or

Str0

) is the string variable to which you want the equation to be stored as a string.

Equ4String(Y

n

,Str

n

) expr( expr(

converts the character string contained in string to an expression and executes it. string can be a string or a string variable.

expr(

string

) inString( inString(

returns the character position in string of the first character of substring. string can be a string or a string variable.

start is an optional character position at which to start the search; the default is 1.

inString(

string

,

substring[

,

start]

)

Note: If string does not contain substring, or start is greater than the length of string,

inString( returns 0.

CATALOG

, Strings, Hyperbolic Functions 15–7

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String Functions and Instructions in the CATALOG

(cont.) length( length(

returns the number of characters in string. string can be a string or string variable.

Note: An instruction or function name, such as

sin( or cos(, counts as one character.

length(

string

)

String4Equ( String4Equ(

converts string into an equation and stores the equation to

Y

n. string can be a string or string variable.

String4Equ(

is the inverse of

Equ4String(

.

String4Equ(

string

,Y

n

)

15–8

CATALOG

, Strings, Hyperbolic Functions

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sub( sub(

returns a string that is a subset of an existing string. string can be a string or a string variable. begin is the position number of the first character of the subset. length is the number of characters in the subset.

sub(

string

,

begin

,

length

)

Entering a

Function to

Graph during

Program

Execution

In a program, you can enter a function to graph during program execution using these commands.

Note: When you execute this program, enter a function to store to

Y3

at the

ENTRY= prompt.

CATALOG

, Strings, Hyperbolic Functions 15–9

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Hyperbolic Functions in the CATALOG

Hyperbolic

Functions sinh(, cosh(, tanh(

The hyperbolic functions are available only from the

CATALOG

.

The table below lists the hyperbolic functions in the order in which they appear among the other

CATALOG

menu items. The ellipses in the table indicate the presence of additional

CATALOG

items.

CATALOG

...

cosh( cosh

L1

(

...

sinh( sinh

L1

(

...

tanh( tanh

L1

(

...

Hyperbolic cosine

Hyperbolic arccosine

Hyperbolic sine

Hyperbolic arcsine

Hyperbolic tangent

Hyperbolic arctangent

sinh(

,

cosh(

, and

tanh(

are the hyperbolic functions. Each is valid for real numbers, expressions, and lists.

sinh(

value

) cosh(

value

) tanh(

value

) sinh L1 (, cosh L1 (, tanh L1 ( sinh

L1

(

is the hyperbolic arcsine function.

cosh

L1

(

is the hyperbolic arccosine function.

tanh

L1

(

is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists.

sinh

L1

(

value

) cosh

L1

( sinh

L1

(

value

)

value

)

15–10

CATALOG

, Strings, Hyperbolic Functions

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16

Programming

Contents

Getting Started: Volume of a Cylinder

.....................................................

Creating and Deleting Programs

...................................................................

Entering Command Lines and Executing Programs

........................

Editing Programs

....................................................................................................

Copying and Renaming Programs

...............................................................

PRGM CTL

(Control) Instructions

..............................................................

PRGM I/O

(Input/Output) Instructions

.....................................................

16

Calling Other Programs as Subroutines

...................................................

22

7

8

5

6

2

4

Programming 16–1

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Getting Started: Volume of a Cylinder

Getting Started is a fast-paced introduction. Read the chapter for details.

A program is a set of commands that the TI-82 STATS executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume.

1. Press  ~ ~ to display the

PRGM NEW menu.

2. Press Í to select

1:Create New

. The

Name=

prompt is displayed, and alpha-lock is on. Press [

C

] [

Y

] [

L

] [

I

] [

N

] [

D

] [

E

] [

R

], and then press Í to name the program

CYLINDER

.

You are now in the program editor. The colon

(

:

) in the first column of the second line indicates the beginning of a command line.

3. Press  ~

2

to select

2:Prompt

from the

PRGM I/O

menu.

Prompt

is copied to the command line. Press ƒ [

R

] ¢ ƒ [

H

] to enter the variable names for radius and height. Press Í.

4. Press y ãpä ƒ [

R

] ¡ ƒ [

H

] ¿

ƒ [

V

] Í to enter the expression

pR

2

H

and store it to the variable

V

.

16–2 Programming

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PM Page 2 of 22

5. Press  ~

3

to select

3:Disp

from the

PRGM I/O

menu.

Disp

is pasted to the command line. Press y [

A

.

LOCK

] ããä [

V

] [

O

]

[

L

] [

U

] [

M

] [

E

][

'

] [

I

] [

S

] ããä ƒ ¢ ƒ

[

V

] Í to set up the program to display the text

VOLUME IS

on one line and the calculated value of

V

on the next.

6. Press y [

QUIT

] to display the home screen.

7. Press  to display the

PRGM EXEC menu.

The items on this menu are the names of stored programs.

8. Press Í to paste

prgmCYLINDER

to the current cursor location. (If

CYLINDER

is not item

1

on your

PRGM EXEC menu, move the cursor to

CYLINDER

before you press Í.)

9. Press Í to execute the program. Enter

1.5

for the radius, and then press Í. Enter

3

for the height, and then press Í. The text

VOLUME IS

, the value of

V

, and

Done

are displayed.

Repeat steps 7 through 9 and enter different values for

R

and

H

.

Programming 16–3

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Creating and Deleting Programs

What Is a

Program?

Creating a New

Program

A program is a set of one or more command lines. Each line contains one or more instructions. When you execute a program, the TI-82 STATS performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-82 STATS can store is limited only by available memory.

To create a new program, follow these steps.

1. Press  | to display the

PRGM NEW

menu.

Managing

Memory and

Deleting a

Program

2. Press Í to select

1:Create New

. The

Name=

prompt is displayed, and alpha-lock is on.

3. Press a letter from A to Z or q to enter the first character of the new program name.

Note: A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.

4. Enter zero to seven letters, numbers, or q to complete the new program name.

5. Press Í. The program editor is displayed.

6. Enter one or more program commands (page 16.5).

7. Press y [

QUIT

] to leave the program editor and return to the home screen.

To check whether adequate memory is available for a program you want to enter, press y [

MEM

], and then select

1:Check RAM

from the

MEMORY

menu (Chapter 18).

To increase available memory, press y [

MEM

], and then select

2:Delete

from the

MEMORY

menu (Chapter 18).

To delete a specific program, press y [

MEM

], select

2:Delete

from the

MEMORY

menu, and then select

7:Prgm

from the

DELETE FROM

secondary menu (Chapter 18).

16–4 Programming

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Entering Command Lines and Executing Programs

Entering a

Program

Command Line

You can enter on a command line any instruction or expression that you could execute from the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon.

Note: A command line can be longer than the screen is wide; long command lines wrap to the next screen line.

While in the program editor, you can display and select from menus. You can return to the program editor from a menu in either of two ways.

Select a menu item, which pastes the item to the current command line.

Press ‘.

When you complete a command line, press Í. The cursor moves to the next command line.

Programs can access variables, lists, matrices, and strings saved in memory. If a program stores a new value to a variable, list, matrix, or string, the program changes the value in memory during execution.

You can call another program as a subroutine (page 16.15 and page 16.22).

Executing a

Program

Breaking a

Program

To execute a program, begin on a blank line on the home screen and follow these steps.

1. Press  to display the

PRGM EXEC

menu.

2. Select a program name from the

PRGM EXEC

menu (page

16.7).

prgm

name is pasted to the home screen (for example,

prgmCYLINDER

).

3. Press Í to execute the program. While the program is executing, the busy indicator is on.

Last Answer (

Ans

) is updated during program execution. Last

Entry is not updated as each command is executed (Chapter 1).

The TI-82 STATS checks for errors during program execution.

It does not check for errors as you enter a program.

To stop program execution, press É. The

ERR:BREAK

menu is displayed.

To return to the home screen, select

1:Quit

.

To go where the interruption occurred, select

2:Goto

.

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Editing Programs

Editing a

Program

To edit a stored program, follow these steps.

1. Press  ~ to display the

PRGM EDIT

menu.

2. Select a program name from the

PRGM EDIT

menu (page

16.7). Up to the first seven lines of the program are displayed.

Note: The program editor does not display a $ to indicate that a program continues beyond the screen.

3. Edit the program command lines.

Move the cursor to the appropriate location, and then delete, overwrite, or insert.

Press ‘ to clear all program commands on the command line (the leading colon remains), and then enter a new program command.

Tip: To move the cursor to the beginning of a command line, press y |; to move to the end, press y ~. To scroll the cursor down seven command lines, press

ƒ †. To scroll the cursor up seven command lines, press

ƒ }.

Inserting and

Deleting

Command Lines

To insert a new command line anywhere in the program, place the cursor where you want the new line, press y [

INS

], and then press Í. A colon indicates a new line.

To delete a command line, place the cursor on the line, press

‘ to clear all instructions and expressions on the line, and then press { to delete the command line, including the colon.

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Copying and Renaming Programs

Copying and

Renaming a

Program

To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating a New Program

(page 16.4), and then follow these steps.

1. Press y [

RCL

].

Rcl

is displayed on the bottom line of the program editor in the new program (Chapter 1).

2. Press  | to display the

PRGM EXEC

menu.

3. Select a name from the menu.

prgm

name is pasted to the bottom line of the program editor.

4. Press Í. All command lines from the selected program are copied into the new program.

Copying programs has at least two convenient applications.

You can create a template for groups of instructions that you use frequently.

You can rename a program by copying its contents into a new program.

Note: You also can copy all the command lines from one existing program to another existing program using

RCL.

Scrolling the

PRGM EXEC and

PRGM EDIT

Menus

The TI-82 STATS sorts

PRGM EXEC

and

PRGM EDIT

menu items automatically into alphanumerical order. Each menu only labels the first 10 items using

1

through

9

, then

0

.

To jump to the first program name that begins with a particular alpha character or q, press ƒ [letter from A to Z or q

].

Tip: From the top of either the

PRGM EXEC or PRGM EDIT menu, press

} to move to the bottom. From the bottom, press † to move to the top. To scroll the cursor down the menu seven items, press

ƒ

†. To scroll the cursor up the menu seven items, press ƒ }.

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PRGM CTL (Control) Instructions

PRGM CTL Menu

To display the

PRGM CTL

(program control) menu, press  from the program editor only.

CTL I/O EXEC

1: If

2: Then

3: Else

4: For(

5: While

6: Repeat

7: End

8: Pause

9: Lbl

0: Goto

A: IS>(

B: DS<(

C: Menu(

D: prgm

E: Return

F: Stop

G: DelVar

H: GraphStyle(

Creates a conditional test.

Executes commands when

If

is true.

Executes commands when

If

is false.

Creates an incrementing loop.

Creates a conditional loop.

Creates a conditional loop.

Signifies the end of a block.

Pauses program execution.

Defines a label.

Goes to a label.

Increments and skips if greater than.

Decrements and skips if less than.

Defines menu items and branches.

Executes a program as a subroutine.

Returns from a subroutine.

Stops execution.

Deletes a variable from within program.

Designates the graph style to be drawn.

These menu items direct the flow of an executing program.

They make it easy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a command line in the program.

To return to the program editor without selecting an item, press

‘.

Controlling

Program Flow

Program control instructions tell the TI-82 STATS which command to execute next in a program.

If

,

While

, and

Repeat

check a defined condition to determine which command to execute next. Conditions frequently use relational or Boolean tests (Chapter 2), as in:

If A<7:A+1

!A or

If N=1 and M=1:Goto Z

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If

Use

If

for testing and branching. If condition is false (zero), then the command immediately following

If

is skipped. If condition is true (nonzero), then the next command is executed.

If

instructions can be nested.

:If

condition

:

command (if true)

:

command

Program Output

If.Then

Then

following an

If

executes a group of commands if condition is true (nonzero).

End

identifies the end of the group of

commands.

:If

condition

:Then

:

command (if true)

:

command (if true)

:End

:

command

Program Output

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PRGM CTL (Control) Instructions

(continued)

If.Then.Else

Else

following

If.Then

executes a group of commands if

condition is false (zero).

End

identifies the end of the group of

commands.

:If

condition

:Then

:

command (if true)

:

command (if true)

:Else

:

command (if false)

:

command (if false)

:End

:

command

Program Output

For(

For(

loops and increments. It increments variable from begin to

end by increment. increment is optional (default is 1) and can be negative (end<begin). end is a maximum or minimum value not to be exceeded.

End

identifies the end of the loop.

For(

loops can be nested.

:For(

variable

,

begin

,

end[

,

increment]

)

:

command (while end not exceeded)

:

command (while end not exceeded)

:End

:

command

Program Output

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While While

performs a group of commands while condition is true.

condition is frequently a relational test (Chapter 2). condition is tested when

While

is encountered. If condition is true (nonzero), the program executes a group of commands.

End

signifies the end of the group. When condition is false (zero), the program executes each command following

End

.

While

instructions can be nested.

:While

condition

:

command (while condition is true)

:

command (while condition is true)

:End

:

command

Program Output

Repeat

Repeat

repeats a group of commands until condition is true

(nonzero). It is similar to

While

, but condition is tested when

End

is encountered; therefore, the group of commands is always executed at least once.

Repeat

instructions can be nested.

:Repeat

condition

:

command (until condition is true)

:

command (until condition is true)

:End

:

command

Program Output

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PRGM CTL (Control) Instructions

(continued)

End

Pause

End

identifies the end of a group of commands. You must include an

End

instruction at the end of each

For(

,

While

, or

Repeat

loop. Also, you must paste an

End

instruction at the end of each

If.Then

group and each

If.Then.Else

group.

Pause

suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the top-right corner. Press Í to resume execution.

Pause

without a value temporarily pauses the program. If the

DispGraph

or

Disp

instruction has been executed, the appropriate screen is displayed.

Pause

with value displays value on the current home screen.

value can be scrolled.

Pause

[value]

Program Output

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Lbl, Goto Lbl

(label) and

Goto

(go to) are used together for branching.

Lbl

specifies the label for a command. label can be one or two characters (

A

through

Z

,

0

through

99

, or

q

).

Lbl

label

Goto

causes the program to branch to label when

Goto

is encountered.

Goto

label

Program Output

IS>(

IS>(

(increment and skip) adds 1 to variable. If the answer is >

value (which can be an expression), the next command is skipped; if the answer is { value, the next command is executed.

variable cannot be a system variable.

:IS>(

variable

,

value

)

:

command (if answer  value)

:

command (if answer > value)

Program Output

Note:

IS>( is not a looping instruction.

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PRGM CTL (Control) Instructions

(continued)

DS<( DS<(

(decrement and skip) subtracts 1 from variable. If the answer is < value (which can be an expression), the next

command is skipped; if the answer is | value, the next command is executed. variable cannot be a system variable.

:DS<(

variable

,

value

)

:

command (if answer ‚ value)

:

command (if answer < value)

Program Output

Menu(

Note: DS<( is not a looping instruction.

Menu(

sets up branching within a program. If

Menu(

is encountered during program execution, the menu screen is displayed with the specified menu items, the pause indicator is on, and execution pauses until you select a menu item.

The menu title is enclosed in quotation marks (

"

). Up to seven pairs of menu items follow. Each pair comprises a text item

(also enclosed in quotation marks) to be displayed as a menu selection, and a label item to which to branch if you select the corresponding menu selection.

Menu("

title

","

text1

",

label1

,"

text2

",

label2

,

. . .

)

Program Output

The program above pauses until you select

1

or

2

. If you select

2

, for example, the menu disappears and the program continues execution at

Lbl B

.

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prgm

Return

Stop

DelVar

Use

prgm

to execute other programs as subroutines (page

16.22). When you select

prgm

, it is pasted to the cursor location. Enter characters to spell a program name. Using

prgm

is equivalent to selecting existing programs from the

PRGM

EXEC

menu; however, it allows you to enter the name of a program that you have not yet created.

prgm

name

Note: You cannot directly enter the subroutine name when using

RCL. You must paste the name from the PRGM EXEC menu (page

16.7).

Return

quits the subroutine and returns execution to the calling program (page 16.22), even if encountered within nested loops.

Any loops are ended. An implied

Return

exists at the end of any program that is called as a subroutine. Within the main program,

Return

stops execution and returns to the home screen.

Stop

stops execution of a program and returns to the home screen.

Stop

is optional at the end of a program.

DelVar

deletes from memory the contents of variable.

DelVar

variable

GraphStyle( GraphStyle(

designates the style of the graph to be drawn.

function# is the number of the

Y=

function name in the current graphing mode. graphstyle is a number from

1

to

7

that corresponds to the graph style, as shown below.

1

2

3

= ç (line)

= è (thick)

= é (shade above)

4

= ê (shade below)

5

= ë (path)

6

= ì (animate)

7

= í (dot)

GraphStyle(

function#

,

graphstyle

)

For example,

GraphStyle(1,5)

in

Func

mode sets the graph style for

Y

1

to ë (path;

5

).

Not all graph styles are available in all graphing modes. For a detailed description of each graph style, see the Graph Styles table in Chapter 3.

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PRGM I/O (Input/Output) Instructions

PRGM I/O Menu

To display the

PRGM I/O

(program input/output) menu, press

 ~ from within the program editor only.

CTL I/O EXEC

1: Input

2: Prompt

3: Disp

4: DispGraph

5: DispTable

6: Output(

7: getKey

8: ClrHome

9: ClrTable

0: GetCalc(

A: Get(

B: Send(

Enters a value or uses the cursor.

Prompts for entry of variable values.

Displays text, value, or the home screen.

Displays the current graph.

Displays the current table.

Displays text at a specified position.

Checks the keyboard for a keystroke.

Clears the display.

Clears the current table.

Gets a variable from another TI-82 STATS.

Gets a variable from CBL or CBR.

Sends a variable to CBL or CBR.

These instructions control input to and output from a program during execution. They allow you to enter values and display answers during program execution.

To return to the program editor without selecting an item, press

‘.

Displaying a

Graph with Input

Input

without a variable displays the current graph. You can move the free-moving cursor, which updates

X

and

Y

(and

R

and

q

for

PolarGC

format). The pause indicator is on. Press Í to resume program execution.

Input

Program Output

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Storing a

Variable Value with Input

Input

with variable displays a

?

(question mark) prompt during execution. variable may be a real number, complex number, list, matrix, string, or

Y=

function. During program execution, enter a value, which can be an expression, and then press Í. The value is evaluated and stored to variable, and the program resumes execution.

Input

[variable]

You can display text or the contents of

Str

n (a string variable) of up to 16 characters as a prompt. During program execution, enter a value after the prompt and then press Í. The value is stored to variable, and the program resumes execution.

Input

[

"

text

",

variable]

Input

[

Str

n

,

variable]

Program Output

Note: When a program prompts for input of lists and

Yn functions during execution, you must include the braces ( { } ) around the list elements and quotation marks (

" ) around the expressions.

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PRGM I/O (Input/Output) Instructions

(continued)

Prompt

During program execution,

Prompt

displays each variable, one at a time, followed by

=?

. At each prompt, enter a value or expression for each variable, and then press Í. The values are stored, and the program resumes execution.

Prompt

variableA[

,

variableB

,

...

,

variable n]

Program Output

Displaying the

Home Screen

Displaying

Values and

Messages

Note: Y= functions are not valid with Prompt.

Disp

(display) without a value displays the home screen. To view the home screen during program execution, follow the

Disp

instruction with a

Pause

instruction.

Disp

Disp

with one or more values displays the value of each.

Disp

[valueA

,

valueB

,

valueC

,

...

,

value n]

If value is a variable, the current value is displayed.

If value is an expression, it is evaluated and the result is displayed on the right side of the next line.

If value is text within quotation marks, it is displayed on the left side of the current display line.

!

is not valid as text.

Program Output

If

Pause

is encountered after

Disp

, the program halts temporarily so you can examine the screen. To resume execution, press Í.

Note: If a matrix or list is too large to display in its entirety, ellipses

(...) are displayed in the last column, but the matrix or list cannot be scrolled. To scroll, use Pause value (page 16.12).

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DispGraph

DispTable

Output(

DispGraph

(display graph) displays the current graph. If

Pause

is encountered after

DispGraph

, the program halts temporarily so you can examine the screen. Press Í to resume execution.

DispTable

(display table) displays the current table. The program halts temporarily so you can examine the screen. Press

Í to resume execution.

Output(

displays text or value on the current home screen beginning at row (

1

through

8

) and column (

1

through

16

), overwriting any existing characters.

Tip: You may want to precede

Output( with ClrHome (page 16.20).

Expressions are evaluated and values are displayed according to the current mode settings. Matrices are displayed in entry format and wrap to the next line. !

is not valid as text.

Output(

row

,

column

,"

text

")

Output(

row

,

column

,

value

)

Program Output

For

Output(

on a

Horiz

split screen, the maximum value for row is 4.

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PRGM I/O (Input/Output) Instructions

(continued) getKey getKey

returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed,

getKey

returns 0. Use

getKey

inside loops to transfer control, for example, when creating video games.

Program Output

TI-82 STATS Key

Code Diagram

Note:

, , , and

Í were pressed during program execution.

Note: You can press

É at any time during execution to break the program (page 16.5).

ClrHome,

ClrTable

ClrHome

(clear home screen) clears the home screen during program execution.

ClrTable

(clear table) clears the values in the table during program execution.

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GetCalc(

Get(, Send(

GetCalc(

gets the contents of variable on another TI-82 STATS and stores it to variable on the receiving TI-82 STATS. variable can be a real or complex number, list element, list name, matrix element, matrix name, string,

Y=

variable, graph database, or picture.

GetCalc(

variable

)

Note:

GetCalc( does not work between TI.82 and TI-82 STATS.

Get(

gets data from the Calculator-Based Laboratoryé (CBLé)

System or Calculator-Based Rangeré (CBRé) and stores it to

variable on the receiving TI-82 STATS. variable can be a real number, list element, list name, matrix element, matrix name, string,

Y=

variable, graph database, or picture.

Get(

variable

)

Note: If you transfer a program that references the

Get( command to the TI-82 STATS from a TI.82, the TI-82 STATS will interpret it as the

Get( described above. Use GetCalc( to get data from another

TI-82 STATS.

Send(

sends the contents of variable to the CBL or CBR. You cannot use it to send to another TI-82 STATS. variable can be a real number, list element, list name, matrix element, matrix name, string,

Y=

variable, graph database, or picture. variable can be a list of elements.

Send(

variable

)

Note: This program gets sound data and time in seconds from CBL.

Note: You can access

Get(, Send(, and GetCalc( from the

CATALOG to execute them from the home screen (Chapter 15).

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Calling Other Programs as Subroutines

Calling a

Program from

Another Program

On the TI-82 STATS, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself.

You can enter a program name on a command line in either of two ways.

Press  | to display the

PRGM EXEC

menu and select the name of the program (page 16

.

7).

prgm

name is pasted to the current cursor location on a command line.

Select

prgm

from the

PRGM CTL

menu, and then enter the program name (page 16

.

15).

prgm

name

When

prgm

name is encountered during execution, the next command that the program executes is the first command in the second program. It returns to the subsequent command in the first program when it encounters either

Return

or the implied

Return

at the end of the second program.

Program Output

&

Subroutine ( '

Notes about

Calling Programs

Variables are global.

label used with

Goto

and

Lbl

is local to the program where it is located. label in one program is not recognized by another program. You cannot use

Goto

to branch to a label in another program.

Return

exits a subroutine and returns to the calling program, even if it is encountered within nested loops.

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17

Applications

Contents

Comparing Test Results Using Box Plots

...............................................

Graphing Piecewise Functions

.......................................................................

Graphing Inequalities

...........................................................................................

Solving a System of Nonlinear Equations

..............................................

Using a Program to Create the Sierpinski Triangle

..........................

Graphing Cobweb Attractors

..........................................................................

Using a Program to Guess the Coefficients

...........................................

9

Graphing the Unit Circle and Trigonometric Curves

......................

10

7

8

5

6

2

4

Finding the Area between Curves

................................................................

11

Using Parametric Equations: Ferris Wheel Problem

........................

12

Demonstrating the Fundamental Theorem of Calculus

..................

14

Computing Areas of Regular N-Sided Polygons

................................

16

Computing and Graphing Mortgage Payments

...................................

18

Applications 17–1

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Comparing Test Results Using Box Plots

Problem

Procedure

An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women.

The test involved 30 small objects, which participants were not allowed to see. First, they held 15 of the objects one by one in their left hands and guessed what they were. Then they held the other 15 objects one by one in their right hands and guessed what they were. Use box plots to compare visually the correct-guess data from this table.

Correct Guesses

Women

Left

8

9

12

11

10

8

12

7

9

11

Women

Right

12

11

11

13

4

1

8

12

11

12

Men

Left

5

7

8

11

7

8

7

4

10

14

13

5

Men

Right

12

6

12

12

7

11

12

8

12

11

9

9

1. Press …

5

to select

5:SetUpEditor

. Enter list names

WLEFT

,

WRGHT

,

MLEFT

, and

MRGHT

, separated by commas. Press Í. The stat list editor now contains only these four lists.

2. Press …

1

to select

1:Edit

.

3. Enter into

WLEFT

the number of correct guesses each woman made using her left hand ( Women Left ). Press ~ to move to

WRGHT

and enter the number of correct guesses each woman made using her right hand ( Women Right ).

4. Likewise, enter each man’s correct guesses in

MLEFT

( Men

Left) and

MRGHT

( Men Right ).

5. Press y [

STAT PLOT

]. Select

1:Plot1

. Turn on plot 1; define it as a modified box plot

Õ

that uses

WLEFT

. Move the cursor to the top line and select

Plot2

. Turn on plot 2; define it as a modified box plot that uses

WRGHT

.

17–2 Applications

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PM Page 2 of 20

Procedure

(continued)

6. Press o. Turn off all functions.

7. Press p. Set

Xscl=1

and

Yscl=0

. Press q

9

to select

9:ZoomStat

. This adjusts the viewing window and displays the box plots for the women’s results.

8. Press r.

%

Women’s left-hand data

%

Women’s right-hand data

Use | and ~ to examine

minX

,

Q

1

,

Med

,

Q

3

, and

maxX

for each plot. Notice the outlier to the women’s right-hand data.

What is the median for the left hand? For the right hand?

With which hand were the women more accurate guessers, according to the box plots?

9. Examine the men’s results. Redefine plot 1 to use

MLEFT

, redefine plot 2 to use

MRGHT

. Press r.

%

Men’s left-hand data

%

Men’s right-hand data

Press | and ~ to examine

minX

,

Q

1

,

Med

,

Q

3

, and

maxX

for each plot. What difference do you see between the plots?

10.Compare the left-hand results. Redefine plot 1 to use

WLEFT

, redefine plot 2 to use

MLEFT

, and then press r to examine

minX

,

Q

1

,

Med

,

Q

3

, and

maxX

for each plot. Who were the better left-hand guessers, men or women?

11.Compare the right-hand results. Define plot 1 to use

WRGHT

, define plot 2 to use

MRGHT

, and then press r to examine

minX

,

Q

1

,

Med

,

Q

3

, and

maxX

for each plot. Who were the better right-hand guessers?

In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults. Do you think that this is because adults have learned to adapt or because our sample was not large enough?

Applications 17–3

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 3 of 20

Graphing Piecewise Functions

Problem

Procedure

The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to

55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket.

The fine (Y) as a function of kilometers per hour (X) is:

Y = 0

Y = 50 + 5 (X N 45)

Y = 50 + 5 … 10 + 10 (X N 55)

Y = 50 + 5 … 10 + 10 … 10 + 20 (X N 65)

0 < X  45

45 < X  55

55 < X  65

65 < X

1. Press z. Select

Func

and the default settings.

2. Press o. Turn off all functions and stat plots. Enter the

Y=

function to describe the fine. Use the

TEST

menu operations to define the piecewise function. Set the graph style for

Y

1

to í (dot).

3. Press p and set

Xmin=L2

,

Xscl=10

,

Ymin=L5

, and

Yscl=10

. Ignore

Xmax

and

Ymax

; they are set by

@X

and

@Y

in step 4.

4. Press y [

QUIT

] to return to the home screen. Store

1

to

@X

, and then store

5

to

@Y

.

@X

and

@Y

are on the

VARS Window

X/Y

secondary menu.

@X

and

@Y

specify the horizontal and vertical distance between the centers of adjacent pixels.

Integer values for

@X

and

@Y

produce nice values for tracing.

5. Press r to plot the function. At what speed does the ticket exceed 250?

17–4 Applications

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PM Page 4 of 20

Graphing Inequalities

Problem

Procedure

Graph the inequality 0

.

4X

3 is true and where it is false.

N 3X + 5 < 0

.

2X + 4. Use the

TEST menu operations to explore the values of X where the inequality

1. Press z. Select

Dot

,

Simul

, and the default settings.

Setting

Dot

mode changes all graph style icons to í (dot) in the

Y=

editor.

2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as

Y

4

and the right side as

Y

5

.

3. Enter the statement of the inequality as

Y

6

. This function evaluates to

1

if true or

0

if false.

4. Press q

6

to graph the inequality in the standard window.

5. Press r † † to move to

Y

6

. Then press | and ~ to trace the inequality, observing the value of

Y

.

6. Press o. Turn off

Y

4

,

Y

5

, and

Y

6

. Enter equations to graph only the inequality.

7. Press r. Notice that the values of

Y

7

and

Y

8

are zero where the inequality is false.

Applications 17–5

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 5 of 20

Solving a System of Nonlinear Equations

Problem

Procedure

Using a graph, solve the equation X 3

N 2X = 2cos(X). Stated another way, solve the system of two equations and two unknowns: Y = X 3

N2X and Y = 2cos(X). Use ZOOM

factors to control the decimal places displayed on the graph.

1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions.

2. Press q

4

to select

4:ZDecimal

. The display shows that two solutions may exist (points where the two functions appear to intersect).

3. Press q ~

4

to select

4:SetFactors

from the

ZOOM

MEMORY

menu. Set

XFact=10

and

YFact=10

.

4. Press q

2

to select

2:Zoom In

. Use |, ~, }, and † to move the free-moving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the

X

and

Y

values have one decimal place.

5. Press Í to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the

X

and

Y

values have two decimal places.

6. Press Í to zoom in again. Move the free-moving cursor onto a point exactly on the intersection. Notice the number of decimal places.

7. Press y [

CALC

]

5

to select

5:intersect

. Press Í to select the first curve and Í to select the second curve.

To guess, move the trace cursor near the intersection. Press

Í. What are the coordinates of the intersection point?

8. Press q

4

to select

4:ZDecimal

to redisplay the original graph.

9. Press q. Select

2:Zoom In

and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display.

17–6 Applications

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 6 of 20

Using a Program to Create the Sierpinski Triangle

Setting up the

Program

Program

This program creates a drawing of a famous fractal, the

Sierpinski Triangle, and stores the drawing to a picture. To begin, press  ~ ~

1

. Name the program

SIERPINS

, and then press Í. The program editor is displayed.

PROGRAM:SIERPINS

:FnOff :ClrDraw

:PlotsOff

:AxesOff

!

!

Set viewing window.

:For(K,1,3000)

:rand!

:If N1 à 3

:Then

:.5X!

!

:End

:If 1 à 3 <N and N2 à 3

:Then

!

!

:End

:If 2 à 3 <N

:Then

:.5(1+X)!

:.5Y!

:End

:Pt-On(X,Y)

:End

:StorePic 6

Beginning of

If

If

If

/

Then

group

/

Then

group.

/

Then

group.

For

Draw point.

End of

For

group.

Store picture.

group.

After you execute the program above, you can recall and display the picture with the instruction

RecallPic 6

.

Applications 17–7

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 7 of 20

Graphing Cobweb Attractors

Problem

Procedure

Using

Web

format, you can identify points with attracting and repelling behavior in sequence graphing.

1. Press z. Select

Seq

and the default mode settings. Press y [

FORMAT

]. Select

Web

format and the default format settings.

2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K

X(1NX).

u(n)=Ku(nN1)(1Nu(nN1)) u(nMin)=.01

3. Press y [

QUIT

] to return to the home screen, and then store

2.9

to

K

.

4. Press p. Set the window variables.

nMin=0 Xmin=0

nMax=10

PlotStart=1

PlotStep=1

Xmax=1

Xscl=1

Ymin=M.26

Ymax=1.1

Yscl=1

5. Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor.

6. Change

K

to

3.44

and trace the graph to show a cobweb with two attractors.

7. Change

K

to

3.54

and trace the graph to show a cobweb with four attractors.

17–8 Applications

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

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Using a Program to Guess the Coefficients

Setting Up the

Program

Program

This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct.

PROGRAM:GUESS

:PlotsOff :Func

:FnOff :Radian

:ClrHome

!

!

:GraphStyle(1,1)

:GraphStyle(2,5)

:FnOff 2

!

:randInt(1,10)!

:0!

!

!Xmin

!

!

!

:L10!

!

!

:1!

!

:DispGraph

:Pause

:FnOn 2

:Lbl Z

:Prompt C,D

:DispGraph

:Pause

:If C=A

:Text(1,1,"C IS OK")

:If CƒA

:Text(1,1,"C IS WRONG")

:If D=B

:Text(1,50,"D IS OK")

:If DƒB

:Text(1,50,"D IS WRONG")

:DispGraph

:Pause

:If C=A and D=B

:Stop

:Goto Z

Define equations.

Set line and path graph styles.

Initialize coefficients.

Set viewing window.

Display graph.

Prompt for guess.

Display graph.

Display results.

Display graph.

Quit if guesses are correct.

Applications 17–9

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PM Page 9 of 20

Graphing the Unit Circle and Trigonometric Curves

Problem

Procedure

Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them.

Any function that can be plotted in

Func

mode can be plotted in

Par

mode by defining the

X

component as

T

and the

Y

component as F

(T)

.

1. Press z. Select

Par

,

Simul

, and the default settings.

2. Press p. Set the viewing window.

Tmin=0

Tmax=2p

Tstep=.1

Xmin=L2

Xmax=7.4

Xscl=pà2

Ymin=L3

Ymax=3

Yscl=1

3. Press o. Turn off all functions and stat plots. Enter the expressions to define the unit circle centered on (0,0).

4. Enter the expressions to define the sine curve.

5. Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function “unwrap” from the unit circle.

Note: You can generalize the unwrapping. Replace

sin(T) in Y

2T

with any other trig function to unwrap that function.

17–10 Applications

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 10 of 20

Finding the Area between Curves

Problem

Procedure

Find the area of the region bounded by f(x) g(x) x

= 300x / ( x 2 + 625)

= 3cos(

= 75

.

1x)

1. Press z. Select the default mode settings.

2. Press p. Set the viewing window.

Xmin=0

Xmax=100

Xscl=10

Ymin=L5

Ymax=10

Yscl=1

Xres=1

3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions.

Y

1

=300Xà(X

2

+625)

Y

2

=3cos(.1X)

4. Press y [

CALC

]

5

to select

5:Intersect

. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of

X

at the intersection, which is the lower limit of the integral, is stored in

Ans

and

X

.

5. Press y [

QUIT

] to go to the home screen. Press y [

DRAW

]

7

and use

Shade(

to see the area graphically.

Shade(Y

2

,Y

1

,Ans,75)

6. Press y [

QUIT

] to return to the home screen. Enter the expression to evaluate the integral for the shaded region.

fnInt(Y

1

–Y

2

,X,Ans,75)

The area is

325.839962

.

Applications 17–11

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 11 of 20

Using Parametric Equations: Ferris Wheel Problem

Problem

Procedure

Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane.

A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds. The parametric equations below describe the location of a ferris wheel passenger at time T, where a is the angle of rotation, (0,0) is the bottom center of the ferris wheel, and

(10,10) is the passenger’s location at the rightmost point, when

T=0.

X(T) = r cos a

Y(T) = r + r sin a where a = 2pTs and r = d à2

A person standing on the ground throws a ball to the ferris wheel passenger. The thrower’s arm is at the same height as the bottom of the ferris wheel, but 25 meters (b) to the right of the ferris wheel’s lowest point (25,0). The person throws the ball with velocity (v

0

) of 22 meters per second at an angle (q) of 66¡ from the horizontal. The parametric equations below describe the location of the ball at time T.

X(T) = b N Tv

Y(T) = Tv

0

cosq

sinq N (g à2 ) T

2

9.8 m/ sec

2

0 where g =

1. Press z. Select

Par

,

Simul

, and the default settings.

Simul

(simultaneous) mode simulates the two objects in motion over time.

2. Press p. Set the viewing window.

Tmin=0

Tmax=12

Xmin=L13

Xmax=34

Tstep=.1

Xscl=10

Ymin=0

Ymax=31

Yscl=10

3. Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for

X

2T

to ëëëë (path).

17–12 Applications

Tip: Try setting the graph styles to

ëëëë X

1T

and

ìììì X

2T

, which simulates a chair on the ferris wheel and the ball flying through the air when you press s.

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Procedure

(continued)

4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel.

5. Press p. Change the viewing window to concentrate on this portion of the graph.

Tmin=1 Xmin=0 Ymin=10

Tmax=3

Tstep=.03

Xmax=23.5

Xscl=10

Ymax=25.5

Yscl=10

6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross.

Notice the values of

X

,

Y

, and

T

.

7. Press † to move to the path of the ball. Notice the values of

X

and

Y

(

T

is unchanged). Notice where the cursor is located.

This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first?

You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.

Applications 17–13

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 13 of 20

Demonstrating the Fundamental Theorem of Calculus

Problem 1

Procedure 1

Using the functions

fnInt(

and

nDeriv(

from the

MATH

menu to graph functions defined by integrals and derivatives demonstrates graphically that:

F(x) =

D x

[‰

1 x

1àt dt = ln(x), x > 0 and that

1 x

1àt dt

]

= 1àx

1. Press z. Select the default settings.

2. Press p. Set the viewing window.

Xmin=.01

Xmax=10

Xscl=1

Ymin=M1.5

Ymax=2.5

Yscl=1

Xres=3

3. Press o. Turn off all functions and stat plots. Enter the numerical integral of 1àT from 1 to X and the function ln(X). Set the graph style for

Y

1

to ç (line) and

Y

2

to

ë (path).

4. Press r. Press |, }, ~, and † to compare the values of

Y

1

and

Y

2

.

5. Press o. Turn off

Y

1

and

Y

2

, and then enter the numerical derivative of the integral of 1àX and the function 1àX. Set the graph style for

Y

3

to

çççç

(line) and

Y

4

to

è

(thick).

6. Press r. Again, use the cursor keys to compare the values of the two graphed functions,

Y

3

and

Y

4

.

17–14 Applications

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PM Page 14 of 20

Problem 2

Procedure 2

Explore the functions defined by y =

M

2 x

t 2 dt,

0 x

t 2 dt, and

2 x

t 2 dt

1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in

Y

5.

2. Press q

6

to select

6:ZStandard

.

3. Press r. Notice that the functions appear identical, only shifted vertically by a constant.

4. Press o. Enter the numerical derivative of

Y

5

in

Y

6

.

5. Press r. Notice that although the three graphs defined by

Y

5

are different, they share the same derivative.

Applications 17–15

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 15 of 20

Computing Areas of Regular N-Sided Polygons

Problem

Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr 2 .

Consider the formula A = NB 2 sin(pàN) cos(pàN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex.

Procedure

N = 4 sides N = 8 sides N = 12 sides

1. Press 

0

to select

0:Solver

from the

MATH

menu. Either the equation editor or the interactive solver editor is displayed. If the interactive solver editor is displayed, press

} to display the equation editor.

2. Enter the formula as

0=ANNB

2 sin(p / N)cos(p / N)

, and then press Í. The interactive solver editor is displayed.

3. Enter

N=4

and

B=6

to find the area (

A

) of a square with a distance (

B

) from center to vertex of 6 centimeters.

4. Press } } to move the cursor onto

A

, and then press ƒ

[

SOLVE

]. The solution for

A

is displayed on the interactive solver editor.

5. Now solve for

B

for a given area with various number of sides. Enter

A=200

and

N=6

. To find the distance

B

, move the cursor onto

B

, and then press ƒ [

SOLVE

].

6. Enter

N=8

. To find the distance

B

, move the cursor onto

B

, and then press ƒ [

SOLVE

]. Find

B

for

N=9

, and then for

N=10

.

17–16 Applications

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PM Page 16 of 20

Procedure

(continued)

Find the area given

B=6

, and

N=10

,

100

,

150

,

1000

, and

10000

.

Compare your results with p6

2

(the area of a circle with radius

6), which is approximately 113.097.

7. Enter

B=6

. To find the area

A

, move the cursor onto

A

, and then press ƒ [

SOLVE

]. Find

A

for

N=10

, then

N=100

, then

N=150

, then

N=1000

, and finally

N=10000

. Notice that as

N

gets large, the area

A

approaches

pB

2

.

Now graph the equation to see visually how the area changes as the number of sides gets large.

8. Press z. Select the default mode settings.

9. Press p. Set the viewing window.

Xmin=0

Xmax=200

Xscl=10

Ymin=0

Ymax=150

Yscl=10

Xres=1

10.Press o. Turn off all functions and stat plots. Enter the equation for the area. Use

X

in place of

N

. Set the graph styles as shown.

11.Press r. After the graph is plotted, press

100

Í to trace to

X=100

. Press

150

Í. Press

188

Í. Notice that as

X

increases, the value of approximately 113.097.

Y

2

=pB

2

Y

converges to p6 , which is

(the area of the circle) is a horizontal asymptote to

Y

1

. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr large.

2

2

) as N gets

Applications 17–17

82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04

PM Page 17 of 20

Computing and Graphing Mortgage Payments

Problem

Procedure

You are a loan officer at a mortgage company, and you recently closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now.

1. Press z and set the fixed-decimal mode to

2

decimal places. Set the other mode settings to the defaults.

2. Press y [

FINANCE

]

1

to display the

TVM Solver

. Enter these values.

Note: Enter a positive number (

800) to show PMT as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter

0 for FV, since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period.

3. Move the cursor onto the

PV=

prompt, and then press ƒ

[

SOLVE

]. The present value, or mortgage amount, of the house is displayed at the

PV=

prompt.

17–18 Applications

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PM Page 18 of 20

Procedure

(continued)

Now compare the graph of the amount of interest with the graph of the amount of principal for each payment.

4. Press z. Set

Par

and

Simul

.

5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown.

Note: GPrn( and GInt( are located on the FINANCE CALC menu.

6. Press p. Set these window variables.

Tmin=1 Xmin=0 Ymin=0

Tmax=360

Tstep=12

Xmax=360

Xscl=10

Ymax=1000

Yscl=100

Tip: To increase the graph speed, change

Tstep to 24.

7. Press r. After the graph is drawn, press

240

Í to move the trace cursor to

T=240

, which is equivalent to 20 years of payments.

The graph shows that for the 240th payment (

X=240

), 358.03

of the 800 payment is applied to principal (

Y=358.03

).

Note: The sum of the payments (

Y

3T

=Y

1T

+Y

2T

) is always 800.

Applications 17–19

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PM Page 19 of 20

Computing and Graphing Mortgage Payments

(cont.)

Procedure

(continued)

8. Press † to move the cursor onto the function for interest defined by

X

2T

and

Y

2T

. Enter

240

.

The graph shows that for the 240th payment (

X=240

), 441.97

of the 800 payment is interest (

Y=441.97

).

9. Press y [

QUIT

] y [

FINANCE

]

9

to paste

9:bal(

to the home screen. Check the figures from the graph.

At which monthly payment will the principal allocation surpass the interest allocation?

17–20 Applications

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18

Memory

Management

Contents

Checking Available Memory

..........................................................................

Deleting Items from Memory

.........................................................................

Clearing Entries and List Elements

.............................................................

Resetting the TI-82 STATS

.............................................................................

4

5

2

3

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Checking Available Memory

MEMORY Menu

Displaying the

Check RAM

Screen

To display the

MEMORY

menu, press y [

MEM

].

MEMO

RY

1: Check RAM...

2: Delete...

3: Clear Entries

4: ClrAllLists

5: Reset...

Reports memory availability/usage.

Displays

Clears

Displays

DELETE FROM

ENTRY

(last-entry storage).

Clears all lists in memory.

RESET menu.

menu (all/defaults).

Check RAM

displays the

Check RAM

screen. The top line reports the total amount of available memory. The remaining lines report the amount of memory each variable type is using.

You can check this screen to see whether you need to delete variables from memory to make room for new data, such as programs.

To check RAM usage, follow these steps.

1. Press y [

MEM

] to display the

MEMORY

menu.

2. Select

1:Check RAM

to display the

Check RAM

screen. The

TI-82 STATS expresses memory quantities in bytes.

Note: The $ in the left column of the bottom row indicates that you can scroll or page down to view more variable types.

Note:

Real, List, Y.Vars, and Prgm variable types never reset to zero, even after memory is cleared.

To leave the

Check RAM

screen, press either y [

QUIT

] or

‘. Both options display the home screen.

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Deleting Items from Memory

Deleting an Item

To increase available memory by deleting the contents of any variable (real or complex number, list, matrix,

Y=

variable, program, picture, graph database, or string), follow these steps.

1. Press y [

MEM

] to display the

MEMORY

menu.

2. Select

2:Delete

to display the

DELETE FROM

secondary menu.

3. Select the type of data you want to delete, or select

1:All

for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using.

For example, if you select

4:List

, the

DELETE:List

screen is displayed.

4. Press } and † to move the selection cursor (

4

) next to the item you want to delete, and then press Í. The variable is deleted from memory. You can delete individual variables one by one from this screen.

To leave any

DELETE:

screen without deleting anything, press y [

QUIT

], which displays the home screen.

Note: You cannot delete some system variables, such as the lastanswer variable Ans and the statistical variable RegEQ.

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Clearing Entries and List Elements

Clear Entries Clear Entries

clears the contents of the

ENTRY

(last entry) storage area (Chapter 1). To clear the

ENTRY

storage area, follow these steps.

1. Press y [

MEM

] to display the

MEMORY

menu.

2. Select

3:Clear Entries

to paste the instruction to the home screen.

3. Press Í to clear the

ENTRY

storage area.

ClrAllLists

To cancel

Clear Entries

, press ‘.

Note: If you select

3:Clear Entries from within a program, the Clear

Entries instruction is pasted to the program editor, and the Entry

(last entry) is cleared when the program is executed.

ClrAllLists

sets to

0

the dimension of each list in memory.

To clear all elements from all lists, follow these steps.

1. Press y [

MEM

] to display the

MEMORY

menu.

2. Select

4:ClrAllLists

to paste the instruction to the home screen.

3. Press Í to set to

0

the dimension of each list in memory.

To cancel

ClrAllLists

, press ‘.

ClrAllLists

does not delete list names from memory, from the

LIST NAMES

menu, or from the stat list editor.

Note: If you select

4:ClrAllLists from within a program, the

ClrAllLists instruction is pasted to the program editor. The lists are cleared when the program is executed.

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Resetting the TI-82 STATS

RESET

Secondary Menu

The

RESET

secondary menu gives you the option of resetting all memory (including default settings) or resetting the default settings while preserving other data stored in memory, such as programs and

Y=

functions.

Resetting All

Memory

Resetting all memory on the TI-82 STATS restores memory to the factory settings. It deletes all nonsystem variables and all programs. It resets all system variables to the default settings.

Tip: Before you reset all memory, consider restoring sufficient available memory by deleting only selected data (page 18 .3).

To reset all memory on the TI-82 STATS, follow these steps.

1. Press y [

MEM

] to display the

MEMORY

menu.

2. Select

5:Reset

to display the

RESET

secondary menu.

3. Select

1:All Memory

to display the

RESET MEMORY

tertiary menu.

4. Read the message below the

RESET MEMORY

menu.

To cancel memory reset and return to the home screen, select

1:No

.

To erase from memory all data and programs, select

2:Reset

. All factory defaults are restored.

Mem cleared

is displayed on the home screen.

Note: When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast (Chapter 1).

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Resetting the TI-82 STATS

(continued)

Resetting

Defaults

When you reset defaults on the TI-82 STATS, all defaults are restored to the factory settings. Stored data and programs are not changed.

These are some examples of TI-82 STATS defaults that are restored by resetting the defaults.

Mode settings such as

Normal

(notation);

Func

(graphing);

Real

(numbers); and

Full

(screen)

Y=

functions off

Window variable values such as

Xmin=L10

;

Xmax=10

;

Xscl=1

;

Yscl=1

; and

Xres=1

Stat plots off

Format settings such as

CoordOn

(graphing coordinates on);

AxesOn

; and

ExprOn

(expression on)

rand

seed value to 0

To reset all TI-82 STATS factory defaults, follow these steps.

1. Press y [

MEM

] to display the

MEMORY

menu.

2. Select

5:Reset

to display the

RESET

secondary menu.

3. Select

2:Defaults

to display the

RESET DEFAULTS

tertiary menu.

4. Consider the consequences of resetting defaults.

To cancel reset and return to the home screen, select

1:No

.

To restore factory default settings, select

2:Reset

.

Default settings are restored.

Defaults set

is displayed on the home screen.

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19

Communication

Link

Contents

Getting Started: Sending Variables

.............................................................

TI-82 STATS LINK

...............................................................................................

Selecting Items to Send

.......................................................................................

Receiving Items

.......................................................................................................

Transmitting Items

.................................................................................................

Transmitting Lists to a TI

-

82

..........................................................................

Transmitting from a TI

-

82 to a TI-82 STATS

.....................................

9

Backing Up Memory

............................................................................................

10

6

8

4

5

2

3

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Getting Started: Sending Variables

Getting Started is a fast-paced introduction. Read the chapter for details.

Create and store a variable and a matrix, and then transfer them to another

TI-82 STATS.

1. On the home screen of the sending unit, press

5

Ë

5

¿ ƒ

Q

. Press Í to store

5.5 to

Q

.

2. Press y [

[

] y [

[

]

1

¢

2

y [

]

] y [

[

]

3

¢

4

y [

]

] y [

]

] ¿ 

1

. Press

Í to store the matrix to

[A]

.

3. Connect the calculators with the link cable.

Push both ends in firmly.

4. On the receiving unit, press y [

LINK

] ~ to display the

RECEIVE

menu. Press

1

to select

1:Receive

. The message

Waiting...

is displayed and the busy indicator is on.

5. On the sending unit, press y [

LINK

] to display the

SEND

menu.

6. Press

2

to select

2:AllN

. The

AllN SELECT screen is displayed.

7. Press † until the selection cursor (

4

) is next to

[A] MATRX

. Press Í.

8. Press † until the selection cursor is next to

Q REAL

. Press Í. A square dot next to

[A]

and

Q

indicates that each is selected to send.

9. On the sending unit, press ~ to display the

TRANSMIT

menu.

10. On the sending unit, press

1

to select

1:Transmit

and begin transmission. The receiving unit displays the message

Receiving...

.When the items are transmitted, both units display the name and type of each transmitted variable.

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TI-82 STATS LINK

TI-82 STATS Link

Capabilities

The TI-82 STATS has a port to connect and communicate with another TI-82 STATS, a TI-82 STATS, the Calculator-Based

Laboratoryé (CBLé) System, the Calculator-Based Rangeré

(CBRé), or a personal computer. The unit-to-unit link cable is included with the TI-82 STATS. This chapter describes how to communicate with another calculator.

Linking Two

TI-82 STATS calculators

You can transfer all variables and programs to another

TI-82 STATS or backup the entire memory of a TI-82 STATS.

The software that enables this communication is built into the

TI-82 STATS. To transmit from one TI-82 STATS to another, follow the steps on pages 19

.

6 and 19

.

7.

Linking a TI-82 and a

TI-82 STATS

You can transfer from a TI

-

82 to a TI-82 STATS all variables and programs. Also, you can transfer from a TI-82 STATS to a TI

-

82 lists

L

1

through

L

6

.

The software that enables this communication is built into the

TI-82 STATS. To transmit data from a TI

-

82 to a TI-82 STATS, follow the steps on pages 19

.

6 and 19

.

7.

You cannot perform a memory backup from a TI

-

82 to a

TI-82 STATS.

The only data type you can transmit from a TI-82 STATS to a TI

-

82 is list data stored in

L

1

through

L

6

. Use the

LINK

SEND

menu item

5:Lists to TI82

(page 19

.

8).

Connecting Two

Calculators with the Cable

1. Insert either end of the cable into the port very firmly.

2. Insert the other end of the cable into the other calculator’s port.

Linking to a CBR or the CBL

System

CBR and the CBL System are optional accessories that connect to a TI-82 STATS with the unit-to-unit link cable. With a CBR or a CBL and a TI-82 STATS, you can collect and analyze realworld data.

Linking to a PC or Macintoshë

You can connect your TI-82 STATS to a personal computer using TI Connect™ software and a TI Connectivity cable. The software is included on the CD in the TI-82 STATS package.

When you connect to the TI Connect™ software, the TI-82

STATS calculator will be identified by TI Connect™ as a TI-83 calculator. Everything else should function as expected.

For more information, consult the TI Connect™ Help.

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Selecting Items to Send

LINK SEND Menu

To display the

LINK SEND

menu, press y [

LINK

].

SEND RECEIVE

1: All+...

2: AllN...

3: Prgm...

4: List...

5: Lists to TI82...

6: GDB...

7: Pic...

8: Matrix...

9: Real...

0: Complex...

A: Y-Vars...

B: String...

C: Back Up...

Displays all items selected.

Displays all items deselected.

Displays all programs names.

Displays all list names.

Displays list names

L

1

through

L

6

.

Displays all graph databases.

Displays all picture data types.

Displays all matrix data types.

Displays all real variables.

Displays all complex variables.

Displays all

Y= variables.

Displays all string variables.

Selects all for backup to TI-82 STATS.

When you select an item on the

LINK SEND

menu, the corresponding

SELECT

screen is displayed.

Note: Each

SELECT screen, except All+ SELECT, is displayed initially with no data selected.

Selecting Items to Send

To select items to send on the sending unit, follow these steps.

1. Press y [

LINK

] to display the

LINK SEND

menu.

2. Select the menu item that describes the data type to send.

The corresponding

SELECT

screen is displayed.

3. Press } and † to move the selection cursor (

4

) to an item you want to select or deselect.

4. Press Í to select or deselect the item. Selected names are marked with a

0

.

5. Repeat steps 3 and 4 to select or deselect additional items.

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Receiving Items

LINK RECEIVE

Menu

Receiving Unit

DuplicateName

Menu

Insufficient

Memory in

Receiving Unit

To display the

LINK RECEIVE

menu, press y [

LINK

] ~.

SEND RECEIVE

1: Receive

Sets unit to receive data transmission.

When you select

1:Receive

from the

LINK RECEIVE

menu on the receiving unit, the message

Waiting...

and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press

É, and then select

1:Quit

from the

Error in Xmit

menu.

To transmit, follow the steps on page 19

.

6.

When transmission is complete, the unit exits the receive mode.

You can select

1:Receive

again to receive more items. The receiving unit then displays a list of items received. Press y

[

QUIT

] to exit the receive mode.

During transmission, if a variable name is duplicated, the

DuplicateName

menu is displayed on the receiving unit.

DuplicateName

1: Rename

2: Overwrite

3: Omit

4: Quit

Prompts to rename receiving variable.

Overwrites data in receiving variable.

Skips transmission of sending variable.

Stops transmission at duplicate variable.

When you select

1:Rename

, the

Name=

prompt is displayed, and alpha-lock is on. Enter a new variable name, and then press

Í. Transmission resumes.

When you select

2:Overwrite

, the sending unit’s data overwrites the existing data stored on the receiving unit. Transmission resumes.

When you select

3:Omit

, the sending unit does not send the data in the duplicated variable name. Transmission resumes with the next item.

When you select

4:Quit

, transmission stops, and the receiving unit exits receive mode.

During transmission, if the receiving unit does not have sufficient memory to receive an item, the

Memory Full

menu is displayed on the receiving unit.

To skip this item for the current transmission, select

1:Omit

.

Transmission resumes with the next item.

To cancel the transmission and exit receive mode, select

2:Quit

.

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Transmitting Items

Transmitting

Items

To transmit selected items after you have selected items to send on the sending unit (page 19

.

4) and set the receiving unit to receive (page 19

.

5), follow these steps.

1. Press ~ on the sending unit to display the

TRANSMIT

menu.

2. Confirm that

Waiting...

is displayed on the receiving unit, which indicates it is set to receive (page 19

.

5).

3. Press Í to select

1:Transmit

. The name and type of each item are displayed line by line on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted.

Stopping a

Transmission

After all selected items have been transmitted, the message

Done

is displayed on both calculators. Press } and † to scroll through the names.

To stop a link transmission, press É. The

Error in Xmit

menu is displayed on both units. To leave the error menu, select

1:Quit

.

Error Conditions

A transmission error occurs after one or two seconds if:

A cable is not attached to the sending unit.

A cable is not attached to the receiving unit.

Note: If the cable is attached, push it in firmly and try again.

The receiving unit is not set to receive transmission.

You attempt a backup between a TI

-

82 and a TI-82 STATS.

You attempt a data transfer from a TI-82 STATS to a TI

-

82 with data other than lists

L

1

through

L

6

or without using menu item

5:Lists to TI82

.

Although a transmission error does not occur, these two conditions may prevent successful transmission.

You try to use

Get(

with a calculator instead of a CBL or

CBR.

You try to use

GetCalc(

with a TI

-

82 instead of a

TI-82 STATS.

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Transmitting

Items to an

Additional

TI-82 STATS

After sending or receiving data, you can repeat the same transmission to additional TI-82 STATS units—from either the sending unit or the receiving unit—without having to reselect data to send. The current items remain selected.

Note: You cannot repeat transmission if you selected All+ or All ..

To transmit to an additional TI-82 STATS, follow these steps.

1. Set the TI-82 STATS to receive (page 19

.

5).

2. Do not select or deselect any new items to send. If you select or deselect an item, all selections or deselections from the previous transmission are cleared.

3. Disconnect the link cable from one TI-82 STATS and connect it to the additional TI-82 STATS.

4. Set the additional TI-82 STATS to receive (page 19

.

5).

5. Press y [

LINK

] on the sending TI-82 STATS to display the

LINK SEND

menu.

6. Select the menu item that you used for the last transmission.

The data from your last transmission is still selected.

7. Press ~ to display the

LINK TRANSMIT

menu.

8. Confirm that the receiving unit is set to receive (page 19

.

5).

9. Press Í to select

1:Transmit

and begin transmitting.

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Transmitting Lists to a TI

-

82

Transmitting

Lists to a TI-82

The only data type you can transmit from a TI-82 STATS to a

TI

-

82 is list data stored in

L

1

through

L

6

.

To transmit to a TI

-

82 the list data that is stored to

TI-82 STATS lists

L

1

,

L

2

,

L

3

,

L

4

,

L

5

, or

L

6

, follow these steps.

1. Set the TI

-

82 to receive (page 19

.

5).

2. Press y [

LINK

]

5

on the sending TI-82 STATS to select

5:Lists to TI82

. The

SELECT

screen is displayed.

3. Select each list to transmit.

4. Press ~ to display the

LINK TRANSMIT

menu.

5. Confirm that the receiving unit is set to receive (page 19

.

5).

6. Press Í to select

1:Transmit

and begin transmitting.

Note: If dimension > 99 for a TI-82 STATS list that is selected to send, the receiving TI-82 will truncate the list at the ninety-ninth element during transmission.

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Transmitting from a TI

-

82 to a TI-82 STATS

Resolved

Differences between the

TI-82 and

TI-82 STATS

Unresolved

Differences between the

TI-82 and

TI-82 STATS

Generally, you can transmit items to a TI-82 STATS from a

TI

-

82, but differences between the two products may affect some transmitted data. This table shows differences for which the software built into the TI-82 STATS automatically adjusts when a TI-82 STATS receives TI

-

82 data.

TI.82

nMin

nStart

Un

Vn

UnStart

VnStart

TblMin

TI-82 STATS u v

PlotStart

nMin u(nMin) v(nMin)

TblStart

For example, if you transmit from a TI

-

82 to a TI-82 STATS a program that contains

nStart

on a command line and then display the program on the receiving TI-82 STATS, you will see that

nMin

has automatically replaced

nStart

on the command line.

The software built into the TI-82 STATS cannot resolve some differences between the TI

-

82 and TI-82 STATS, which are described below. You must edit the data on the TI-82 STATS after you transmit to account for these differences, or the

TI-82 STATS will misinterpret the data.

The TI-82 STATS reinterprets TI-82 STATS prefix functions to include open parentheses, which may add extraneous parentheses to transmitted expressions.

For example, if you transmit

sin X+5

from a TI

-

82 to a

TI-82 STATS, the TI-82 STATS reinterprets it as

sin(X+5

.

Without a closing parenthesis after

X

, the TI-82 STATS interprets this as

sin(X+5)

, not the sum of

5

and

sin(X)

.

If a TI

-

82 instruction that the TI-82 STATS cannot translate is transmitted, the

ERR:INVALID

menu is displayed when the

TI-82 STATS attempts to execute the instruction. For example, on the TI

-

82, the character group

U n-1

is pasted to the cursor location when you press y [

UnN1

]. The TI-82 STATS cannot directly translate

U n-1

to the TI-82 STATS syntax

u(nN1)

, so the

ERR:INVALID

menu is displayed.

Note: TI-82 STATS implied multiplication rules differ from those of the

äääX,

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Backing Up Memory

Memory Backup

To copy the exact contents of memory in the sending

TI-82 STATS to the memory of the receiving TI-82 STATS, put the other unit in receive mode. Then, on the receiving unit, select

C:Back Up

from the

LINK SEND

menu.

Warning:

C:Back Up

overwrites the memory in the receiving unit; all information in the memory of the receiving unit is lost.

Note: If you do not want to do a backup, select

2:Quit to return to the LINK SEND menu.

Select

1:Transmit

to begin transmission.

Receiving Unit

As a safety check to prevent accidental loss of memory, the message

WARNING . Backup

is displayed when the receiving unit receives notice of a backup.

To continue with the backup process, select

1:Continue

. The backup transmission begins.

To prevent the backup, select

2:Quit

.

Note: If a transmission error is returned during a backup, the receiving unit is reset.

Memory Backup

Complete

When the backup is complete, both the sending calculator and receiving calculator display a confirmation screen.

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Contents

A

Tables and Reference

Information

Table of Functions and Instructions

............................................................

2

TI-82 STATS Menu Map

..................................................................................

39

Variables

.......................................................................................................................

49

Statistics Formulas

.................................................................................................

50

Financial Formulas

................................................................................................

54

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Table of Functions and Instructions

Functions return a value, list, or matrix. You can use functions in an expression.

Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.

From the

CATALOG

, you can paste any function or instruction to the home screen or to a command line in the program editor. However, some functions and instructions are not valid on the home screen. The items in this table appear in the same order as they appear in the

CATALOG

.

indicates keystrokes that are valid in the program editor only. Some keystrokes display

menus that are available only in the program editor. Others paste mode, format, or tableset instructions only when you are in the program editor.

Function or Instruction/

Arguments

abs(

value

) abs(

complex value

)

valueA

and

valueB

angle(

value

)

ANOVA(

list1

,

list2

[

,

list3

,

...

,

list20]

)

Ans

Result

Returns the absolute value of a real number, expression, list, or matrix.

Returns the magnitude of a complex number or list.

Returns 1 if both valueA and

valueB are ƒ 0. valueA and

valueB can be real numbers, expressions, or lists.

Returns the polar angle of a complex number or list of complex numbers.

Performs a one-way analysis of variance for comparing the means of two to 20 populations.

Returns the last answer.

Key or Keys/

Menu or Screen/Item

NUM

1:abs(

2-13

10-10

CPX

5:abs(

2-19 y [

TEST

]

LOGIC

1:and

2-26

CPX

4:angle(

2-19

TESTS

F:ANOVA(

13-25 y [

ANS

] 1-18

A–2 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 2 of 58

Function or Instruction/

Arguments Result

augment(

matrixA

,

matrixB

)

Returns a matrix, which is matrixB appended to matrixA as new columns.

augment(

listA

,

listB

)

Returns a list, which is listB concatenated to the end of listA.

AxesOff

AxesOn a+b

i

bal(

npmt[

,

roundvalue]

) binomcdf(

numtrials

,

p[

,

x]

) binompdf(

numtrials

,

p[

,

x]

) c

2 cdf(

lowerbound

,

upperbound

,

df

)

Turns off the graph axes.

Turns on the graph axes.

Sets the mode to rectangular complex number mode (a+bi).

Computes the balance at npmt for an amortization schedule using stored values for

PV

,

æ

, and

PMT

and rounds the computation to roundvalue.

Computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.

Computes a probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.

Computes the c 2 distribution probability between lowerbound and upperbound for the specified degrees of freedom df.

Key or Keys/

Menu or Screen/Item

MATH

7:augment(

10-14 y [

LIST

]

OPS

9:augment(

11-15

† y [

FORMAT

]

AxesOff

† y [

FORMAT

]

AxesOn

† z

a+b

i

y [

FINANCE

]

CALC

9:bal(

3-14

3-14

1-12 y [

DISTR

]

DISTR

A:binomcdf(

y [

DISTR

]

DISTR

0:binompdf(

y [

DISTR

]

DISTR

7:c

2 cdf(

14-9

13-33

13-33

13-31

Tables and Reference Information A–3

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 3 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

c

2 pdf(

x

,

df

) c

2

.Test(

observedmatrix

,

expectedmatrix

[

,

drawflag]

)

Circle(

X

,

Y

,

radius

)

Clear Entries

ClrAllLists

ClrDraw

ClrHome

ClrList

listname1

[

,

listname2

, ...,

listname n]

ClrTable conj(

value

)

Connected

Result

Computes the probability density function (pdf) for the c 2 distribution at a specified x value for the specified degrees of freedom df.

Performs a chi-square test.

drawflag=

1

draws results;

drawflag=

0

calculates results.

Draws a circle with center (X,Y) and radius.

Clears the contents of the Last

Entry storage area.

Sets to

0

the dimension of all lists in memory.

Clears all drawn elements from a graph or drawing.

Clears the home screen.

Sets to

0

the dimension of one or more listnames.

Clears all values from the table.

Returns the complex conjugate of a complex number or list of complex numbers.

Sets connected plotting mode; resets all Y= editor graph-style settings to ç .

Key or Keys/

Menu or Screen/Item y [

DISTR

]

DISTR

6:c

2 pdf(

13-31

† …

TESTS

C:c

2

.Test(

y [

DRAW

]

DRAW

9:Circle( y [

MEM

]

MEMORY

3:Clear Entries

y [

MEM

]

MEMORY

4:ClrAllLists

y [

DRAW

]

DRAW

1:ClrDraw

13-22

8-11

18-4

18-4

8-4

† 

I/O

8:ClrHome

16-20

EDIT

4:ClrList

12-20

† 

I/O

9:ClrTable

16-20

CPX

1:conj(

2-18

† z

Connected

1-11

A–4 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 4 of 58

Function or Instruction/

Arguments

CoordOff

CoordOn cos(

value

) cos L1 (

value

) cosh(

value

) cosh

L1

(

value

)

CubicReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

cumSum(

list

) cumSum(

matrix

) dbd(

date1

,

date2

)

value

4Dec

Result

Turns off cursor coordinate value display.

Turns on cursor coordinate value display.

Returns cosine of a real number, expression, or list.

Key or Keys/

Menu or Screen/Item

† y [

FORMAT

]

CoordOff

† y [

FORMAT

]

CoordOn

3-14

3-14

Returns arccosine of a real number, expression, or list.

Returns hyperbolic cosine of a real number, expression, or list.

Returns hyperbolic arccosine of a real number, expression, or list.

Fits a cubic regression model to

Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

2-3 y [

COS

L1

]

2-3 y [

CATALOG

]

cosh(

15-10 y [

CATALOG

]

cosh

L1

(

15-10

CALC

6:CubicReg

12-26

Returns a list of the cumulative sums of the elements in list, starting with the first element.

Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom.

Calculates the number of days between date1 and date2 using the actual-day-count method.

Displays a real or complex number, expression, list, or matrix in decimal format.

y [

LIST

]

OPS

6:cumSum(

MATH

0:cumSum(

y [

FINANCE

]

CALC

D:dbd(

MATH

2:4Dec

11-12

10-15

14-13

2-5

Tables and Reference Information A–5

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 5 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

Degree

DelVar

variable

DependAsk

DependAuto det(

matrix

)

DiagnosticOff

DiagnosticOn dim(

listname

) dim(

matrixname

)

length

!

listname

)

{

rows

,

columns

}

!

dim(

matrixname

)

Disp

Disp

[valueA

,

valueB

,

valueC

,

...

,

value n]

Result

Sets degree angle mode.

Deletes from memory the contents of variable.

Sets table to ask for dependentvariable values.

Sets table to generate dependentvariable values automatically.

Returns determinant of matrix.

Sets diagnostics-off mode;

r

,

r

2

and

R

2

are not displayed as regression model results.

,

Sets diagnostics-on mode;

r

,

r

2

, and

R

2

are displayed as regression model results.

Returns the dimension of

listname.

Returns the dimension of

matrixname as a list.

Assigns a new dimension (length) to a new or existing listname.

Assigns new dimensions to a new or existing matrixname.

Displays the home screen.

Displays each value.

Key or Keys/

Menu or Screen/Item

† z

Degree

† 

CTL

G:DelVar

† 

I/O

3:Disp

1-11

16-15

† y [

TBLSET

]

Depend: Ask

7-3

† y [

TBLSET

]

Depend: Auto

7-3

MATH

1:det(

y [

CATALOG

]

DiagnosticOff

10-12

12-23 y [

CATALOG

]

DiagnosticOn

12-23 y [

LIST

]

OPS

3:dim(

MATH

3:dim(

y [

LIST

]

OPS

3:dim(

MATH

3:dim(

11-11

10-12

11-11

10-13

† 

I/O

3:Disp

16-18

16-18

A–6 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 6 of 58

Function or Instruction/

Arguments

DispGraph

DispTable

value

4DMS

Dot

DrawF

expression

DrawInv

expression

:DS<(

:

variable

,

value

)

commandA

:

commands

e^(

power

) e^(

list

)

Exponent:

value

E

exponent

Exponent:

list

E

exponent

Exponent:

matrix

E

exponent

4Eff(

nominal rate

,

compounding periods

)

Else

See

If:Then:Else

Result

Displays the graph.

Displays the table.

Displays value in DMS format.

Sets dot plotting mode; resets all

Y=

editor graph-style settings to í .

Draws expression (in terms of

X

) on the graph.

Draws the inverse of expression by plotting

X

values on the y-axis and

Y

values on the x-axis.

Decrements variable by 1; skips

commandA if variable < value.

Returns

e

raised to power.

Returns a list of

e

raised to a list of powers.

Returns value times 10 to the

exponent.

Returns list elements times 10 to the exponent.

Returns matrix elements times 10 to the exponent.

Computes the effective interest rate.

Key or Keys/

Menu or Screen/Item

† 

I/O

4:DispGraph

16-19

† 

I/O

5:DispTable

16-19 y [

ANGLE

]

ANGLE

4:4DMS

2-24

† z

Dot

1-11 y [

DRAW

]

DRAW

6:DrawF

y [

DRAW

]

DRAW

8:DrawInv

8-9

8-9

† 

CTL

B:DS<(

y [ e

x

]

16-14

2-4 y [ e

x

]

2-4 y [

EE

]

1-7 y [

EE

]

1-7 y [

EE

]

1-7 y [

FINANCE

]

CALC

C:4Eff(

14-12

Tables and Reference Information A–7

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 7 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

End

Eng

Equ4String(Y=

var

,Str

n

) expr(

string

)

ExpReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

ExprOff

ExprOn

lowerbound

,

upperbound

,

numerator df

,

denominator df

)

Fill(

value

,

matrixname

)

Fill(

value

,

listname

)

Fix

#

Float

Result

Identifies end of

For(

,

If

-

Then

-

Else

,

Repeat

, or

While

loop.

Sets engineering display mode.

Converts the contents of a Y=

var

to a string and stores it in

Str

n.

Converts string to an expression and executes it.

Fits an exponential regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Turns off the expression display during TRACE .

Turns on the expression display during TRACE .

Computes the Û distribution probability between lowerbound and upperbound for the specified

numerator df (degrees of freedom) and denominator df.

Key or Keys/

Menu or Screen/Item

† 

CTL

7:End

† z

Eng

y [

CATALOG

]

Equ4String(

16-12

1-10

15-7 y [

CATALOG

]

expr(

CALC

0:ExpReg

15-7

† y [

FORMAT

]

ExprOff

† y [

FORMAT

]

ExprOn

y [

DISTR

]

DISTR

9:

ÛÛ

cdf(

12-26

3-14

3-14

Stores value to each element in

matrixname.

Stores value to each element in

listname.

Sets fixed-decimal mode for # of decimal places.

Sets floating decimal mode.

13-32

MATH

4:Fill(

y [

LIST

]

OPS

4:Fill(

10-13

† z

Float

11-11

† z

0123456789

(select one) 1-10

1-10

A–8 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 8 of 58

Function or Instruction/

Arguments

fMax(

expression

,

variable

,

lower

,

upper[

,

tolerance]

) fMin(

expression

,

variable

,

lower

,

upper[

,

tolerance]

) fnInt(

expression

,

variable

,

lower

,

upper[

,

tolerance]

)

FnOff

[function#

,

function#

,...,

function n]

FnOn

[function#

,

function#

,...,

function n]

:For(

variable

,

begin

,

end

:

[

,

increment]

)

commands

:End

:

commands

fPart(

value

)

x

,

numerator df

,

denominator df

)

Result

Returns the value of variable where the local maximum of

expression occurs, between lower and upper, with specified

tolerance.

Returns the value of variable where the local minimum of

expression occurs, between lower and upper, with specified

tolerance.

Returns the function integral of

expression with respect to

variable, between lower and

upper, with specified tolerance.

Key or Keys/

Menu or Screen/Item

MATH

7:fMax(

MATH

6:fMin(

MATH

9:fnInt(

2-6

2-6

2-7

Deselects all Y= functions or specified

Y= functions.

Selects all

Y= functions or specified Y= functions.

Executes commands through

End

, incrementing variable from

begin by increment until

variable>end.

Y-VARS On/Off

2:FnOff

Y-VARS On/Off

1:FnOn

† 

CTL

4:For(

3-8

3-8

16-10

Returns the fractional part or parts of a real or complex number, expression, list, or matrix.

NUM

4:fPart(

2-14

10-11

Computes the Û distribution probability between lowerbound and upperbound for the specified

numerator df (degrees of freedom) and denominator df.

y [

DISTR

]

DISTR

8:

ÛÛ

13-32

Tables and Reference Information A–9

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 9 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

value

4Frac

Full

Func gcd(

valueA,valueB

) geometcdf(

p

,

x

) geometpdf(

p

,

x

)

Get(

variable

)

GetCalc(

variable

) getKey

Goto

label

Result

Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms.

Sets full screen mode.

Sets function graphing mode.

Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists.

Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.

Key or Keys/

Menu or Screen/Item

MATH

1:4Frac

2-5

† z

Full

1-12

† z

Func

NUM

9:gcd(

1-11

2-15 y [

DISTR

]

DISTR

E:geometcdf(

Computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. y [

DISTR

]

DISTR

D:geometpdf(

Gets data from the CBL System or

CBR and stores it in variable.

Gets contents of variable on another TI-82 STATS and stores it to variable on the receiving

TI-82 STATS.

Returns the key code for the current keystroke, or

0

, if no key is pressed.

Transfers control to label.

13-34

† 

I/O

A:Get(

16-21

† 

I/O

0:GetCalc(

16-21

† 

I/O

7:getKey

† 

CTL

0:Goto

13-34

16-20

16-13

A–10 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 10 of 58

Function or Instruction/

Arguments

GraphStyle(

function#

,

graphstyle#

)

GridOff

GridOn

G-T

Horiz

Horizontal

y

identity(

dimension

)

:

:

:If

condition commandA commands

:If

condition

:Then

:

commands

:End

:

commands

:If

condition

:Then

:

commands

:Else

:

commands

:End

:

commands

imag(

value

)

Result

Sets a graphstyle for function#.

Turns off grid format.

Turns on grid format.

Sets graph-table vertical split-screen mode.

Sets horizontal split-screen mode.

Draws a horizontal line at y.

Returns the identity matrix of

dimension rows × dimension columns.

If condition = 0 (false), skips

commandA.

Executes commands from

Then

to

End

if condition = 1 (true).

Key or Keys/

Menu or Screen/Item

† 

CTL

H:GraphStyle(

16-15

† y [

FORMAT

]

GridOff

3-14

† y [

FORMAT

]

GridOn

† z

G-T

† z

Horiz

y [

DRAW

]

DRAW

3:Horizontal

MATH

5:identity(

3-14

1-12

1-12

8-6

10-13

† 

CTL

1:If

† 

CTL

2:Then

16-9

16-9

Executes commands from

Then

to

Else

if condition = 1 (true); from

Else

to

End

if condition = 0

(false).

† 

CTL

3:Else

16-10

Returns the imaginary (nonreal) part of a complex number or list of complex numbers.

CPX

3:imag(

2-18

Tables and Reference Information A–11

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 11 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

IndpntAsk

IndpntAuto

Input

Input

[variable]

Input

[

"

text

",

variable]

Input [

Str

n

,

variable]

inString(

string

,

substring

[

,

start]

) int(

value

)

GInt(

pmt1

,

pmt2

[

,

roundvalue]

) invNorm(

area[

,

m

,

s]

) iPart(

value

)

Result

Sets table to ask for independentvariable values.

Sets table to generate independent-variable values automatically.

Displays graph.

Prompts for value to store to

variable.

Displays

Str

n and stores entered value to variable.

Returns the character position in

string of the first character of

substring beginning at start.

Returns the largest integer  a real or complex number, expression, list, or matrix.

Computes the sum, rounded to

roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule.

Key or Keys/

Menu or Screen/Item

† y [

TBLSET

]

Indpnt: Ask

† y [

TBLSET

]

Indpnt: Auto

7-3

7-3

† 

I/O

1:Input

† 

I/O

1:Input

† 

I/O

1:Input

y [

CATALOG

]

inString(

16-16

16-17

16-17

15-7

NUM

5:int(

2-14

10-11 y [

FINANCE

]

CALC

A:GInt(

14-9

Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by and s

.

m

Returns the integer part of a real or complex number, expression, list, or matrix.

y [

DISTR

]

DISTR

3:invNorm(

NUM

3:iPart(

13-30

2-14

10-11

A–12 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 12 of 58

Function or Instruction/

Arguments

irr(

CF0

,

CFList[

,

CFFreq]

)

:IS>(

variable

,

value

)

:

commandA

:

commands

ÙÙÙÙ

listname

LabelOff

LabelOn

Lbl

label

lcm(

valueA,valueB

) length(

string

)

Line(

X1

,

Y1

,

X2

,

Y2

)

Line(

X1

,

Y1

,

X2

,

Y2

,0)

Result

Returns the interest rate at which the net present value of the cash flows is equal to zero.

Increments variable by 1; skips commandA if

variable>value.

Identifies the next one to five characters as a user-created list name.

Turns off axes labels.

Turns on axes labels.

Creates a label of one or two characters.

Returns the least common multiple of valueA and valueB, which can be real numbers or lists.

Returns the number of characters in string.

Draws a line from (X1,Y1) to

(X2,Y2).

Erases a line from (X1,Y1) to

(X2,Y2).

Key or Keys/

Menu or Screen/Item y [

FINANCE

]

CALC

8:irr(

14-8

† 

CTL

A:IS>(

16-13 y [

LIST

]

OPS

B:

ÙÙÙÙ

† y [

FORMAT

]

LabelOff

† y [

FORMAT

]

LabelOn

† 

CTL

9:Lbl

NUM

8:lcm(

11-16

3-14

3-14

16-13

2-15 y [

CATALOG

]

length(

y [

DRAW

]

DRAW

2:Line(

y [

DRAW

]

DRAW

2:Line(

15-8

8-5

8-5

Tables and Reference Information A–13

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 13 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

LinReg(a+bx)

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

LinReg(ax+b)

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

LinRegTTest

[Xlistname

,

Ylistname

,

freqlist

,

alternative

,

regequ]

@List(

list

)

List

4 matr(

listname1

,

...

,

listname n

,

matrixname

) ln(

value

)

LnReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

log(

value

)

Result

Fits a linear regression model to

Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Key or Keys/

Menu or Screen/Item

CALC

8:LinReg(a+bx)

CALC

4:LinReg(ax+b)

12-26

Fits a linear regression model to

Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Performs a linear regression and a

t-test. alternative=

L1

is <;

alternative=

0

is ƒ; alternative=

1

is >.

Returns a list containing the differences between consecutive elements in list.

Fills matrixname column by column with the elements from each specified listname.

Returns the natural logarithm of a real or complex number, expression, or list.

Fits a logarithmic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

12-25

† …

TESTS

E:LinRegTTest

13-24 y [

LIST

]

OPS

11-12

7:@List(

y [

LIST

]

OPS

0:List

4 matr(

10-14

11-15

µ

CALC

9:LnReg

2-4

12-26

Returns logarithm of a real or complex number, expression, or list.

«

2-4

A–14 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 14 of 58

Function or Instruction/

Arguments

Logistic

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

Matr

4 list(

matrix

,

listnameA

,

...

,

listname n

)

Matr

4 list(

matrix

,

column#

,

listname

) max(

valueA

,

valueB

) max(

list

) max(

listA

,

listB

) max(

value,list

) mean(

list[

,

freqlist]

) median(

list[

,

freqlist]

)

Med-Med

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

Menu("

title

","

text1

",

label1

[

,

...

,"

text7

",

label7]

)

Result

Fits a logistic regression model to

Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Key or Keys/

Menu or Screen/Item

CALC

B:Logistic

12-27

Fills each listname with elements from each column in matrix.

Fills a listname with elements from a specified column# in matrix.

Returns the larger of valueA and

valueB.

Returns largest real or complex element in list.

Returns a real or complex list of the larger of each pair of elements in listA and listB.

y [

LIST

]

OPS

A:Matr

4 list(

y [

LIST

]

OPS

A:Matr

4 list(

NUM

7:max(

y [

LIST

]

MATH

2:max(

y [

LIST

]

MATH

2:max(

10-14

11-16

10-14

11-16

2-15

11-16

11-16

Returns a real or complex list of the larger of value or each list element.

Returns the mean of list with frequency freqlist.

Returns the median of list with frequency freqlist.

Fits a median-median model to

Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

y [

LIST

ä

MATH

2:max(

y [

LIST

]

MATH

3:mean(

y [

LIST

]

MATH

4:median(

CALC

3:Med-Med

11-16

11-16

11-16

12-25

Generates a menu of up to seven items during program execution.

† 

CTL

C:Menu(

16-14

Tables and Reference Information A–15

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PM Page 15 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

min(

valueA

,

valueB

) min(

list

) min(

listA

,

listB

) min(

value,list

)

valueA

nCr

valueB

value

nCr

list

list

nCr

value

listA

nCr

listB

nDeriv(

expression

,

variable

,

value[

,

H]

)

4Nom(

effective rate

,

compounding periods

)

Normal

Result

Returns smaller of valueA and

valueB.

Returns smallest real or complex element in list.

Returns real or complex list of the smaller of each pair of elements in listA and listB.

Returns a real or complex list of the smaller of value or each list element.

Returns the number of combinations of valueA taken

valueB at a time.

Returns a list of the combinations of value taken each element in list at a time.

Returns a list of the combinations of each element in list taken value at a time.

Returns a list of the combinations of each element in listA taken each element in listB at a time.

Returns approximate numerical derivative of expression with respect to variable at value, with specified H.

PRB

3:nCr

PRB

3:nCr

PRB

3:nCr

Key or Keys/

Menu or Screen/Item

NUM

6:min(

2-15 y [

LIST

]

MATH

1:min(

y [

LIST

]

MATH

1:min(

y [

LIST

]

MATH

1:min(

11-16

11-16

11-16

2-21

2-21

2-21

PRB

3:nCr

2-21

MATH

8:nDeriv(

2-7

Computes the nominal interest rate.

Sets normal display mode.

y [

FINANCE

]

CALC

B:4Nom(

† z

Normal

14-12

1-10

A–16 Tables and Reference Information

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PM Page 16 of 58

Function or Instruction/

Arguments

normalcdf(

lowerbound

,

upperbound[

,

m

,

s]

) normalpdf(

x[

,

m

,

s]

) not(

value

)

valueA

nPr

valueB

value

nPr

list

list

nPr

value

listA

nPr

listB

npv(

interest rate

,

CF0

,

CFList[

,

CFFreq]

)

valueA

or

valueB

Result

Computes the normal distribution probability between lowerbound and upperbound for the specified m

and s

.

Key or Keys/

Menu or Screen/Item y [

DISTR

]

DISTR

2:normalcdf(

13-27

Computes the probability density function for the normal distribution at a specified x value for the specified m

and s

.

Returns

0

if value is ƒ 0. value can be a real number, expression, or list.

Returns the number of permutations of valueA taken

valueB at a time.

Returns a list of the permutations of value taken each element in list at a time.

Returns a list of the permutations of each element in list taken value at a time.

Returns a list of the permutations of each element in listA taken each element in listB at a time.

y [

DISTR

]

DISTR

1:normalpdf(

y [

TEST

]

LOGIC

4:not(

PRB

2:nPr

PRB

2:nPr

PRB

2:nPr

PRB

2:nPr

13-29

2-26

2-21

2-21

2-21

2-21

Computes the sum of the present values for cash inflows and outflows.

Returns 1 if valueA or valueB is ƒ

0. valueA and valueB can be real numbers, expressions, or lists.

y [

FINANCE

]

CALC

7:npv(

y [

TEST

]

LOGIC

2:or

14-8

2-26

Tables and Reference Information A–17

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PM Page 17 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments Result

Output(

row

,

column

,"

text

")

Displays text beginning at specified row and column.

Output(

row

,

column

,

value

)

Param

Pause

Pause

[value]

Plot

#

(

type

,

Xlistname

,

Ylistname

,

mark

)

Plot

#

(

type

,

Xlistname

,

freqlist

)

Plot

#

(

type

,

Xlistname

,

freqlist

,

mark

)

Plot

#

(

type

,

datalistname

,

data axis

,

mark

)

PlotsOff

[

1,2,3

]

PlotsOn

[

1,2,3

]

Displays value beginning at specified row and column.

Sets parametric graphing mode.

Suspends program execution until you press Í.

Displays value; suspends program execution until you press Í.

Defines

Plot

# (

1

,

2

, or

3

) of type

Scatter

or

xyLine

for Xlistname and Ylistname using mark.

Defines

Plot

# (

1

,

2

, or

3

) of type

Histogram

or

Boxplot

for

Xlistname with frequency freqlist.

Defines

Plot

# (

1

,

2

, or

3

) of type

ModBoxplot

for Xlistname with frequency freqlist using mark.

Defines

Plot

# (

1

,

2

, or

3

) of type

NormProbPlot

for datalistname on data axis using mark. data

axis can be

X

or

Y

.

Deselects all stat plots or one or more specified stat plots (

1

,

2

, or

3

).

Selects all stat plots or one or more specified stat plots (

1

,

2

, or

3

).

Key or Keys/

Menu or Screen/Item

† 

I/O

6:Output(

† 

I/O

6:Output(

† z

Par

16-19

16-19

1-11

† 

CTL

8:Pause

† 

CTL

8:Pause

16-12

16-12

† y [

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

12-37

† y [

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

12-37

† y [

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

12-37

† y [

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

y [

STAT PLOT

]

12-37

STAT PLOTS

4:PlotsOff

12-35 y [

STAT PLOT

]

STAT PLOTS

5:PlotsOn

12-35

A–18 Tables and Reference Information

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PM Page 18 of 58

Function or Instruction/

Arguments

Pmt_Bgn

Pmt_End poissoncdf(

m

,

x

) poissonpdf(

m

,

x

)

Polar

complex value

4Polar

PolarGC prgm

name

GPrn(

pmt1

,

pmt2

[

,

roundvalue]

) prod(

list[

,

start

,

end]

)

Prompt

variableA

[

,

variableB

,

...

,

variable n

]

Result

Specifies an annuity due, where payments occur at the beginning of each payment period.

Specifies an ordinary annuity, where payments occur at the end of each payment period.

Computes a cumulative probability at x for the discrete

Poisson distribution with specified mean m.

Computes a probability at x for the discrete Poisson distribution with the specified mean m.

Sets polar graphing mode.

Displays complex value in polar format.

Sets polar graphing coordinates format.

Executes the program name.

Computes the sum, rounded to

roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule.

Key or Keys/

Menu or Screen/Item y [

FINANCE

]

CALC

F:Pmt_Bgn

14-13 y [

FINANCE

]

CALC

E:Pmt_End

y [

DISTR

]

DISTR

C:poissoncdf(

14-13

13-34 y [

DISTR

]

DISTR

B:poissonpdf(

13-33

† z

Pol

CPX

7:4Polar

† y [

FORMAT

]

PolarGC

† 

CTRL

D:prgm

y [

FINANCE

]

CALC

0:GPrn(

1-11

2-19

3-13

16-15

14-9

Returns product of list elements between start and end.

Prompts for value for variableA, then variableB, and so on.

y [

LIST

]

MATH

6:prod(

† 

I/O

2:Prompt

11-18

16-18

Tables and Reference Information A–19

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PM Page 19 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

1.PropZInt(

x

,

n

[

,

confidence level]

)

2.PropZInt(

x1

,

n1

,

x2

,

n2

[

,

confidence level]

)

1.PropZTest(

p0

,

x

,

n

[

,

alternative

,

drawflag]

)

2.PropZTest(

x1

,

n1

,

x2

,

n2

[

,

alternative

,

drawflag]

)

Pt.Change(

x

,

y

)

Pt.Off(

x

,

y[

,

mark]

)

Pt.On(

x

,

y[

,

mark]

)

PwrReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

Result

Computes a one-proportion

z confidence interval.

Computes a two-proportion

z confidence interval.

Key or Keys/

Menu or Screen/Item

† …

TESTS

A:1.PropZInt(

13-20

† …

TESTS

B:2.PropZInt(

13-21

† …

TESTS

5:1.PropZTest(

Computes a one-proportion z test.

alternative=

L1

is <; alternative=

0

is ƒ; alternative=

1

is >.

drawflag=

1

draws results;

drawflag=

0

calculates results.

Computes a two-proportion z test.

alternative=

L1

is <; alternative=

0

is ƒ; alternative=

1

is >.

drawflag=

1

draws results;

drawflag=

0

calculates results.

13-14

† …

TESTS

6:2.PropZTest(

13-15

Reverses a point at (x,y).

Erases a point at (x,y) using mark.

Draws a point at (x,y) using mark.

Fits a power regression model to

Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

y [

DRAW

]

POINTS

3:Pt.Change(

y [

DRAW

]

POINTS

2:Pt.Off(

y [

DRAW

]

POINTS

1:Pt.On(

CALC

A:PwrReg

8-15

8-15

8-14

12-27

A–20 Tables and Reference Information

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PM Page 20 of 58

Function or Instruction/

Arguments

Pxl.Change(

row

,

column

)

Pxl.Off(

row

,

column

)

Pxl.On(

row

,

column

) pxl.Test(

row

,

column

)

P4Rx(

r

,

P4Ry(

r

,

q

)

q

)

QuadReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

QuartReg

[Xlistname

,

Ylistname

,

freqlist

,

regequ]

Radian rand

[

(

numtrials

)

]

randBin(

numtrials

,

prob

[

,

numsimulations]

)

Result

Reverses pixel at (row,column);

0  row  62 and

0  column  94.

Erases pixel at (row,column);

0  row  62 and

0  column  94.

Draws pixel at (row,column);

0  row  62 and

0  column  94.

Returns 1 if pixel (row, column) is on, 0 if it is off; 0  row  62 and 0  column  94.

Returns

X

, given polar coordinates r and q or a list of polar coordinates.

Returns

Y

, given polar coordinates r and q or a list of polar coordinates.

Fits a quadratic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Key or Keys/

Menu or Screen/Item y [

DRAW ä

POINTS

6:Pxl.Change(

y [

DRAW

]

POINTS

5:Pxl.Off(

y [

DRAW

]

POINTS

4:Pxl.On(

y [

DRAW

]

POINTS

7:pxl.Test(

8-16

8-16

8-16

8-16 y [

ANGLE

]

ANGLE

7:P4Rx(

y [

ANGLE

]

ANGLE

8:P4Ry(

CALC

5:QuadReg

2-24

2-24

12-25

Fits a quartic regression model to

Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

CALC

7:QuartReg

12-26

Sets radian angle mode.

Returns a random number between 0 and 1 for a specified number of trials numtrials.

† z

Radian

PRB

1:rand

1-11

2-20

Generates and displays a random real number from a specified

Binomial distribution.

PRB

7:randBin(

2-22

Tables and Reference Information A–21

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PM Page 21 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

randInt(

lower,upper

[,numtrials]

)

Result

Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials.

Returns a random matrix of rows

(

1

99

) × columns (

1

99

).

Key or Keys/

Menu or Screen/Item

PRB

5:randInt(

2-22

randM(

rows

,

columns

) randNorm(

m

,

s

[

,

numtrials]

)

Generates and displays a random real number from a specified

Normal distribution specified by m and s for a specified number of trials numtrials.

r

e

^q

i

Real real(

value

)

RecallGDB

n

RecallPic

n

complex value

4Rect

RectGC ref(

matrix

)

Sets the mode to polar complex number mode (

r

e

^q

i).

Sets mode to display complex results only when you enter complex numbers.

Returns the real part of a complex number or list of complex numbers.

Restores all settings stored in the graph database variable

GDB

n.

Displays the graph and adds the picture stored in

Pic

n.

Displays complex value or list in rectangular format.

Sets rectangular graphing coordinates format.

Returns the row-echelon form of a matrix.

MATH

6:randM(

PRB

6:randNorm(

10-13

2-22

† z

r

e

^q

i

1-12

† z

Real

CPX

2:real(

y [

DRAW

]

STO

4:RecallGDB

y [

DRAW

]

STO

2:RecallPic

CPX

6:4Rect

1-12

2-18

8-20

8-18

2-19

† y [

FORMAT

]

RectGC

MATH

A:ref(

3-13

10-15

A–22 Tables and Reference Information

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PM Page 22 of 58

Function or Instruction/

Arguments

:Repeat

condition

:

commands

:End

:

commands

Return round(

value[

,

#decimals]

)

äääärow(

value

,

matrix

,

row

) row+(

matrix

,

rowA

,

rowB

)

äääärow+(

value

,

matrix

,

rowA

,

rowB

) rowSwap(

matrix

,

rowA

,

rowB

) rref(

matrix

)

R4Pr(

x

,

y

)

R4Pq(

x

,

y

)

Result

Executes commands until

condition is true.

Key or Keys/

Menu or Screen/Item

† 

CTL

6:Repeat

16-11

Returns to the calling program.

Returns a number, expression, list, or matrix rounded to

#decimals ( 9).

Returns a matrix with row of

matrix multiplied by value and stored in row.

Returns a matrix with rowA of

matrix added to rowB and stored in rowB.

Returns a matrix with rowA of

matrix multiplied by value, added to rowB, and stored in rowB.

† 

CTL

E:Return

NUM

2:round(

MATH

E:

äääärow(

MATH

D:row+(

MATH

F:

äääärow+(

Returns a matrix with rowA of

matrix swapped with rowB.

Returns the reduced row-echelon form of a matrix.

Returns

R

, given rectangular coordinates x and y or a list of rectangular coordinates.

Returns

q

, given rectangular coordinates x and y or a list of rectangular coordinates.

MATH

C:rowSwap(

MATH

B:rref(

y [

ANGLE

]

ANGLE

5:R4Pr(

y [

ANGLE

]

ANGLE

6:R4Pq(

16-15

2-13

10-16

10-16

10-16

10-16

10-15

2-24

2-24

Tables and Reference Information A–23

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PM Page 23 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

[listname1

,

listname2

,

freqlist1

,

freqlist2

,

alternative

,

drawflag]

(Data list input)

Sx1

,

n1

,

Sx2

,

n2[

,

alternative

,

drawflag]

(Summary stats input)

2.SampTInt

[listname1

,

listname2

,

freqlist1

,

freqlist2

,

confidence level

,

pooled]

(Data list input)

2.SampTInt

v

1

,

Sx1

,

n1

,

v

2

,

Sx2

,

n2

[

,

confidence level

,

pooled]

(Summary stats input)

2.SampTTest

[listname1

,

listname2

,

freqlist1

,

freqlist2

,

alternative

,

pooled

,

drawflag]

(Data list input)

Result

Performs a two-sample Û test.

alternative=

L1

is

<

; alternative=

0

is

ƒ

; alternative=

1

is

>

.

drawflag=

1

draws results;

drawflag=

0

calculates results.

Key or Keys/

Menu or Screen/Item

† …

TESTS

D:2.SampÛ

13-23

Performs a two-sample Û test.

alternative=

L1

is

<

; alternative=

0

is

ƒ

; alternative=

1

is

>

.

drawflag=

1

draws results;

drawflag=

0

calculates results.

† …

TESTS

D:2.SampÛ

† …

TESTS

0:2.SampTInt

13-23

Computes a two-sample t confidence interval. pooled=

1

pools variances; pooled=

0

does not pool variances.

Computes a two-sample t confidence interval. pooled=

1

pools variances; pooled=

0

does not pool variances.

Computes a two-sample t test.

alternative=

L1

is

<

; alternative=

0

is

ƒ

; alternative=

1

is

>

. pooled=

1

pools variances; pooled=

0

does not pool variances. drawflag=

1

draws results; drawflag=

0

calculates results.

13-19

† …

TESTS

0:2.SampTInt

13-19

† …

TESTS

4:2.SampTTest

13-13

A–24 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 24 of 58

Function or Instruction/

Arguments

2.SampTTest

v

1

,

Sx1

,

n1

,

v

2

,

Sx2

,

n2[

,

alternative

,

pooled

,

drawflag]

(Summary stats input)

2.SampZInt(

s v

1

,

n1

,

v

2

,

n2

1

,

s

freqlist1

,

freqlist2

,

confidence level]

)

(Data list input)

2

[

,

listname1

,

listname2

,

2.SampZInt(

s

1

,

s

2

,

v

1

,

n1

,

v

2

,

n2

[

,

confidence level]

)

(Summary stats input)

2.SampZTest(

s 1, s

freqlist1

,

freqlist2

,

alternative

,

drawflag]

)

(Data list input)

2

[

,

listname1

,

listname2

,

2.SampZTest(

s

1, s

2

,

[

,

alternative

,

drawflag]

)

(Summary stats input)

Sci

Select(

Xlistname

,

Ylistname

)

Result

Computes a two-sample t test.

alternative=

L1

is

<

; alternative=

0

is

ƒ

; alternative=

1

is

>

. pooled=

1

pools variances; pooled=

0

does not pool variances. drawflag=

1

draws results; drawflag=

0

calculates results.

Computes a two-sample z confidence interval.

Key or Keys/

Menu or Screen/Item

† …

TESTS

4:2.SampTTest

† …

TESTS

9:2.SampZInt(

13-13

Computes a two-sample z confidence interval.

Computes a two-sample z test.

alternative=

L1

is

<

; alternative=

0

is

ƒ

; alternative=

1

is

>

.

drawflag=

1

draws results;

drawflag=

0

calculates results.

Computes a two-sample z test.

alternative=

L1

is

<

; alternative=

0

is

ƒ

; alternative=

1

is

>

.

drawflag=

1

draws results;

drawflag=

0

calculates results.

† …

TESTS

13-18

† …

TESTS

9:2.SampZInt(

13-18

3:2.SampZTest(

13-12

† …

TESTS

3:2.SampZTest(

13-12

Sets scientific notation display mode.

Selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, Xlistname and

Ylistname.

† z

Sci

y [

LIST

]

OPS

8:Select(

1-10

11-12

Tables and Reference Information A–25

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PM Page 25 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

Send(

variable

) seq(

expression

,

variable

,

begin

,

end[

,

increment]

)

Seq

Sequential

SetUpEditor

SetUpEditor

listname1

[

,

listname2

,

...

,

listname20]

Shade(

lowerfunc

,

upperfunc[

,

Xleft

,

Xright

,

pattern

,

patres]

)

Shadec

2

(

lowerbound

,

upperbound

,

df

)

Result

Sends contents of variable to the

CBL System or CBR.

Returns list created by evaluating

expression with regard to

variable, from begin to end by

increment.

Sets sequence graphing mode.

Sets mode to graph functions sequentially.

Removes all list names from the stat list editor, and then restores list names

L

1

through

L

6

to columns

1

through

6

.

Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column

1

.

Draws lowerfunc and upperfunc in terms of

X

on the current graph and uses pattern and patres to shade the area bounded by

lowerfunc, upperfunc, Xleft, and

Xright.

Draws the density function for the c

2 distribution specified by degrees of freedom df and shades the area between lowerbound and

upperbound.

y [

DRAW

]

DRAW

7:Shade(

y [

DISTR

]

DRAW

3:Shadec

2

(

Key or Keys/

Menu or Screen/Item

† 

I/O

B:Send(

y [

LIST

]

OPS

5:seq(

16-21

11-11

† z

Seq

† z

Sequential

EDIT

5:SetUpEditor

1-11

1-12

12-21

EDIT

5:SetUpEditor

12-21

8-10

13-36

A–26 Tables and Reference Information

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PM Page 26 of 58

Function or Instruction/

Arguments

Shade

Ü(

lowerbound

,

upperbound

,

numerator df

,

denominator df

)

ShadeNorm(

lowerbound

,

upperbound[

,

m

,

s]

)

Shade_t(

lowerbound

,

upperbound

,

df

)

Simul sin(

value

) sin

L1

(

value

) sinh(

value

) sinh

L1

(

value

)

Result

Draws the density function for the

Û distribution specified by

numerator df and denominator df and shades the area between

lowerbound and upperbound.

Key or Keys/

Menu or Screen/Item y [

DISTR

]

DRAW

4:Shade

Ü

Draws the normal density function specified by m and s and shades the area between

lowerbound and upperbound.

Draws the density function for the

Student-t distribution specified by degrees of freedom df, and shades the area between lowerbound and

upperbound.

y [

DISTR

]

DRAW

1:ShadeNorm(

13-36

13-35 y [

DISTR

]

DRAW

2:Shade_t(

Sets mode to graph functions simultaneously.

Returns the sine of a real number, expression, or list.

Returns the arcsine of a real number, expression, or list.

Returns the hyperbolic sine of a real number, expression, or list.

Returns the hyperbolic arcsine of a real number, expression, or list.

13-36

† z

Simul

˜

1-12

2-3 y [

SIN

L1 ]

2-3 y [

CATALOG

]

sinh(

15-10 y [

CATALOG

]

sinh L1 (

15-10

Tables and Reference Information A–27

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PM Page 27 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

SinReg

[iterations

,

Xlistname

,

Ylistname

,

period

,

regequ]

solve(

expression

,

variable

,

guess

,{

lower

,

upper

})

SortA(

listname

)

SortA(

keylistname

,

dependlist1[

,

dependlist2

,

...,

dependlist n]

)

SortD(

listname

)

SortD(

keylistname

,

dependlist1[

,

dependlist2

,

...

,

dependlist n]

) stdDev(

list[

,

freqlist]

)

Stop

Store: value

!

variable

StoreGDB

n

Result

Attempts iterations times to fit a sinusoidal regression model to

Xlistname and Ylistname using a

period guess, and stores the regression equation to regequ.

Solves expression for variable, given an initial guess and lower and upper bounds within which the solution is sought.

Sorts elements of listname in ascending order.

Sorts elements of keylistname in ascending order, then sorts each

dependlist as a dependent list.

Key or Keys/

Menu or Screen/Item

CALC

C:SinReg

12-27

† 

MATH

0:solve(

2-12 y [

LIST

]

OPS

1:SortA(

y [

LIST

]

OPS

1:SortA(

11-10

12-20

11-10

12-20

Sorts elements of listname in descending order.

Sorts elements of keylistname in descending order, then sorts each

dependlist as a dependent list.

y [

LIST

]

OPS

2:SortD(

y [

LIST

]

OPS

2:SortD(

11-10

12-20

11-10

12-20

Returns the standard deviation of the elements in list with frequency freqlist.

Ends program execution; returns to home screen.

Stores value in variable.

Stores current graph in database

GDB

n.

y [

LIST

]

MATH

7:stdDev(

† 

CTL

F:Stop

¿ y [

DRAW

]

STO

3:StoreGDB

11-18

16-15

1-14

8-19

A–28 Tables and Reference Information

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PM Page 28 of 58

Function or Instruction/

Arguments

StorePic

n

String4Equ(

string

,Y=

var

) sub(

string

,

begin

,

length

) sum(

list[

,

start

,

end]

) tan(

value

) tan

L1

(

value

)

Tangent(

expression

,

value

) tanh(

value

) tanh

L1

(

value

) tcdf(

lowerbound

,

upperbound

,

df

)

Text(

row

,

column

,

text1

,

text2

,

...

,

text n

)

Result

Stores current picture in picture

Pic

n.

Converts string into an equation and stores it in

Y=

var.

Returns a string that is a subset of another string, from begin to

length.

Returns the sum of elements of

list from start to end.

Returns the tangent of a real number, expression, or list.

Returns the arctangent of a real number, expression, or list.

Key or Keys/

Menu or Screen/Item y [

DRAW

]

STO

1:StorePic

y [

CATALOG

]

String4Equ(

8-17

15-8 y [

CATALOG

]

sub(

15-9 y [

LIST

]

MATH

5:sum(

11-18

š y [

TAN

L1

]

2-3

Draws a line tangent to

expression at

X

=value.

Returns hyperbolic tangent of a real number, expression, or list.

Returns the hyperbolic arctangent of a real number, expression, or list.

2-3 y [

DRAW ä

DRAW

5:Tangent(

y [

CATALOG

]

tanh(

y [

CATALOG

]

tanh

L1

(

8-8

15-10

15-10

Computes the Student-t distribution probability between

lowerbound and upperbound for the specified degrees of freedom

df.

Writes text on graph beginning at pixel (row,column), where

0  row  57 and

0  column  94.

y [

DISTR

]

DISTR

5:tcdf(

y [

DRAW

]

DRAW

0:Text(

13-31

8-12

Then

See

If:Then

Tables and Reference Information A–29

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PM Page 29 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

Time

TInterval

[listname

,

freqlist

,

confidence level]

(Data list input)

TInterval

v

,

Sx

,

n

[

,

confidence level]

(Summary stats input)

tpdf(

x

,

df

)

Trace

T-Test

m

0[

,

listname

freqlist

,

alternative

,

drawflag]

(Data list input)

,

T-Test

m

0

,

v

,

Sx

,

n

[

,

alternative

,

drawflag]

(Summary stats input)

Result

Sets sequence graphs to plot with respect to time.

Computes a t confidence interval.

Computes a t confidence interval.

Key or Keys/

Menu or Screen/Item

† y [

FORMAT

]

Time

6-8

† …

TESTS

8:TInterval

13-17

† …

TESTS

8:TInterval

13-17 y [

DISTR

]

DISTR

4:tpdf(

Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom

df.

Displays the graph and enters

TRACE

mode.

Performs a t test with frequency

freqlist. alternative=

L1

is

<

;

alternative=

0

is

ƒ

; alternative=

1

is

>

. drawflag=

1

draws results;

drawflag=

0

calculates results.

r

† …

TESTS

2:T-Test

13-30

3-18

13-11

Performs a t test with frequency

freqlist. alternative=

L1

is < ;

alternative=

0

is ƒ ; alternative=

1

is >. drawflag=

1

draws results;

drawflag=

0

calculates results.

† …

TESTS

2:T-Test

13-11

A–30 Tables and Reference Information

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PM Page 30 of 58

Function or Instruction/

Arguments

tvm_FV

[

(

Ú

P/Y

,

C/Y

)

]

,

æ

,

PV

,

PMT

, tvm_

æ

[

(

Ú

P/Y

,

C/Y

)

]

,

PV

,

PMT

,

FV

, tvm_

Ú

[

(

æ

P/Y

,

C/Y

)

]

,

PV

,

PMT

,

FV

, tvm_Pmt

[

(

P/Y

,

C/Y

)

]

Ú

,

æ

,

PV

,

FV

, tvm_PV

[

(

Ú

P/Y

,

C/Y

)

]

,

æ

,

PMT

,

FV

, uvAxes uwAxes

1-Var Stats

[Xlistname

,

freqlist]

2-Var Stats

[Xlistname

,

Ylistname

,

freqlist]

variance(

list[

,

freqlist]

)

Vertical

x

vwAxes

Web

Result

Computes the future value.

Computes the annual interest rate.

Computes the number of payment periods.

Computes the amount of each payment.

Computes the present value.

Sets sequence graphs to plot

u(n)

on the x-axis and

v(n)

on the y-axis.

Sets sequence graphs to plot

u(n)

on the x-axis and

w(n)

on the yaxis.

Performs one-variable analysis on the data in Xlistname with frequency freqlist.

Performs two-variable analysis on the data in Xlistname and

Ylistname with frequency freqlist.

Returns the variance of the elements in list with frequency

freqlist.

Draws a vertical line at x.

Sets sequence graphs to plot

v(n)

on the x-axis and

w(n)

on the yaxis.

Sets sequence graphs to trace as webs.

Key or Keys/

Menu or Screen/Item y [

FINANCE

]

CALC

6:tvm_FV

14-7 y [

FINANCE

]

CALC

3:tvm_

æ y [

FINANCE

]

CALC

5:tvm_

Ú y [

FINANCE

]

CALC

2:tvm_Pmt

14-7

14-7

14-6 y [

FINANCE

]

CALC

4:tvm_PV

14-7

† y [

FORMAT

]

uv

6-8

† y [

FORMAT

]

uw

6-8

CALC

1:1-Var Stats

CALC

2:2-Var Stats

12-25

12-25 y [

LIST

]

MATH

8:variance(

y [

DRAW

]

DRAW

4:Vertical

11-18

8-6

† y [

FORMAT

]

vw

6-8

† y [

FORMAT

]

Web

6-8

Tables and Reference Information A–31

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PM Page 31 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

:While

condition

:

commands

:End

:

command

valueA

xor

valueB

ZBox

ZDecimal

ZInteger

ZInterval

s

[

,

listname

(Data list input)

,

freqlist

,

confidence level]

ZInterval

s

,

v

,

n

[

,

confidence level]

(Summary stats input)

Zoom In

Zoom Out

Result

Executes commands while

condition is true.

Key or Keys/

Menu or Screen/Item

† 

CTL

5:While

16-11

Returns 1 if only valueA or

valueB = 0. valueA and valueB can be real numbers, expressions, or lists.

Displays a graph, lets you draw a box that defines a new viewing window, and updates the window.

y [

TEST

]

LOGIC

3:xor

† q

ZOOM

1:ZBox

2-26

3-20

Adjusts the viewing window so that

@

X=0.1

and

@Y=0.1

, and displays the graph screen with the origin centered on the screen.

† q

ZOOM

4:ZDecimal

Redefines the viewing window using these dimensions:

@X=1

Xscl=10

@Y=1

Yscl=10

Computes a z confidence interval.

Computes a z confidence interval.

Magnifies the part of the graph that surrounds the cursor location.

Displays a greater portion of the graph, centered on the cursor location.

3-21

† q

ZOOM

8:ZInteger

3-22

† …

TESTS

7:ZInterval

13-16

† …

TESTS

7:ZInterval

13-16

† q

ZOOM

2:Zoom In

3-21

† q

ZOOM

3:Zoom Out

3-21

A–32 Tables and Reference Information

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PM Page 32 of 58

Function or Instruction/

Arguments

ZoomFit

ZoomRcl

ZoomStat

ZoomSto

ZPrevious

ZSquare

ZStandard

Result

Recalculates

Ymin

and

Ymax

to include the minimum and maximum

Y

values, between

Xmin

and

Xmax

, of the selected functions and replots the functions.

Graphs the selected functions in a user-defined viewing window.

Redefines the viewing window so that all statistical data points are displayed.

Immediately stores the current viewing window.

Replots the graph using the window variables of the graph that was displayed before you executed the last

ZOOM instruction.

Adjusts the

X

or

Y

window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window.

Key or Keys/

Menu or Screen/Item

† q

ZOOM

0:ZoomFit

3-22

† q

MEMORY

3:ZoomRcl

3-23

† q

ZOOM

9:ZoomStat

3-22

† q

MEMORY

2:ZoomSto

3-23

† q

MEMORY

1:ZPrevious

† q

ZOOM

5:ZSquare

3-23

3-21

Replots the functions immediately, updating the window variables to the default values.

† q

ZOOM

6:ZStandard

3-22

Tables and Reference Information A–33

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PM Page 33 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

ZNTest(

m

0

,s [

,

listname

freqlist

,

alternative

,

drawflag]

)

(Data list input)

,

ZNTest(

m

0

,s,v,

n

[

,

alternative

,

drawflag]

)

(Summary stats input)

ZTrig

Factorial: value

!

Factorial: list

!

Degrees notation: value

¡

Radian: angle

r

Transpose: matrix

T

Result

Performs a z test with frequency

freqlist. alternative=

L1

is

<

;

alternative=

0

is

ƒ

; alternative=

1

is

>

. drawflag=

1

draws results;

drawflag=

0

calculates results.

Key or Keys/

Menu or Screen/Item

† …

TESTS

1:Z.Test(

13-10

Performs a z test. alternative=

L1

is

<

; alternative=

0

is

ƒ

;

alternative=

1

is

>

. drawflag=

1

draws results; drawflag=

0

calculates results.

† …

TESTS

1:Z.Test(

13-10

Replots the functions immediately, updating the window variables to preset values for plotting trig functions.

† q

ZOOM

7:ZTrig

3-22

Returns factorial of value.

Returns factorial of list elements.

Interprets value as degrees; designates degrees in DMS format.

Interprets angle as radians.

Returns a matrix in which each element (row, column) is swapped with the corresponding element

(column, row) of matrix.

PRB

4:!

PRB

4:!

y [

ANGLE

]

ANGLE

1:¡

y [

ANGLE

]

ANGLE

3: r

MATH

2:

T

2-21

2-21

2-23

2-24

10-12

A–34 Tables and Reference Information

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PM Page 34 of 58

Function or Instruction/

Arguments

x th root

x

value x th root

x

list list

x

value listA

x

listB

Cube: value

3

Cube root:

3

‡(

value

)

Equal: valueA

=

valueB

Not equal: valueA

ƒ

valueB

Less than: valueA

<

valueB

Result

Returns x

th

root of value.

Returns x

th

root of list elements.

Returns list roots of value.

Returns listA roots of listB.

Returns the cube of a real or complex number, expression, list, or square matrix.

Returns the cube root of a real or complex number, expression, or list.

Returns 1 if valueA = valueB.

Returns 0 if valueA ƒ valueB.

valueA and valueB can be real or complex numbers, expressions, lists, or matrices.

Returns 1 if valueA ƒ valueB.

Returns 0 if valueA = valueB.

valueA and valueB can be real or complex numbers, expressions, lists, or matrices.

Returns 1 if valueA < valueB.

Returns 0 if valueA valueB.

valueA and valueB can be real or complex numbers, expressions, or lists.

Key or Keys/

Menu or Screen/Item

MATH

5: x

MATH

5: x

MATH

5: x

MATH

5: x

MATH

3:

3

2-6

2-6

2-6

2-6

2-6

10-10

MATH

4:

3

‡(

y [

TEST

]

TEST

1:=

2-6

2-25

10-11 y [

TEST

]

TEST

2:ƒ

2-25

10-11 y [

TEST

]

TEST

5:<

2-25

Tables and Reference Information A–35

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PM Page 35 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

Greater than:

valueA

>

valueB

Less than or equal:

valueA

valueB

Greater than or equal:

valueA

valueB

Inverse: value

L1

Inverse: list

L1

Inverse: matrix

L1

Square: value

2

Square: list

2

Square: matrix

2

Powers: value

^

power

Powers: list

^

power

Powers: value

^

list

Result

Returns 1 if valueA > valueB.

Returns 0 if valueA valueB.

valueA and valueB can be real or complex numbers, expressions, or lists.

Returns 1 if valueA valueB.

Returns 0 if valueA > valueB.

valueA and valueB can be real or complex numbers, expressions, or lists.

Returns 1 if valueA

valueB.

Returns 0 if valueA < valueB.

valueA and valueB can be real or complex numbers, expressions, or lists.

Returns 1 divided by a real or complex number or expression.

Key or Keys/

Menu or Screen/Item y [

TEST

]

TEST

3:>

y [

TEST

]

TEST

6:

y [

TEST

]

TEST

4:‚

2-25

2-25

2-25

2-3

Returns 1 divided by list elements.

Returns matrix inverted.

Returns value multiplied by itself.

value can be a real or complex number or expression.

¡

2-3

10-10

2-3

Returns list elements squared.

¡

2-3

¡

Returns matrix multiplied by itself.

Returns value raised to power.

value can be a real or complex number or expression.

Returns list elements raised to

power.

Returns value raised to list elements.

10-10

2-3

2-3

2-3

A–36 Tables and Reference Information

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PM Page 36 of 58

Function or Instruction/

Arguments

Powers: matrix

^

power

Negation:

L

value

Power of ten:

10

^(

value

)

Power of ten:

10

^(

list

)

Square root:

‡(

value

)

Multiplication:

valueA

ääää

valueB

Multiplication:

value

ääää

list

Multiplication:

list

ääää

value

Multiplication:

listA

ääää

listB

Multiplication:

value

ääää

matrix

Multiplication:

matrixA

ääää

matrixB

Division: valueA

à

valueB

Division: list

à

value

Division: value

à

list

Division: listA

à

listB

Result

Returns matrix elements raised to

power.

Returns the negative of a real or complex number, expression, list, or matrix.

Returns 10 raised to the value power. value can be a real or complex number or expression.

Key or Keys/

Menu or Screen/Item

10-10

Ì

2-4

10-9 y [

10

x]

2-4 y [

10

x]

Returns a list of 10 raised to the

list power.

Returns square root of a real or complex number, expression, or list.

Returns valueA times valueB.

y [

¯

]

2-4

2-3

2-3

¯

Returns value times each list element.

Returns each list element times

value.

Returns listA elements times listB elements.

Returns value times matrix elements.

Returns matrixA times matrixB.

¯

¯

¯

¯

2-3

2-3

2-3

10-9

10-9

¥

Returns valueA divided by

valueB.

Returns list elements divided by value.

Returns value divided by list elements.

Returns listA elements divided by

listB elements.

¥

¥

¥

2-3

2-3

2-3

2-3

Tables and Reference Information A–37

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PM Page 37 of 58

Table of Functions and Instructions

(continued)

Function or Instruction/

Arguments

Addition: valueA

+

valueB

Addition: list

+

value

Addition: listA

+

listB

Addition:

matrixA

+

matrixB

Concatenation:

string1

+

string2

Subtraction:

valueA

N

valueB

Subtraction:

value

N

list

Subtraction:

list

N

value

Subtraction:

listA

N

listB

Subtraction:

matrixA

N

matrixB

Minutes notation:

degrees

¡

minutes

'

seconds

"

Seconds notation:

degrees

¡

minutes

'

seconds

"

Result

Returns valueA plus valueB.

Returns list in which value is added to each list element.

Returns listA elements plus listB elements.

Returns matrixA elements plus

matrixB elements.

Concatenates two or more strings.

Subtracts valueB from valueA.

Subtracts list elements from

value.

Subtracts value from list elements.

Subtracts listB elements from

listA elements.

Subtracts matrixB elements from

matrixA elements.

Interprets minutes angle measurement as minutes.

Interprets seconds angle measurement as seconds.

Key or Keys/

Menu or Screen/Item

Ã

Ã

2-3

2-3

Ã

2-3

Ã

10-9

Ã

15-6

¹

2-3

¹

2-3

¹

2-3

¹

2-3

¹

10-9 y [

ANGLE

]

ANGLE

2:'

ƒ [

ã

]

2-23

2-23

A–38 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 38 of 58

TI-82 STATS Menu Map

The TI-82 STATS Menu Map begins at the top-left corner of the keyboard and follows the keyboard layout from left to right. Default values and settings are shown.

o

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(Func mode) (Par mode) (Pol mode) (Seq mode)

Plot1 Plot2 Plot3

ççççY1=

ççççY2=

ççççY3=

ççççY4=

...

ççççY9=

ççççY0=

Plot1 Plot2 Plot3

ççççX1T=

Y1T=

ççççX2T=

Y2T=

...

ççççX6T=

Y6T=

Plot1 Plot2 Plot3

ççççr1=

ççççr2=

ççççr3=

ççççr4=

ççççr5=

ççççr6=

Plot1 Plot2 Plot3

nMin=1

í

u(nMin)=

í

v(nMin)=

í

w(nMin)=

y [

STAT PLOT

]

¸¶¶¶¶¶»

STAT PLOTS

1:Plot1…Off

"

2:Plot2…Off

"

3:Plot3…Off

"

4:PlotsOff

5:PlotsOn

y [

STAT PLOT

]

¸¶¶¶¶¶¿¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹

(PRGM editor) (PRGM editor) (PRGM editor)

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

4:PlotsOff

5:PlotsOn

TYPE

1:Scatter

2:xyLine

3:Histogram

4:ModBoxplot

5:Boxplot

6:NormProbPlot

MARK

1:

2:+

3:¦

p

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(Func mode) (Par mode) (Pol mode) (Seq mode)

WINDOW

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

Xres=1

WINDOW

Tmin=0

Tmax=2

Tstep=24

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

WINDOW

qmin=0

qmax=2

qstep=24

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

WINDOW

nMin=1

nMax=10

PlotStart=1

PlotStep=1

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

y [

TBLSET

]

¸¶¶¶»

TABLE SETUP

TblStart=0

@Tbl=1

Indpnt:Auto Ask

Depend:Auto Ask

y [

TBLSET

]

¸¶¶¶¶»

(PRGM editor)

TABLE SETUP

Indpnt:Auto Ask

Depend:Auto Ask

Tables and Reference Information A–39

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 39 of 58

TI-82 STATS Menu Map

(continued)

q

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

ZOOM MEMORY

1:ZBox

2:Zoom In

3:Zoom Out

4:ZDecimal

5:ZSquare

6:ZStandard

7:ZTrig

8:ZInteger

9:ZoomStat

0:ZoomFit

1:ZPrevious

2:ZoomSto

3:ZoomRcl

4:SetFactors…

MEMORY

(Set Factors...)

ZOOM FACTORS

XFact=4

YFact=4

y [

FORMAT

]

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(Func/Par/Pol modes) (Seq mode)

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

Time Web uv vw uw

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

y [

CALC

]

¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(Func mode)

CALCULATE

1:value

2:zero

3:minimum

4:maximum

5:intersect

6:dy/dx

7:f(x)dx

(Par mode)

CALCULATE

1:value

2:dy/dx

3:dy/dt

4:dx/dt

(Pol mode)

CALCULATE

1:value

2:dy/dx

3:dr/dq

(Seq mode)

CALCULATE

1:value

z

¸»

Normal Sci Eng

Float 0123456789

Radian Degree

Func Par Pol Seq

Connected Dot

Sequential Simul

Real a+b

×××× re^q××××

Full Horiz G-T

A–40 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 40 of 58

y [

LINK

]

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

SEND RECEIVE

1:Receive 1:All+…

2:AllN…

3:Prgm…

4:List…

5:Lists to TI82…

6:GDB…

7:Pic…

8:Matrix…

9:Real…

0:Complex…

A:Y-Vars…

B:String…

C:Back Up…

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

EDIT

1:Edit…

2:SortA(

3:SortD(

4:ClrList

5:SetUpEditor

CALC

1:1-Var Stats

2:2-Var Stats

3:Med-Med

4:LinReg(ax+b)

5:QuadReg

6:CubicReg

7:QuartReg

8:LinReg(a+bx)

9:LnReg

0:ExpReg

A:PwrReg

B:Logistic

C:SinReg

TESTS

1:Z-Test…

2:T-Test…

3:2-SampZTest…

4:2-SampTTest…

5:1-PropZTest…

6:2-PropZTest…

7:ZInterval…

8:TInterval…

9:2-SampZInt…

0:2-SampTInt…

A:1-PropZInt…

B:2-PropZInt…

C:c 2 -Test…

ÛTest…

E:LinRegTTest…

F:ANOVA(

Tables and Reference Information A–41

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 41 of 58

TI-82 STATS Menu Map

(continued)

y [

LIST

]

¸¶¶¿¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹

NAMES

1:listname

OPS

1:SortA(

MATH

1:min(

2:listname

3:listname

...

2:SortD(

3:dim(

4:Fill(

5:seq(

6:cumSum(

7:@List(

8:Select(

9:augment(

0:List4matr(

A:Matr4list(

2:max(

3:mean(

4:median(

5:sum(

6:prod(

7:stdDev(

8:variance(

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹

MATH NUM CPX PRB

1:4Frac

2:4Dec

3:

3

4:

3

‡(

5:x‡

6:fMin(

7:fMax(

8:nDeriv(

9:fnInt(

0:Solver…

1:abs(

2:round(

3:iPart(

4:fPart(

5:int(

6:min(

7:max(

8:lcm(

9:gcd(

1:conj(

2:real(

3:imag(

4:angle(

5:abs(

6:4Rect

7:4Polar

1:rand

2:nPr

3:nCr

4:!

5:randInt(

6:randNorm(

7:randBin(

y [

TEST

]

¸¶¶¶¶¿¶¶¶¶¶¶¶¶¹

TEST LOGIC

1:=

2:ƒ

3:>

4:‚

5:<

6:

1:and

2:or

3:xor

4:not(

A–42 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 42 of 58

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹

NAMES MATH EDIT

1:[A]

2:[B]

3:[C]

4:[D]

5:[E]

6:[F]

7:[G]

8:[H]

9:[I]

0:[J]

1:det(

2:

T

3:dim(

4:Fill(

5:identity(

6:randM(

7:augment(

8:Matr4list(

9:List4matr(

0:cumSum(

A:ref(

B:rref(

C:rowSwap(

D:row+(

E:…row(

F:…row+(

1:[A]

2:[B]

3:[C]

4:[D]

5:[E]

6:[F]

7:[G]

8:[H]

9:[I]

0:[J]

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¹

EXEC EDIT NEW

1:name

2:name

...

1:name

2:name

...

1:Create New

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(PRGM editor)

CTL

1:If

2:Then

3:Else

4:For(

5:While

6:Repeat

7:End

8:Pause

9:Lbl

0:Goto

A:IS>(

B:DS<(

C:Menu(

D:prgm

E:Return

F:Stop

G:DelVar

H:GraphStyle(

(PRGM editor)

I/O

1:Input

2:Prompt

3:Disp

4:DispGraph

5:DispTable

6:Output(

7:getKey

8:ClrHome

9:ClrTable

0:GetCalc(

A:Get(

B:Send(

(PRGM editor)

EXEC

1:name

2:name

...

y [

ANGLE

]

¸¶¶¶¶»

ANGLE

1:¡

2:'

3:r

4:4DMS

5:R4Pr(

6:R4Pq(

7:P4Rx(

8:P4Ry(

Tables and Reference Information A–43

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 43 of 58

TI-82 STATS Menu Map

(continued)

y [

DRAW

]

¸¶¶¶¶¶¿¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¹

DRAW POINTS STO

1:ClrDraw

2:Line(

3:Horizontal

4:Vertical

5:Tangent(

6:DrawF

7:Shade(

8:DrawInv

9:Circle(

0:Text(

A:Pen

1:Pt-On(

2:Pt-Off(

3:Pt-Change(

4:Pxl-On(

5:Pxl-Off(

6:Pxl-Change(

7:pxl-Test(

1:StorePic

2:RecallPic

3:StoreGDB

4:RecallGDB

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

VARS

1:Window…

Y-VARS

1:Function…

2:Zoom…

3:GDB…

4:Picture…

5:Statistics…

6:Table…

7:String…

2:Parametric…

3:Polar…

4:On/Off…

VARS

¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾

(Window…)

X/Y

1:Xmin

2:Xmax

3:Xscl

4:Ymin

5:Ymax

6:Yscl

7:Xres

8:

@

X

9:

@

Y

0:XFact

A:YFact

(Window…)

T/q

1:Tmin

2:Tmax

3:Tstep

4:qmin

5:qmax

6:qstep

(Window…)

U/V/W

1:u(nMin)

2:v(nMin)

3:w(nMin)

4:nMin

5:nMax

6:PlotStart

7:PlotStep

A–44 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 44 of 58

VARS

¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾

(Zoom…)

ZX/ZY

1:ZXmin

2:ZXmax

3:ZXscl

4:ZYmin

5:ZYmax

6:ZYscl

7:ZXres

(Zoom…)

ZT/Zq

1:ZTmin

2:ZTmax

3:ZTstep

4:Zqmin

5:Zqmax

6:Zqstep

(Zoom…)

ZU

1:Zu(nMin)

2:Zv(nMin)

3:Zw(nMin)

4:ZnMin

5:ZnMax

6:ZPlotStart

7:ZPlotStep

VARS

¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾

(GDB…) (Picture…)

GRAPH DATABASE

1:GDB1

2:GDB2

...

9:GDB9

0:GDB0

PICTURE

1:Pic1

2:Pic2

...

9:Pic9

0:Pic0

VARS

¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¾

(Statistics…)

XY

1:n

2:v

3:Sx

4:sx

5:w

6:Sy

7:sy

8:minX

9:maxX

0:minY

A:maxY

(Statistics…)

G

1:Gx

2:Gx

2

3:Gy

4:Gy

2

5:Gxy

(Statistics…)

EQ

1:RegEQ

2:a

3:b

4:c

5:d

6:e

7:r

8:r

2

9:R

2

(Statistics…)

TEST

1:p

2:z

3:t

4:c

Û

2

6:df

7:Ç

Ç1

9:Ç

0:s

A:ü

(Statistics…)

PTS

1:x1

2:y1

3:x2

4:y2

5:x3

6:y3

7:Q 1

8:Med

9:Q 3

C:Sx1

D:Sx2

E:Sxp

F:n1

G:n2

H:lower

I:upper

Tables and Reference Information A–45

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 45 of 58

TI-82 STATS Menu Map

(continued)

VARS

¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(Table…)

TABLE

1:TblStart

2:

@

Tbl

3:TblInput

(String…)

STRING

1:Str1

2:Str2

3:Str3

4:Str4

...

9:Str9

0:Str0

Y-VARS

¸¶¿¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¹

(Function…)

FUNCTION

(Parametric…)

PARAMETRIC

(Polar…)

POLAR

(On/Off…)

ON/OFF

1:Y

1

2:Y

2

3:Y

3

4:Y

4

...

9:Y

9

0:Y

0

1:X

1T

2:Y

1T

3:X

2T

4:Y

2T

...

A:X

6T

B:Y

6T

1:r

1

2:r

2

3:r

3

4:r

4

5:r

5

6:r

6

1:FnOn

2:FnOff

A–46 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 46 of 58

y [

DISTR

]

¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¹

DISTR

1:normalpdf(

DRAW

1:ShadeNorm(

2:normalcdf(

3:invNorm(

4:tpdf(

5:tcdf(

6:c

2 pdf(

7:c

ÛÛ

2 cdf(

Ûpdf(

2:Shade_t(

3:Shadec

2

Û(

(

0:binompdf(

A:binomcdf(

B:poissonpdf(

C:poissoncdf(

D:geometpdf(

E:geometcdf(

y [

FINANCE

]

¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¹

CALC VARS

1:TVM Solver…

2:tvm_Pmt

3:tvm_æ

4:tvm_PV

5:tvm_Ú

6:tvm_FV

7:npv(

8:irr(

9:bal(

0:GPrn(

A:GInt(

B:4Nom(

C:4Eff(

D:dbd(

E:Pmt_End

F:Pmt_Bgn

1:Ú

2:æ

3:PV

4:PMT

5:FV

6:P/Y

7:C/Y

Tables and Reference Information A–47

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 47 of 58

TI-82 STATS Menu Map

(continued)

y [

MEM

]

¸¶¶»

MEMORY

1:Check RAM…

2:Delete…

3:Clear Entries

4:ClrAllLists

5:Reset…

MEMORY

¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(Check RAM…) (Delete…) (Reset…)

MEM FREE 27225

Real 15

Complex 0

List 0

Matrix 0

Y-Vars 240

Prgm 14

Pic 0

GDB 0

String 0

DELETE FROM…

1:All…

2:Real…

3:Complex…

4:List…

5:Matrix…

6:Y-Vars…

7:Prgm…

8:Pic…

9:GDB…

0:String…

RESET

1:All Memory…

2:Defaults…

MEMORY (Reset...)

¸¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹

(All Memory…)

RESET MEMORY

(Defaults…)

RESET DEFAULTS

1:No

2:Reset

1:No

2:Reset

Resetting memory erases all data and programs.

y [

CATALOG

]

¸¶¶»

CATALOG cosh( cosh

L1

(

...

Equ4String( expr(

...

inString(

...

length(

...

sinh( sinh

L1

(

...

String4Equ( sub(

...

tanh( tanh

L1

(

A–48 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 48 of 58

Variables

User Variables

The TI-82 STATS uses the variables listed below in various ways. Some variables are restricted to specific data types.

The variables

A

through

Z

and

q

are defined as real or complex numbers. You may store to them. The TI-82 STATS can update

X

,

Y

,

R

,

q

, and

T

during graphing, so you may want to avoid using these variables to store nongraphing data.

The variables (list names)

L

1

through

L

6

are restricted to lists; you cannot store another type of data to them.

The variables (matrix names)

[A]

through

[J]

are restricted to matrices; you cannot store another type of data to them.

The variables

Pic1

through

Pic9

and

Pic0

are restricted to pictures; you cannot store another type of data to them.

The variables

GDB1

through

GDB9

and

GDB0

are restricted to graph databases; you cannot store another type of data to them.

The variables

Str1

through

Str9

and

Str0

are restricted to strings; you cannot store another type of data to them.

You can store any string of characters, functions, instructions, or variables to the functions

Y

n, (

1

through

9

, and

0

),

X

n

T

/

Y

n

T

(

1

through

6

),

r

n (

1

through

6

),

u(n)

,

v(n)

, and

w(n)

directly or through the

Y=

editor. The validity of the string is determined when the function is evaluated.

System Variables

The variables below must be real numbers. You may store to them. Since the TI-82 STATS can update some of them, as the result of a

ZOOM

, for example, you may want to avoid using these variables to store nongraphing data.

Xmin

,

Xmax

,

Xscl

,

@X

,

XFact

,

Tstep

,

PlotStart

,

nMin

, and other window variables.

ZXmin

,

ZXmax

,

ZXscl

,

ZTstep

,

ZPlotStart

,

Zu(nMin)

, and other

ZOOM

variables.

The variables below are reserved for use by the TI-82 STATS.

You cannot store to them.

n

,

v

,

Sx

,

sx

,

minX

,

maxX

,

Gy

,

Gy y1

,

z

,

t

,

F

,

c

2

,

Ç

,

v1

statistical variables.

,

Sx1

,

n1

,

2

,

Gxy

,

a

,

b

,

c

,

RegEQ

,

x

1

,

x

2,

lower

,

upper

,

r

2

,

R

2

and other

Tables and Reference Information A–49

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 49 of 58

Statistics Formulas

This section contains statistics formulas for the

Logistic

and

SinReg

regressions,

ANOVA

,

2.SampÜ

, and

2.SampTTest

.

Logistic

The logistic regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function:

J

=

i

N

=

1



1

+

c ae

bx i

y i



2 which is the sum of the squares of the residual errors, where: x = the independent variable list

y = the dependent variable list

N = the dimension of the lists

This technique attempts to estimate the constants a, b, and c recursively to make J as small as possible.

SinReg

The sine regression algorithm applies nonlinear recursive leastsquares techniques to optimize the following cost function:

J

=

i

N

[

a

sin( )

i

]

2

=

1

bx i

+ + − which is the sum of the squares of the residual errors, where: x = the independent variable list

y = the dependent variable list

N = the dimension of the lists

This technique attempts to recursively estimate the constants a,

b, c, and d to make J as small as possible.

A–50 Tables and Reference Information

826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09

PM Page 50 of 58

ANOVA(

The

ANOVA

Û statistic is:

Û

=

Factor MS

Error MS

The mean squares (MS) that make up Û are:

Factor MS

=

Factor SS

Factor df

Error MS

=

Error SS

Error df

The sum of squares (SS) that make up the mean squares are:

Factor SS

=

i

I

=

1

(

i

x

)

2

Error SS

=

i

I

=

1

(

n i

1 )

Sx i

2

The degrees of freedom df that make up the mean squares are:

Factor df I

1 numerator

df

for Û

=

i

I

=

1

n i

1

df

for

Û where:

x i

I = number of populations

= the mean of each list

Sxi = the standard deviation of each list

ni = the length of each list

x

= the mean of all lists

Tables and Reference Information A–51

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Statistics Formulas

(continued)

Below is the definition for the

2

.

Samp

Ü .

Sx1, Sx2 = Sample standard deviations having n

1

-1 and n

2

-1 degrees of freedom df, respectively.

Û = Û-statistic =



Sx

Sx

1

2



2

df(x, n

1

-1, n

2

-1)

= Ûpdf( ) with degrees of freedom

df, n

1

-1, and n

2

-1

p = reported p value

2

.

Samp

Ü

p

=

F

(

for the alternative hypothesis s

1

> s

2

.

1

1

, n

2

1 )

dx

2

.

Samp

Ü

p

=

0

F

(

for the alternative hypothesis s

1

< s

2

.

1

1

, n

2

1 )

dx

2

.

Samp

Ü

for the alternative hypothesis s must satisfy the following:

1

ƒ s

2

. Limits

p

2

=

0

L bnd

,

1

1

, n

2

1 )

dx

=

U bnd

,

1

1

, n

2

1 )

dx

where: [Lbnd,Ubnd] = lower and upper limits

The Û-statistic is used as the bound producing the smallest integral. The remaining bound is selected to achieve the preceding integral’s equality relationship.

A–52 Tables and Reference Information

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2.SampTTest

The following is the definition for the

2.SampTTest

. The twosample t statistic with degrees of freedom df is:

t

=

x

1

x

S

2 where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled:

S

=

Sx

1

2

n

1

+

Sx n

2

2

2

df

=

n

1

1

1





Sx n

Sx

1

2

n

1

2

1

1



2

+

+

Sx n

2

2

2



2

n

2

1

1



Sx n

2

2

2



 2 otherwise:

Sx p

=

(

n

1

1 )

Sx

1

2 +

df

(

n

2

1 )

Sx

2

2

S

=

n

1

1

+

n

1

2

Sx p df

=

n

1

+

n

2

2 and Sxp is the pooled variance.

Tables and Reference Information A–53

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Financial Formulas

This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates.

Time Value of

Money

i

=

[

e

(

y

×

ln

(

x

+

1 ))

]

1 where: PMT ƒ 0

y = C/Y

÷

P/Y

x = (.01

×

I%)

÷

C/Y

C/Y = compounding periods per year

P/Y = payment periods per year

I% = interest rate per year

i

=

(

FV

÷

PV

)

( 1

÷

N

) −

1 where: PMT = 0

The iteration used to compute i:

0

=

PV

+

PMT

×

G i

1 ( 1

i i

)

N

+

FV

(

i

)

N

I %

=

1100

×

C Y

×

[

e

(

y

× ln(

x

+

1 ))

1

] where:

x = i

y = P/Y

÷

C/Y

G i

where: k = 0 for end-of-period payments

k = 1 for beginning-of-period payments

N

=

ln



PMT

×

G i

FV

×

i

PMT

×

ln( 1

G

+

i i

+

)

PV

×

i



 where: i ƒ 0

N

=

(

PV

+

FV

)

÷

PMT

where: i = 0

A–54 Tables and Reference Information

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Time Value of

Money

(Continued)

PMT

=

G i i

×

PV

+

(

PV

+

FV

1

+

i

)

N

1

 where: i ƒ 0

PMT

=

(

PV

+

FV

)

÷

N

where: i = 0

PV

=

i i

FV

×

( 1

+

1

i

)

N

− where: i ƒ 0

PV

=

(

FV

+

PMT

×

N

) where: i = 0

FV

=

i

×

i

(

1

+

i )

N

×



PV

+ where: i ƒ 0

FV

=

(

PV

+

PMT

×

N

) where: i = 0

i

×

i i

×

i



Tables and Reference Information A–55

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Financial Formulas

(continued)

Amortization

If computing bal( ), pmt2 = npmt

Let bal(0) = RND(PV)

Iterate from m = 1 to pmt2

I m

=

RND RND

( )

=

(

12

1 )

(

I m

+

(

1 ))]

) then:

bal

( )

=

Σ

Pr n

( )

=

Σ

Int

2 )

2 )

pm t

2

pm t

1 1 )

1 )

)

− Σ

Pr n

( ) where: RND = round the display to the number of decimal places selected

RND12 = round to 12 decimal places

Balance, principal, and interest are dependent on the values of

PMT

,

PV

,

æ

, and pmt1 and pmt2.

A–56 Tables and Reference Information

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Cash Flow

Interest Rate

Conversions

npv

( )

=

CF

0

+

j

N

=

1

CF j

( 1

+

i

)

S j

1

( 1 ( 1

i i

)

n j

) where: S

j

=

i

=

j

1

0

n i j j

1

=

0

Net present value is dependent on the values of the initial cash flow (CF

0

), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i).

irr( ) = 100

×

i, where i satisfies npv( ) = 0

Internal rate of return is dependent on the values of the initial cash flow (CF

0

) and subsequent cash flows (CFj).

i = I%

÷

100

4

Eff

( )

=

100

×

(

e

CP

×

ln

(

x

+

1 ) −

1 ) where:

4

Nom

( )

=

100

x = .01

×

NOM

÷

CP

×

CP

×

[

e

1

÷

CP

×

ln

(

x

+

1 ) −

1

] where: x = .01

×

EFF

EFF = effective rate

CP = compounding periods

NOM = nominal rate

Tables and Reference Information A–57

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PM Page 57 of 58

Financial Formulas

(continued)

Days between

Dates

With the

dbd(

function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049.

Actual/actual day-count method

(assumes actual number of days per month and actual number of days per year):

dbd( (days between dates) =

Number of Days II - Number of Days I

Number of Days I = (Y1

-

YB)

×

365

+ (number of days MB to M1)

+ DT1

+

(

Y

1

YB

4

)

Number of Days II = (Y2

-

YB)

×

365

+ (number of days MB to M2)

+ DT2

+

(

Y

2

YB

4

) where: M1 = month of first date

DT1 = day of first date

Y1 = year of first date

M2 = month of second date

DT2 = day of second date

Y2 = year of second date

MB = base month (January)

DB = base day (1)

YB = base year (first year after leap year)

A–58 Tables and Reference Information

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Contents

B

General Information

Battery Information ................................................................2

In Case of Difficulty...............................................................4

Error Conditions.....................................................................5

Accuracy Information...........................................................10

Texas Instruments Support and Service................................12

General Information B–1

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Battery Information

When to Replace the Batteries

The TI-82 STATS uses five batteries: four AAA alkaline batteries and one lithium battery. The lithium battery provides auxiliary power to retain memory while you replace the AAA batteries.

When the battery voltage level drops below a usable level, the

TI-82 STATS displays this message when you turn on the unit.

Effects of

Replacing the

Batteries

Battery

Precautions

After this message is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage. (This one-week to two-week period is based on tests with alkaline batteries; the performance of other kinds of batteries may vary.)

The low-battery message continues to be displayed each time you turn on the unit until you replace the batteries. If you do not replace the batteries within about two weeks, the calculator may turn off by itself or fail to turn on until you install new batteries.

Replace the lithium battery every three or four years.

Do not remove both types of batteries (AAA and lithium

auxiliary) at the same time. Do not allow the batteries to lose power completely. If you follow these guidelines and the steps for replacing batteries on page B

.

3, you can replace either type of battery without losing any information in memory.

Take these precautions when replacing batteries.

Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries.

Do not mix rechargeable and nonrechargeable batteries.

Install batteries according to polarity (+ and N) diagrams.

Do not place nonrechargeable batteries in a battery recharger.

Properly dispose of used batteries immediately. Do not leave them within the reach of children.

Do not incinerate batteries.

B–2 General Information

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Replacing the

Batteries

To replace the batteries, follow these steps.

1. Turn off the calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the calculator.

Turn the back of the calculator toward you.

2. Hold the calculator upright. Place your thumb on the oval indentation on the battery cover. Push down and toward you to slide the cover about ¼ inch (6 mm). Lift off the cover to expose the battery compartment.

Note: To avoid loss of information stored in memory, you must turn off the calculator. Do not remove the AAA batteries and the lithium battery simultaneously.

3. Replace all four AAA alkaline batteries at the same time. Or, replace the lithium battery.

To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polarity (+ and N) diagrams in the battery compartment.

To remove the lithium battery, place your index finger on the battery. Insert the tip of a ball-point pen (or similar instrument) under the battery at the small opening provided in the battery compartment. Carefully pry the battery upward, holding it with your thumb and finger.

(There is a spring that pushes against the underside of the battery.)

Install the new battery, + side up, by inserting the battery and gently snapping it in with your finger. Use a CR1616 or CR1620 (or equivalent) lithium battery.

4. Replace the battery compartment cover. Turn the calculator on and adjust the display contrast, if necessary (step 1; page

B

.

4).

General Information B–3

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In Case of Difficulty

Handling a

Difficulty

To handle a difficulty, follow these steps.

1. If you cannot see anything on the screen, the contrast may need to be adjusted.

To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark.

To lighten the screen, press and release y, and then press and hold † until the display is sufficiently light.

2. If an error menu is displayed, follow the steps in Chapter 1.

Refer to pages B

.

5 through B

.

9 for details about specific errors, if necessary.

3. If a checkerboard cursor ( # ) is displayed, then either you have entered the maximum number of characters in a prompt, or memory is full. If memory is full, press y

[

MEM

]

2

to select

2:Delete

, and then delete some items from memory (Chapter 18).

4. If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI-82 STATS is waiting for input. Press Í to continue or press É to break.

5. If the calculator does not seem to work at all, be sure the batteries are fresh and that they are installed properly. Refer to battery information on pages B

.

2 and B

.

3.

B–4 General Information

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Error Conditions

When the TI-82 STATS detects an error, it displays

ERR:

message and an error menu.

Chapter 1 describes the general steps for correcting errors. This table contains each error type, possible causes, and suggestions for correction.

Error Type

ARCHIVED VAR

ARGUMENT

BAD GUESS

BOUND

BREAK

DATA TYPE

DIM MISMATCH

DIVIDE BY 0

Possible Causes and Suggested Remedies

A function or instruction is archived and therefore cannot be executed or edited. Use the unarchive command to unarchive the variable before using it.

A function or instruction does not have the correct number of arguments. See Appendix A and the appropriate chapter.

¦ In a CALC operation, you specified a

Guess

that is not between

Left Bound

and

Right Bound

.

¦ For the

solve(

function or the equation solver, you specified a

guess that is not between lower and upper.

¦ Your guess and several points around it are undefined.

Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess.

¦ In a CALC operation or with

Select(, you defined

Left Bound

>

Right Bound

.

¦ In

fMin(

,

fMax(

,

solve(

, or the equation solver, you entered

lower upper.

You pressed the É key to break execution of a program, to halt a

DRAW

instruction, or to stop evaluation of an expression.

You entered a value or variable that is the wrong data type.

¦ For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter.

¦ In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter.

¦ You attempted to store to an incorrect data type, such as a matrix, to a list.

You attempted to perform an operation that references more than one list or matrix, but the dimensions do not match.

¦ You attempted to divide by zero. This error is not returned during graphing. The TI-82 STATS allows for undefined values on a graph.

¦ You attempted a linear regression with a vertical line.

General Information B–5

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Error Conditions

(continued)

Error Type

DOMAIN

Duplicate Name

Error in Xmit

ILLEGAL NEST

INCREMENT

INVALID

Possible Causes and Suggested Remedies

¦ You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI-82 STATS allows for undefined values on a graph. See Appendix A and the appropriate chapter.

¦ You attempted a logarithmic or power regression with a

LX

or an exponential or power regression with a

LY

.

¦ You attempted to compute

GPrn(

or

GInt(

with pmt2 < pmt1.

A variable you attempted to transmit cannot be transmitted because a variable with that name already exists in the receiving unit.

¦ The TI-82 STATS was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode.

¦ You pressed É to break during transmission.

¦ You attempted to perform a backup from a TI

.

82 to a

TI-82 STATS.

¦ You attempted to transfer data (other than

L

1

through

L

6

) from a TI-82 STATS to a TI

.

82.

¦ You attempted to transfer

L

1

through

L

6

from a TI-82 STATS to a TI

.

82 without using

5:Lists to TI82

on the

LINK SEND menu.

You attempted to use an invalid function in an argument to a function, such as

seq(

within expression for

seq(

.

¦ The increment in

seq(

is 0 or has the wrong sign. This error is not returned during graphing. The TI-82 STATS allows for undefined values on a graph.

¦ The increment in a

For(

loop is 0.

¦ You attempted to reference a variable or use a function where it is not valid. For example,

Y

n cannot reference

Y

,

Xmin

,

@X

, or

TblStart

.

¦ You attempted to reference a variable or function that was transferred from the TI

.

82 and is not valid for the

TI-82 STATS. For example, you may have transferred

UnN1

to the TI-82 STATS from the TI

.

82 and then tried to reference it.

¦ In

Seq

mode, you attempted to graph a phase plot without defining both equations of the phase plot.

B–6 General Information

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Error Type

INVALID (cont.)

INVALID DIM

ITERATIONS

LABEL

MEMORY

Possible Causes and Suggested Remedies

¦ In

Seq

mode, you attempted to graph a recursive sequence without having input the correct number of initial conditions.

¦ In

Seq

mode, you attempted to reference terms other than

(nN1)

or

(nN2)

.

¦ You attempted to designate a graph style that is invalid within the current graph mode.

¦ You attempted to use

Select(

without having selected (turned on) at least one xyLine or scatter plot.

¦ You specified dimensions for an argument that are not appropriate for the operation.

¦ You specified a list dimension as something other than an integer between 1 and 999.

¦ You specified a matrix dimension as something other than an integer between 1 and 99.

¦ You attempted to invert a matrix that is not square.

¦ The

solve(

function or the equation solver has exceeded the maximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both.

¦

irr(

has exceeded the maximum number of permitted iterations.

¦ When computing

æ , the maximum number of iterations was exceeded.

The label in the

Goto

instruction is not defined with a

Lbl

instruction in the program.

Memory is insufficient to perform the instruction or function.

You must delete items from memory (Chapter 18) before executing the instruction or function.

Recursive problems return this error; for example, graphing the equation

Y

1

=Y

1

.

Branching out of an

If

/

Then

,

For(

,

While

, or

Repeat

loop with a

Goto

also can return this error because the

End

statement that terminates the loop is never reached.

General Information B–7

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3:16 PM Page 7 of 12

Error Conditions

(continued)

Error Type

MemoryFull

MODE

NO SIGN CHNG

NONREAL ANS

OVERFLOW

RESERVED

SINGULAR MAT

Possible Causes and Suggested Remedies

¦ You are unable to transmit an item because the receiving unit’s available memory is insufficient. You may skip the item or exit receive mode.

¦ During a memory backup, the receiving unit’s available memory is insufficient to receive all items in the sending unit’s memory. A message indicates the number of bytes the sending unit must delete to do the memory backup. Delete items and try again.

You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example,

DrawInv

in a graphing mode other than

Func

.

¦ The

solve(

function or the equation solver did not detect a sign change.

¦ You attempted to compute all ‚ 0, or when

FV

, ( Ú

æ

ÚääääPMT when

FV

, (

Ú

), and

PV

are

), and

PV

are all  0.

¦ You attempted to compute

irr(

when neither CFList nor CFO is > 0, or when neither CFList nor CFO is < 0.

In

Real

mode, the result of a calculation yielded a complex result.

This error is not returned during graphing. The TI-82 STATS allows for undefined values on a graph.

You attempted to enter, or you have calculated, a number that is beyond the range of the calculator. This error is not returned during graphing. The TI-82 STATS allows for undefined values on a graph.

You attempted to use a system variable inappropriately. See

Appendix A.

¦ A singular matrix (determinant = 0) is not valid as the argument for

L1

.

¦ The

SinReg

instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist.

This error is not returned during graphing. The TI-82 STATS allows for undefined values on a graph.

B–8 General Information

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Error Type

SINGULARITY

STAT

STAT PLOT

SYNTAX

TOL NOT MET

UNDEFINED

WINDOW RANGE

ZOOM

Possible Causes and Suggested Remedies

expression in the

solve(

function or the equation solver contains a singularity (a point at which the function is not defined).

Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both.

You attempted a stat calculation with lists that are not appropriate.

¦ Statistical analyses must have at least two data points.

¦

Med.Med

must have at least three points in each partition.

¦ When you use a frequency list, its elements must be ‚ 0.

¦ (

Xmax

N

Xmin

) à

Xscl

must be  47 for a histogram.

You attempted to display a graph when a stat plot that uses an undefined list is turned on.

The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. See Appendix A and the appropriate chapter.

You requested a tolerance to which the algorithm cannot return an accurate result.

You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as

a

after

Med.Med

.

A problem exists with the window variables.

¦ You defined

Xmax

Xmin

or

Ymax

Ymin

.

¦ You defined

qmax

qmin

and

qstep

>

0

(or vice versa).

¦ You attempted to define

Tstep=0

.

¦ You defined

Tmax

Tmin

and

Tstep

>

0

(or vice versa).

¦ Window variables are too small or too large to graph correctly.

You may have attempted to zoom in or zoom out to a point that exceeds the TI-82 STATS numerical range.

¦ A point or a line, instead of a box, is defined in

ZBox.

¦ A ZOOM

operation returned a math error.

General Information B–9

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Accuracy Information

Computational

Accuracy

Graphing

Accuracy

To maximize accuracy, the TI-82 STATS carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a two-digit exponent.

You can store a value in the window variables using up to 10 digits (12 for

Xscl

,

Yscl

,

Tstep

, and

qstep

).

Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent.

RegEQ

displays up to 14 digits in

Float

mode. Using a fixeddecimal setting other than

Float

causes

RegEQ

results to be rounded and stored with the specified number of decimal places.

Xmin

is the center of the leftmost pixel,

Xmax

is the center of the next-to-the-rightmost pixel. (The rightmost pixel is reserved for the busy indicator.)

@X

is the distance between the centers of two adjacent pixels.

In

Full

screen mode,

@X

is calculated as

(

Xmax

N

Xmin

) à 94. In

G.T

split-screen mode,

@X

is calculated as (

Xmax

N

Xmin

) à 46.

If you enter a value for

@X

from the home screen or a program in

Full

screen mode,

Xmax

is calculated as

Xmin

+

@X

… 94. In

G.T

split-screen mode,

Xmax

is calculated as

Xmin

+

@X

… 46.

Ymin

is the center of the next-to-the-bottom pixel;

Ymax

is the center of the top pixel.

@Y

is the distance between the centers of two adjacent pixels.

In

Full

screen mode,

@Y

is calculated as

(

Ymax

N

Ymin

) à 62. In

Horiz

split-screen mode,

@Y

is calculated as (

Ymax

N

Ymin

) à 30. In

G.T

split-screen mode,

@Y

is calculated as (

Ymax

N

Ymin

) à 50.

If you enter a value for

@Y

from the home screen or a program in

Full

screen mode,

Ymax

is calculated as

Ymin

+

@Y

… 62. In

Horiz

split-screen mode,

Ymax

is calculated as

Ymin

+

@Y

… 30. In

G.T

split-screen mode,

Ymax

is calculated as

Ymin

+

@Y

… 50.

B–10 General Information

826FEC~1.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 10/27/05 3:16 PM Printed: 10/27/05

3:16 PM Page 10 of 12

Graphing

Accuracy

(continued)

Cursor coordinates are displayed as eight-character numbers

(which may include a negative sign, decimal point, and exponent) when

Float

mode is selected.

X

and

Y

are updated with a maximum accuracy of eight digits.

minimum

and

maximum

on the

CALCULATE

menu are calculated with a tolerance of 1

EL

5;

‰f(x)dx

is calculated at 1

EL

3.

Therefore, the result displayed may not be accurate to all eight displayed digits. For most functions, at least five accurate digits exist. For

fMin(

,

fMax(

, and

fnInt(

on the

MATH

menu and

solve(

in the

CATALOG

, the tolerance can be specified.

Function Limits

Function Range of Input Values sin

x,

cos

x,

tan

x

sin L1 ln e

x

x,

log

x

10

x

x,

cos L1

x

sinh

x,

cosh

x

tanh

x

sinh

L1 cosh

L1

x x

0  |x| < 10

12

(radian or degree)

L1  x  1

10 L100 < x < 10 100

L10

L10

100

100

< x  230.25850929940

< x < 100

|x|  230.25850929940

|x| < 10

100

|x| < 5 × 10

99

1  x < 5 × 10

99

tanh

L1

x

x (real mode)

L1 < x < 1

0  x < 10 100

x (complex mode) |x| < 10 100

x

!

L.5  x  69, where x is a multiple of .5

Function Results

Function sin

L1 cos

L1

x,

tan

L1

x x

Range of Result

L90¡ to 90¡ or Lpà2 to pà2 (radians)

0¡ to 180¡ or 0 to p (radians)

General Information B–11

826FEC~1.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 10/27/05 3:16 PM Printed: 10/27/05

3:16 PM Page 11 of 12

Texas Instruments Support and Service

For General

Information

Service and warranty information

For more information about TI products and services, contact TI by e-mail or visit the TI Internet address.

E-mail inquiries:

Home Page:

[email protected]

education.ti.com

For information about the length and terms of the warranty or about product service, refer to the warranty statement enclosed with this product or contact your local Texas Instruments retailer/distributor.

B–12 General Information

826FEC~1.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 10/27/05 3:16 PM Printed: 10/27/05

3:16 PM Page 12 of 12

Index

!

ìììì

íííí

çççç

>

L1

'

ääää

à

=

¦

Ö

Ò

Õ

Ô

M

+

3

:

+ c

2 c

2 c

2

(addition), 2 .

3, A .

38

cdf(

(chi-square cdf), 13

pdf(

(chi-square pdf), 13

.

31, A .

3

.

.Test

(chi-square test), 13

31, A .

4

.

22, A .

4

(colon), 6, 16 .

5

(concatenation), 15 .

6, A .

38

3

‡(

(cube), 2 .

6, A

.

35

(cube root), 2 .

6, A

.

35

¡

<

{ }

[ ]

ƒ

( ) p

+

^

(degrees notation), 2 .

3, A .

34

(division), 2 .

3, A

.

37

(equal-to relational test), 2 .

25, A

.

35

(factorial), 2

.

21, A

.

34

(graph style, animate), 3

.

9

(graph style, dot), 3

.

9

(graph style, line), 3

.

9

(greater than), 2

.

25, A

.

35

(greater than or equal to), 2

.

25, A

.

35

(inverse), 2

.

3, 8

.

9, 10

.

10, A

.

36

(less than), 2

.

25, A

.

35

(less than or equal to), 2

.

25, A

.

36

(list indicator), 11

.

4

(matrix indicator), 10

.

7

(minutes notation), 2

.

23, A

.

38

(multiplication), 2

.

3, A

.

37

(negation), 1

.

23, 2

.

4, A

.

37

(not equal to), 2

.

25, A

.

35

(parentheses), 1

.

23

(pi), 2

.

4

(pixel mark), 8

.

15, 12

.

34

(pixel mark), 8

.

15, 12

.

34

(pixel mark), 8

.

15, 12

.

34

(plot type, box), 12

.

33

(plot type, histogram), 12 .

32

(plot type, modified box), 12 .

32

(plot type, normal probability), 12 .

33

(power), 2 .

3, A .

36, A .

37

"

2

10 x

^(

‡(

!

" "

N

(power of ten), 2

(root), 2 .

6, A

.

35

(square) , 2 .

3 , A

(square root) , 2 .

.

4, A .

37

(seconds notation), 2

.

36

.

23, A

.

38

3 , A

.

Store, 1 .

14, A

.

28

(string indicator), 15 .

3

(subtraction), 2 .

3, A

.

38

37

. A .

a+b

i (rectangular complex mode), 1 .

12,

2

.

16, A .

3

above graph style(

éééé

), 3

.

9

abs(

(absolute value), 2 .

13, 2 .

19, 10 .

10,

A

.

2

accuracy information computational and graphing, B .

10

graphing, 3 .

17

function limits and results, B .

11

addition (

+

), 2 .

3, A .

38

alpha cursor, 1 .

5

alpha key, 3 alpha-lock, 1 .

8

alternative hypothesis, 13 .

7

amortization

bal(

(amortization balance), 14

.

9, A

.

3

calculating schedules, 14

.

9

formula, A

.

56

GInt(

(sum of interest),14

.

9, A

.

12

(sum of principal), 14

GPrn( and

(Boolean operator), 2

.

9, A

.

19

.

26, A

.

2

angle(

, 2

.

19, A

.

2

ANGLE

menu, 2

.

23

angle modes, 1

.

11

animate graph style (

ìììì

), 3

.

9

ANOVA(

(one-way variance analysis),

13

.

25, A

.

2

formula, A

.

51

Ans

(last answer), 1

.

18, A

.

2

APDé (Automatic Power Down™), 1

.

2

applications. See examples, applications arccosine (

cos

M1

(

), 2

.

3

arcsine (

sin

M1

(

), 2

.

3

arctangent (

tan

M1

(

), 2

.

3

augment(

, 10

.

14, 11

.

15, A

.

3

Automatic Power Down™ (APDé), 1 .

2

automatic regression equation, 12 .

22

automatic residual list ( RESID ), 12 .

22

axes format, sequence graphing, 6 .

8

axes, displaying (

AxesOn

,

AxesOff

),

3

.

14, A .

3

AxesOff

, 3 .

14, A .

3

AxesOn

, 3 .

14, A .

3

. B .

backing up calculator memory, 19 .

4,

19

.

10

bal(

(amortization balance), 14 .

9, A .

3

batteries, 1 .

2, B .

2

below graph style (

ê

), 3 .

9

binomcdf(

, 13 .

33, A .

3

binompdf(

, 13

.

33, A

.

3

Index-1

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 1 of 16

Index (continued)

Boolean logic, 2 .

26

box pixel mark (

), 8

Boxplot

.

15, 12

plot type (

Ö

), 12

.

.

34

33

busy indicator, 1 .

4

. C .

CALCULATE menu, 3 .

25

Calculate

output option, 13 .

6, 13

.

8

cash flow calculating, 14 .

8

formula, A .

57

irr(

(internal rate of return), 14 .

8, A .

13

npv(

(net present value), 14 .

8, A .

17

CATALOG , 15 .

2

CBLé System, 16

.

21, 19

.

3, A

.

10

CBRé, 16

.

21, 19

.

3, A

.

10

Check RAM (memory screen), 18 chi-square cdf (

c

chi-square pdf ( chi-square test (

c c

2

2

2 cdf( pdf(

), 13

), 13

.Test

), 13

.

2

.

31, A

.

3

.

31, A

.

4

.

22, A

.

4

Circle(

(draw circle), 8

Clear Entries

, 18 clearing

.

11, A

.

4

.

4, A

.

4

entries (

Clear Entries

), 18 all lists (

ClrAllLists

), 18

.

4, A

.

4

.

4, A

.

4

drawing (

ClrDraw

), 8

.

4, A

.

4

home screen (

ClrHome

), 16

.

20, A

.

4

list (

ClrList

), 12

.

20, A

.

4

table (

ClrTable

), 16

.

20, A

.

4

ClrAllLists

(clear all lists), 18

.

4, A

.

4

ClrDraw

(clear drawing), 8

.

4, A

.

4

ClrHome

(clear home screen), 16

.

20, A

.

4

ClrList

(clear list), 12

.

20, A

.

4

ClrTable

(clear table), 16

.

20, A coefficients of determination (

r

2

.

4

,

R

2

),

12

.

23

colon separator (

:

), 6, 16 combinations (

nCr

), 2 .

.

5

21, A .

16

. C (continued) .

complex modes (

a+b

i,

r

e

^q

i), 1 .

12, 2

.

16, A .

3,

A

.

22

numbers, 1 .

12, 2 .

16, 2 .

18, A .

22

compounding-periods-per-year variable

(

C/Y

), 14 .

4, 14

.

14

concatenation (

+

), 15 .

6, A .

38

confidence intervals, 13 .

8, 13

.

16

N

13

.

21

conj(

(conjugate), 2 .

18, A .

4

Index-2

Connected

(plotting mode), 1 .

11, A .

4

contrast (display), 1 .

3

convergence, sequence graphing, 6 conversions

.

12

4Dec

(to decimal), 2 .

5, A .

5

4DMS

(to degrees/minutes/ seconds),

4Eff

2

.

24, A

.

7

(to effective interest rate), 14 .

12,

A

.

7

Equ4String(

(equation-to-string conversion), 15-7, A .

8

4Frac

(to fraction conversion), 2

.

5,

A

.

10

List4matr(

(list-to-matrix conversion),

10

.

14, 11

.

15, A

.

14

Matr4list(

(matrix-to-list conversion),

10

4Nom

.

14, 11

.

16, A

.

15

(to nominal interest rate conversion), 14

4Polar

.

12, A

.

16

(to polar conversion), 2

.

19,

A

.

19

P4Rx(

,

P4Ry(

(polar-to-rectangular conversion), 2

4Rect

.

24, A

.

21

(to rectangular conversion), 2

.

19,

A

.

22

R4Pr(

,

R4Pq(

(rectangular-to-polar conversion), 2

.

24, A

.

23

String4Equ(

(string-to-equation conversion), 15

.

8, A

.

29

CoordOff

, 3

CoordOn

, 3

.

14, A

.

5

.

14, A

.

5

correlation coefficient (

r

), 12

.

23, 12

.

25

N

12

.

27

cos(

(cosine), 2 .

3, A

cos

M1

(

(arccosine), 2

.

.

5

3, A

.

5

cosh(

(hyperbolic cosine), 15 .

10, A

.

5

. D (continued) .

cosh

M1

(

(hyperbolic arccosine), 15 .

10, A

.

5

cosine (

cos(

), 2 .

3, A

.

5

cross pixel mark (

+

), 8 cube (

3

) , 2 cube root (

.

6, A

3

‡(

.

), 2

35

.

6, A

.

15, 12

.

34

.

35

CubicReg

(cubic regression), 12 .

26, A

.

5

cubic regression (

CubicReg

), 12 .

26, A

.

5

cumulative sum (

cumSum(

), 10 .

15,

11

.

12, A

.

5

cumSum(

(cumulative sum), 10 .

15,

11

.

12, A

.

5

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 2 of 16

cursors, 1 .

5, 1 .

8

C/Y

(compounding-periods-per-year variable), 14 .

4, 14

.

14

. D .

Data input option, 13 .

6, 13

.

7

days between dates (

dbd(

), 14 .

13, A

.

5,

A

.

58

dbd(

(days between dates), 14 .

13, A

.

5,

A

.

58

4Dec

(to decimal conversion), 2 .

5, A

.

5

decimal mode (float or fixed), 1 .

10

decrement and skip (

DS<(

), 16 .

14, A

.

7

definite integral, 2 .

7, 3

.

28, 4

.

8, 5

.

6

Degree

angle mode, 1 degrees notation (

¡

) , 2

.

11, 2

.

23, A

.

6

.

3, A

.

34

DELETE FROM menu, 18

.

3

delete variable contents (

DelVar

), 16

.

15,

A

.

6

DelVar

(delete variable contents), 16

.

15,

A

.

6

DependAsk

, 7

.

3, 7

.

5, A

.

6

DependAuto

, 7

.

3, 7

.

5, A

.

6

derivative. See numerical derivative

det(

(determinant), 10 determinant (

det(

), 10

DiagnosticOff

, 12

.

12, A

.

6

.

12, A

.

6

.

23, A

.

6

DiagnosticOn

, 12

.

23, A

.

6

diagnostics display mode(

r

,

r

2

,

R

2

differentiation, 2

.

8, 3

.

28, 4

.

8, 5

.

6

), 12

.

23

. D (continued) .

dimensioning a list or matrix, 10

.

12,

dim(

!

10

.

13, 11

.

11, A

.

6

(dimension), 10

.

12, 11

.

(assign dimension), 10

11, A

.

.

6

13, 11

.

11,

A

.

6

Disp

(display), 16

.

18, A

.

6

DispGraph

(display graph), 16 .

19, A

.

7

display contrast, 1 .

3

display cursors, 1 .

5

DispTable

(display table), 16 .

19, A

.

7

DISTR (distributions menu), 13 .

29

DISTR DRAW (distributions drawing menu), 13 .

35

distribution functions

binomcdf(

, 13 .

33, A

.

3

binompdf(

, 13

c

2 cdf(

, 13 .

.

31, A

33, A

.

3

.

3

c

ÛÛ

2 pdf(

Ûcdf(

, 13

, 13

.

31, A

.

4

.

32, A

.

8

, 13 .

32, A

.

9

geometcdf(

, 13 .

34, A

.

10

geometpdf(

, 13 .

34, A

.

11

invNorm(

, 13 .

30, A

.

12

normalcdf(

, 13 .

30, A

.

17

normalpdf(

, 13 .

29, A

.

17

poissoncdf(

, 13 .

34, A

.

99

poissonpdf(

, 13 .

33, A

.

19

tcdf(

, 13 .

31, A

.

29

tpdf(

, 13

.

30, A

.

29

distribution shading instructions

Shadec

Shade

Û

2

(

, 13

, 13

.

.

36, A

36, A

.

.

26

27

ShadeNorm(

, 13

.

35, A

.

27

Shade_t(

, 13 division (

à

) , 2

.

36, A

.

27

.

3, A

.

37

DMS (degrees/minutes/seconds entry notation), 2

.

23, A

.

38

4DMS

(to degrees/minutes/seconds), 2

.

24,

A

.

7

dot graph style (

íííí

), 3 dot pixel mark (

¦

), 8

.

9

.

15, 12

.

34

Dot

(plotting mode), 1

.

11, A

DrawF

(draw a function), 8

.

7

.

9, A

.

7

Index-3

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 3 of 16

Index (continued)

. D (continued) .

drawing on a graph circles (

Circle(

), 8

.

11

functions and inverses (

DrawF

,

DrawInv

), 8

.

9

lines (

Horizontal

,

Line(

,

Vertical

),

8

.

6, 8

.

7

line segments (

Line(

), 8

.

5

pixels (

Pxl.Change

,

Pxl.Off

,

Pxl.On

,

pxl.Test

), 8

.

16

points (

Pt.Change

,

Pt.Off

,

Pt.On

),

8

.

14

tangents (

Tangent

), 8

.

8

text (

Text

), 8

.

12

using

Pen

, 8

.

13

DrawInv

(draw inverse), 8

.

9, A

.

7

DRAW menu, 8 .

3

DRAW instructions, 8 .

3

N

8

.

16

Draw output option, 13 .

6

N

13

.

8

DRAW POINTS menu, 8 .

14

DRAW STO (draw store menu), 8 .

17

dr/dq

operation on a graph, 5 .

6

DS<(

(decrement and skip), 16 .

14, A

.

7

DuplicateName menu, 19 .

5

dx/dt

operation on a graph, 3 .

28, 4

.

8

dy/dx

operation on a graph, 3 .

28, 4

.

8, 5

.

6

. E .

e (constant), 2 .

4

e^(

(exponential), 2 .

4, A

.

7

åååå

(exponent), 1 .

7, 1

.

10, A

.

7

edit keys table, 1 .

8

4Eff(

(to effective interest rate), 14

.

12, A

.

7

Else

, 16

End

, 16

.

10

.

12, A

.

8

Eng

(engineering notation mode), 1

.

10,

A

.

8

entry cursor, 1

.

5

ENTRY

(last entry key), 1

.

16

EOSé (Equation Operating System), 1

.

22

eqn

(equation variable), 2

.

8, 2

.

12

equal-to relational test (

=

), 2

.

25, A

.

35

Equation Operating System (EOSé), 1

.

22

Equation Solver

, 2

.

8

equations with multiple roots, 2

.

12

. E (continued) .

Equ4String(

(equation-to-string conversion), 15

.

7, A

.

8

Index-4

errors diagnosing and correcting, 1 .

24

messages, B .

5

examples—applications area between curves, 17 .

11

areas of regular n-sided polygons,

17

.

16

box plots, 17 .

2

cobweb attractors, 17 .

8

fundamental theorem of calculus, 17 .

14

guess the coefficients, 17 .

9

inequalities, 17

.

5

mortgage payments 17

.

18

parametric equations: ferris wheel problem, 17

.

12

piecewise functions, 17

Sierpinski triangle, 17

.

7

.

4

solving a system of nonlinear equations,

17

.

6

unit circle and trig curves, 17

.

10

examples—Getting Started box with lid 9 – 16 defining a, 9 defining a table of values, 10 finding calculated maximum, 16 setting the viewing window, 12 tracing the graph, 13 zooming in on the graph, 15 zooming in on the table, 11 coin flip, 2

.

2

compound interest, 14

.

3

drawing a tangent line, 8

.

2

financing a car, 14 .

2

forest and trees, 6 .

2

generating a sequence, 11 .

2

graphing a circle, 3 .

2

mean height of a population, 13 .

2

path of a ball, 4 .

2

pendulum lengths and periods, 12 .

2

polar rose, 5 .

2

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 4 of 16

. E (continued) .

examples—Getting Started (continued) quadratic formula converting to a fraction, 7 displaying complex results, 8 entering a calculation, 6 roots of a, 7

.

2

sending variables, 19

.

2

solving a system of linear equations,

10

.

2

unit circle, 9

.

2

volume of a cylinder, 16

.

2

examples—miscellaneous convergence, 6

.

12

daylight hours in Alaska, 12

.

28

calculating outstanding loan balances,

14

.

10

predator-prey model, 6 .

13

exponential regression (

ExpReg

), 12 .

26,

A

.

8

expr(

(string-to-expression conversion),

15

.

7, A

.

8

ExpReg

(exponential regression), 12 .

26,

A

.

8

expression, 1 .

6

converting from string (

expr(

), 15 .

7,

A

.

8

turning on and off (

ExprOn

,

ExprOff

),

3

.

14, A

.

8

ExprOff

(expression off), 3

ExprOn

(expression on), 3

.

14, A

.

8

.

14, A

.

8

. F .

‰f(x)dx

operation on a graph, 3

.

28

factorial (

!

), 2

.

21, A

.

34

family of curves, 3

.

16

, 13

.

32, A

.

8

Fill(

, 10

.

13, A

.

8

FINANCE CALC

menu, 14

FINANCE VARS

menu, 14

.

5

.

14

financial functions amortization schedules, 14

.

9

cash flows, 14

.

8

days between dates, 14

.

13

interest rate conversions, 14

.

12

payment method, 14

.

13

time value of money (

TVM

), 14

.

6

. F (continued) .

Fix

(fixed-decimal mode), 1

.

10, A

.

8

fixed-decimal mode (

Fix

), 1

.

10, A

.

8

Float

(floating-decimal mode), 1 floating-decimal mode (

Float

), 1

fMax(

(function maximum), 2

.

10, A

.

8

.

10, A

.

8

.

6, A

.

9

fMin(

(function minimum), 2

fnInt(

(function integral), 2

.

6, A

.

9

.

7, A

.

9

FnOff

(function off), 3

FnOn

(function on), 3

.

8, A

.

9

.

8, A

.

9

For(

, 16

.

10, A

.

9

format settings, 3

.

13, 6

.

8

formulas amortization, A

.

56

ANOVA

, A

.

51

cash flow, A

.

57

days between dates, A .

58

factorial, 2 .

21

interest rate conversions, A .

57

logistic regression, A sine regression, A .

50

.

50

time value of money, A .

54

two-sample Û-Test, A two-sample t test, A .

.

53

52

fPart(

(fractional part), 2 .

14, 10 .

11, A

.

9

, 13 .

32, A

.

9

4Frac

(to fraction), 2 .

5, A

.

10

free-moving cursor, 3 .

17

frequency, 12 .

24

Full

(full-screen mode), 1

.

12, A

.

10

full-screen mode (

Full

), 1

.

12, A

.

10

Func

(function graphing mode), 1

.

11,

A

.

10

function, definition of, 1

.

7

function graphing, 3

.

13

.

28

accuracy, 3

.

17

CALC

(calculate menu), 3 defining and displaying, 3

.

25

.

3

defining in the Y= editor, 3

.

5

defining on the home screen, in a program, 3

.

6

deselecting, 3 displaying, 3

.

7

.

3, 3

.

11, 3

.

15

evaluating, 3

.

6

family of curves, 3 format settings, 3

.

16

.

13

. F (continued) .

Function graphing (continued)

Index-5

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 5 of 16

Index (continued)

free-moving cursor, 3 .

17

graph styles, 3 .

9

maximum of (

fMax(

), 2.6, A.9

minimum of (

fMin(

), 2.6, A.9

modes, 1 .

11, 3 .

4, A .

10

moving the cursor to a value, 3 .

19

overlaying functions on a graph, 3 .

16

panning, 3 .

19

pausing or stopping a graph, 3 .

15

Quick Zoom, 3 .

19

selecting, 3 .

7, 3 .

8, A

.

9

shading, 3

.

10

Smart Graph, 3

.

15

tracing, 3

.

18

window variables, 3

.

11, 3

.

12

Y= editor, 3

.

5

viewing window, 3

.

11

@X

and

@Y

window variables, 3

.

12

ZOOM

menu, 3

.

20

ZOOM MEMORY

menu, 3 function integral (

fnInt(

), 2

.

23

.

7, A

.

9

functions and instructions table, A

.

2A

.

2

future value, 14

.

5, 14

.

7, 14

.

14

present value, 14

.

5, 14

.

7, 14

.

14

FV

(future-value variable), 14

.

4, 14

.

14

.G .

gcd(

(greatest common divisor), 2

.

15,

A

.

10

GDB

(graph database), 8

geometcdf(

, 13

.

19

.

34, A

.

10

geometpdf(

, 13

.

34, A

.

10

Get(

(get data from CBL or CBR), 16

.

21,

A

.

10

GetCalc(

(get data from TI-82 STATS),

16

.

21, A

.

10

getKey

, 16 .

20, A

.

10

Getting Started, 118. See also examples,

Getting Started

Goto

, 16 .

13, A

.

10

. G (continued) .

graph database (

GDB

), 8

.

19

graphing modes, 1

.

11

graphing-order modes, 1

.

12

GraphStyle(

, 16

.

15, A

.

11

graph styles, 3

.

9

graph-table split-screen mode (

G.T

), 1

9

.

5, A

.

11

greater than (

>

), 2

.

25, A

.

35

greater than or equal to (

), 2

.

12,

.

25, A

.

35

greatest common divisor (

gcd(

), 2

.

15,

A

.

10

greatest integer (

int(

), 2

.

14, 10

.

11, A

.

12

GridOff

, 3

GridOn

, 3

.

14, A

.

11

.

14, A

.

11

G.T

(graph-table split-screen mode), 1

.

12,

9

.

5, A

.

11

. H .

Histogram

plot type (

Ò

), 12 .

32

home screen, 1 .

4

Horiz

(horizontal split-screen mode), 1 .

12,

9

.

4, A

.

11

hyperbolic functions, 15 .

10

Horizontal

(draw line), 8 .

6

N

8

.

7, A

.

11

hypothesis tests, 13 .

10

N

13

.

15

. I .

i (complex number constant), 2 .

17

(annual interest rate variable), 14 .

4,

14

.

14

identity(

, 10

If

instructions

If

, 16

.

13, A

.

9, A

.

11

.

11

If-Then

, 16 .

9, A

.

11

If-Then-Else

, 16

.

10, A

.

11

imag(

(imaginary part), 2

.

18, A

.

11

imaginary part (

imag(

), 2

.

18, A

.

11

implied multiplication, 1

.

23

increment and skip (

IS>(

), 16

.

13, A

.

13

IndpntAsk

, 7

.

3, A

.

12

IndpntAuto

, 7

.

3, A

.

12

independent variable, 7

.

3, A

.

12

inferential stat editors, 13

.

6

Index-6

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 6 of 16

. I (continued) .

inferential statistics. See also stat tests; confidence intervals alternative hypotheses, 13

.

7

bypassing editors, 13

.

8

calculating test results (

Calculate

),

13

.

8

confidence interval calculations, 13

.

8,

13

.

16

N

13

.

21

data input or stats input, 13

.

7

entering argument values, 13

.

7

graphing test results (

Draw

), 13

.

8

input descriptions table, 13

.

26

pooled option, 13

.

8

STAT TESTS

menu, 13

.

9

test and interval output variables, 13

.

28

Input

, 16 .

16, 16

.

17, A

.

12

insert cursor, 1 .

5

inString(

(in string), 15 .

7, A

.

12

instruction, definition of, 1 .

7

int(

(greatest integer), 2 .

14, 10 .

11, A

.

12

GInt(

(sum of interest), 14 .

9, A

.

12

integer part (

iPart(

), 2 .

14, 10 .

11, A

.

12

integral. See numerical integral interest rate conversions calculating, 14 .

12

4Eff(

(compute effective interest rate),

14

.

12, A

.

7

formula, A .

57

4Nom(

(compute nominal interest rate),

14

.

12, A

.

16

internal rate of return (

irr(

), 14

.

8, A

.

13

intersect

operation on a graph, 3 inverse (

L1

), 2

.

3, 8

.

9, 10

.

10, A

.

36

.

27

inverse cumulative normal distribution

(

invNorm(

), 13

.

30, A

.

12

inverse trig functions, 2

.

3

invNorm(

(inverse cumulative normal distribution), 13

.

30, A

.

12

iPart(

(integer part), 2

.

14, 10

.

11, A

.

12

irr(

(internal rate of return), 14

.

8, A

.

13

IS>(

(increment and skip), 16

.

13, A

.

13

. K .

keyboard layout, 2, 3 math operations, 2

.

3

key-code diagram, 16

.

20

. L .

L

(user-created list name symbol), 11

.

16,

A

.

13

LabelOff

, 3

LabelOn

, 3 labels

.

14, A

.

13

.

14, A

.

13

graph, 3

.

14, A

.

13

program, 16

Last Entry, 1

.

13, A

.

13

.

16

Lbl

(label), 16

.

13, A

.

13

lcm(

(least common multiple), 2 least common multiple (

lcm(

), 2

length(

of string, 15

.

8, A

.

13

.

15, A

.

13

.

15, A

.

13

less than (

<

), 2 .

25, A

.

35

less than or equal to (

), 2 line graph style (

çççç

), 3 .

9

.

25, A

.

36

Line(

(draw line), 8 .

5, A

.

13

line segments, drawing, 8 .

5

lines, drawing, 8 .

6, 8

.

7

linking receiving items, 19 .

5

to a CBL System or CBR, 19 .

3

to a PC or Macintosh, 19 .

3

to a TI.82, 19 .

3, 19

.

8

transmitting items, 19 .

6

two TI-82 STATS units, 19 .

3

LINK RECEIVE

LINK SEND

menu, 19

.

5

menu, 19

.

4

LinReg(a+bx)

(linear regression), 12

.

26,

A

.

14

LinReg(ax+b)

(linear regression), 12

.

25,

A

.

14

LinRegTTest

(linear regression t test),

13

.

24, A

.

14

@List(

, 11

.

12, A

.

14

LIST MATH

menu, 11

.

17

List4matr(

(lists-to-matrix conversion),

10

.

14, 11

LIST NAMES

.

15, A

menu, 11

LIST OPS

menu, 11

.

14

.

10

.

6

. L (continued) .

lists, 11

.

111

.

18

Index-7

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 7 of 16

Index (continued)

accessing an element, 11 .

5

attaching formulas, 11 .

7, 12

.

14

clearing all elements, 12 .

12, 12

.

20

copying, 11 .

5

creating, 11 .

3, 12

.

12

deleting from memory, 11 .

5, 18

.

3

detaching formulas, 11 .

8, 12

.

16

dimension, 11 .

4, 11

.

11

entering list names, 11 .

6, 12

.

11

indicator (

{ }

), 11 .

4

naming lists, 11 .

3

storing and displaying, 11

.

4

transmitting to and from TI.82, 19

.

4

using in expressions, 11

.

9

using to graph a family of curves, 3

.

16,

11

.

5

using to select data points from a plot,

11

.

13

using with math functions, 11

.

9

using with math operations, 2

.

3

ln(

, 2

.

4, A

.

14

LnReg

(logarithmic regression), 12

.

26,

A

.

14

log(

, 2

.

4, A

.

14

logic (Boolean) operators, 2

Logistic

(regression), 12

.

26

.

27, A

.

15

logistic regression formula, A

.

50

. M .

MATH CPX

(complex menu), 2

.

18

MATH

menu, 2

.

5

MATH NUM

(number menu), 2 math operations, keyboard, 2

.

3

.

13

MATH PRB

(probability menu), 2

.

20

Matr4list(

(matrix-to-list conversion),

10

.

14, 11 .

16, A

.

15

matrices, 10 .

110 .

16

accessing elements, 10 .

8

copying, 10 .

8

defined, 10 .

3

deleting from memory, 10 .

4

dimensions, 10 .

3, 10

.

12, 10

.

13

displaying a matrix, 10 .

8

displaying matrix elements, 10 .

4

editing matrix elements, 10 .

6

. M (continued) .

matrices, (continued) indicator (

[ ]

), 10 .

7

Index-8

inverse (

L1

), 10 .

10

math functions, 10 .

910 .

11

matrix math functions (

det(

,

T

,

dim(

,

Fill(

,

identity(

,

randM(

,

augment(

,

Matr4list(

,

List4matr(

,

cumSum(

),

10

.

1210 .

16

referencing in expressions, 10 .

7

relational operations, 10 .

11

row operations(

ref(

,

rref(

,

rowSwap(

,

row+(

,

†row(

,

†row+(

), 10 .

15

selecting, 10 .

3

viewing, 10

MATRX EDIT

.

5

menu, 10

.

3

MATRX MATH menu, 10

.

12

MATRX NAMES

menu, 10

max(

(maximum), 2

.

7

.

15, 11

.

17, A

.

15

maximum of a function (

fMax(

), 2

.

6, A

.

9

maximum

operation on a graph, 3

.

27

mean(

, 11

.

17, A

.

15

median(

, 11

.

17, A

.

15

Med.Med

memory

(median-median), 12

.

25, A

.

15

backing up, 19

.

10

checking available, 18

.

2

clearing all list elements from, 18

.

4

clearing entries from, 18 deleting items from, 18

.

3

.

4

insufficient during transmission, 19

.

5

resetting defaults, 18

.

6

resetting memory, 18

.

5

MEMORY

menu, 18

.

2

Menu(

(define menu), 16

.

14, A

.

15

menus, 4, 1 .

19

defining (

Menu(

), 16 .

14, A

.

15

map, A .

39

scrolling, 1 .

19

min(

(minimum), 2 .

15, 11 .

17, A

.

minimum

operation on a graph, 3

16

.

27

minimum of a function (

fMin(

), 2 .

6, A

.

9

minutes notation (

'

) , 2

ModBoxplot

.

23, A

plot type (

Õ

.

38

), 12 .

32

. M (continued) .

modified box plot type (

Õ

), 12 .

32

mode settings, 1 .

9

a+b

i (complex rectangular), 1 .

12, 2

.

16,

A

.

3

r

e

^q

i (complex polar), 1 .

12, 2

.

16, A

.

22

Connected

(plotting), 1

.

11, A

.

4

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PM Page 8 of 16

Degree

(angle), 1 .

11, 2 .

24, A

.

6

Dot

(plotting), 1 .

11, A

.

7

Eng

(notation), 1 .

10, A

.

8

Fix

(decimal), 1 .

10, A

.

8

Float

(decimal), 1 .

10, A

.

8

Full

(screen), 1 .

12, A

.

10

Func

(graphing), 1 .

11, A

.

10

G.T

(screen), 1 .

12, A

.

11

Horiz

(screen), 1 .

12, A

.

11

Normal

(notation), 1 .

10, A

.

16

Par

/

Param

(graphing), 1 .

11, A

.

18

Pol

/

Polar

(graphing), 1

Radian

(angle), 1

.

11, A

.

19

.

11, 2

.

24, A

.

21

Real

, 1

.

12, A

.

22

Sci

(notation), 1

.

10, A

.

25

Seq

(graphing), 1

.

11, A

.

26

Sequential

(graphing order), 1

.

12,

A

.

26

Simul

(graphing order), 1 modified box plot type (

Õ

), 12 multiple entries on a line, 1 multiplication (

ääää

), 2

.

3, A

multiplicative inverse, 2

.

.

3

.

6

37

.

12, A

.

27

.

32

. N .

(number of payment periods variable),

14

.

4, 14

.

14

nCr

(number of combinations), 2

nDeriv(

(numerical derivative), 2

.

21, A

.

16

.

7, A

.

16

negation (

M

), 1

.

23, 2

.

4, A

.

37

4Nom(

(to nominal interest rate), 14

.

12,

A

.

16

nonrecursive sequences, 6

.

5

normal distribution probability

(

normalcdf(

), 13

.

30, A

.

17

Normal

notation mode, 1 .

10, A

.

16

normal probability plot type (

Ô

), 12 .

33

. N (continued) .

normalcdf(

(normal distribution probability), 13 .

30, A

.

17

normalpdf(

(probability density function),

13

.

29, A

.

17

NormProbPlot

plot type (

Ô

), 12 .

33

not(

(Boolean operator), 2 .

26, A

.

17

not equal to (

ƒ

), 2 .

25, A

.

35

nPr

(permutations), 2 .

21, A

.

17

npv(

(net present value), 14 .

8, A

.

17

numerical derivative, 2 .

7, 3

.

28, 4

.

8, 5

.

6

numerical integral, 2 .

7, 3

.

28

. O .

one-proportion z confidence interval

(

1.PropZInt

), 13 .

20, A

.

20

one-proportion z test (

1.PropZTest

),

13

.

14, A

.

20

one-sample t confidence interval

(

TInterval

), 13 .

17, A

.

30

one-variable statistics (

1.Var Stats

),

12

.

25, A .

31

or

(Boolean) operator, 2 .

26, A

.

17

order of evaluating equations, 1 .

22

Output(

, 9 .

6, 16 .

19, A

.

18

. P .

panning, 3 .

19

Par

/

Param

(parametric graphing mode),

1

.

9, 1

.

11, A

.

18

parametric equations, 4

.

5

parametric graphing

CALC

(calculate operations on a graph),

4

.

8

defining and editing, 4

.

4

free-moving cursor, 4

.

7

graph format, 4 graph styles, 4

.

6

.

4

moving the cursor to a value, 4

.

8

selecting and deselecting, 4 setting parametric mode, 4

.

.

4

5

tracing, 4

.

7

window variables, 4

.

5

Y=

editor, 4

.

4

zoom operations, 4 parentheses, 1

.

23

path (

ëëëë

) graph style, 3

.

8

.

9

. P (continued) .

Pause

, 16

.

12, A

.

18

pausing a graph, 3

.

15

Pen

, 8

.

13

permutations (

nPr

), 2 .

21, A

.

17

phase plots, 6 .

13

Pi (

p

), 2 .

4

Pic (pictures), 8 .

17, 8

.

18

pictures ( Pic ), 8 .

17, 8

.

18

pixel, 8 .

16

pixels in

Horiz

/

G.T

modes, 8 .

16, 9

.

6

Plot1(

, 12 .

34, A

.

18

Index-9

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 9 of 16

Index (continued)

Plot2(

, 12 .

34, A

.

18

Plot3(

, 12 .

34, A

.

18

PlotsOff

, 12 .

35, A

.

18

PlotsOn

, 12 .

35, A

.

18

plotting modes, 1 .

11

plotting stat data, 12 .

31

PMT

(payment amount variable), 14 .

4,

14

.

14

Pmt_Bgn

(payment beginning variable),

14

.

13, A .

19

Pmt_End

(payment end variable), 14 .

13,

A

.

19

poissoncdf(

, 13

poissonpdf(

, 13

.

34, A

.

19

.

33, A

.

19

Pol

/

Polar

(polar graphing mode), 1

.

9,

1

.

11, A

.

19

polar equations, 5

.

4

polar form, complex numbers, 2

.

17

4Polar

(to polar), 2

.

19, A

.

19

polar graphing

CALC

(calculate operations on a graph),

5

.

6

defining and displaying, 5

.

3

equations, 5

.

4

free-moving cursor, 5

.

6

graph format, 5

.

5

graph styles, 5

.

3

moving the cursor to a value, 5

.

6

selecting and deselecting, 5

.

4

mode (

Pol

/

Polar

), 1

.

9, 1

.

11, 5

.

3, A

.

19

tracing, 5

.

6

window variables, 5

.

4

Y= editor, 5 .

3

ZOOM operations, 5 .

6

PolarGC

(polar graphing coordinates),

3

.

13, A .

19

. P (continued) .

pooled option, 13 .

6, 13

.

8

power (

^

), 2 .

3, A .

36, A .

37

power of ten (

10

^(

), 2 .

4, A .

37

present value, 14 .

5, 14 .

7, 14

.

14

previous entry (Last Entry), 1 .

16

PRGM CTL (program control menu), 16 .

8

PRGM EDIT menu, 16 .

7

PRGM EXEC menu, 16 .

7

PRGM I/O (Input/Output menu), 16 .

16

prgm

(program name), 16 .

15, A .

19

PRGM NEW menu, 16

.

4

Index-10

GPrn(

(sum of principal), 14 .

9, A .

19

probability, 2 .

20

probability density function (

normalpdf(

),

13

.

29, A

.

17

prod(

(product), 11 .

18, A .

19

programming copying and renaming, 16 .

7

creating new, 16 .

4

defined, 16 .

4

deleting, 16 .

4

deleting command lines, 16 .

6

editing, 16

.

6

entering command lines, 16

.

5

executing, 16

.

5

instructions, 16

.

9

N

16

.

21

inserting command lines, 16

.

6

name (

prgm

), 16

.

15, A

.

19

renaming, 16 stopping, 16

.

7

.

5

subroutines, 16

.

22

Prompt

, 16

.

18, A

.

19

1.PropZInt

(one-proportion z confidence interval), 13

1.PropZTest

13

.

14, A

.

20

.

20, A

.

20

(one-proportion z test),

2.PropZInt

(two-proportion z confidence interval), 13

2.PropZTest

13

.

15, A

.

20

.

21, A

.

20

(two-proportion z test),

P4Rx(

,

P4Ry(

(polar-to-rectangular conversions), 2

Pt.Change(

, 8

.

24, A

.

21

.

15, A

.

20

Pt.Off(

, 8 .

15, A

.

20

Pt.On(

, 8 .

14, A

.

20

. P (continued) .

PV

(present value variable), 14 .

4, 14

.

14

p-value, 13 .

28

PwrReg

(power regression), 12 .

27, A

.

20

Pxl.Change(

, 8 .

16, A

.

21

Pxl.Off(

, 8 .

16, A

.

21

Pxl.On(

, 8 .

16, A

.

21

pxl.Test(

P/Y

, 8 .

16, A

.

21

(number-of-payment-periods-per-year variable), 14 .

4, 14

.

14

. Q .

QuadReg

(quadratic regression), 12 .

25,

A

.

21

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 10 of 16

QuartReg

(quartic regression), 12 .

26

Quick Zoom, 3 .

19, A

.

21

. R .

r

(radian notation), 2 .

24, A

.

34

r r

(correlation coefficient), 12

2

,

R

2

.

23

(coefficients of determination),

12

.

23

Radian

angle mode, 1 radian notation (

r

), 2

.

11, 2 .

24, A

.

21

.

24, A

.

34

rand

(random number), 2 .

20, A

.

21

randBin(

(random binomial), 2 .

22, A

.

21

randInt(

(random integer), 2 .

22, A

.

22

randM(

(random matrix), 10 .

13, A

.

22

randNorm(

(random Normal), 2

.

22, A

.

22

random seed, 2

.

20, 2

.

22

RCL

(recall), 1

.

15, 11

.

9

r

e

^q

i (polar complex mode), 1

A

.

22

Real

mode, 1

.

12, A

real(

(real part), 2

.

22

.

18, A

.

22

.

12, 2

.

16,

RecallGDB

, 8

RecallPic

, 8

.

20, A

.

22

.

18, A

.

22

4Rect

(to rectangular), 2

.

19, A

.

22

rectangular form, complex numbers, 2

.

17

RectGC

(rectangular graphing coordinates), 3

.

13, A

.

22

recursive sequences, 6

.

6

ref(

(row-echelon form), 10

.

15, A

.

22

. R (continued) .

RegEQ

(regression equation variable),

12

.

22, 12

.

29

regression model automatic regression equation, 12

.

22

automatic residual list feature, 12

.

22

diagnostics display mode, 12

.

23

models, 12

.

25

relational operations, 2 .

25, 10 .

11

Repeat

, 16 .

11, A

.

23

RESET menu, 18 .

5

resetting defaults, 18 .

6

memory, 5, 18 .

5

residual list ( RESID ), 12 .

22

Return

, 16 root (

x

), 2

.

15, A

.

23

.

6, A

.

35

root of a function, 3 .

26

round(

, 2 .

13, 10 .

10, A

.

23

row+(

, 10 .

16, A

.

23

…row(

, 10 .

…row+(

, 10

16, A

.

.

16, A

23

.

23

rowSwap(

, 10 .

16, A

.

23

R4Pr(

,

R4Pq(

(rectangular-to-polar conversions), 2 .

24, A

.

23

rref(

(reduced-row-echelon form), 10 .

15,

A

.

23

. S .

(two-sample Û-Test),

13

.

23, A

.

24

2.SampTInt

(two-sample t confidence interval), 13 .

19, A

.

24

2.SampTTest

(two-sample t test), 13

.

13,

A

.

24, A

.

25

2.SampZInt

(two-sample z confidence interval), 13

.

18, A

.

25

2.SampZTest

(two-sample z test), 13

Scatter

A

.

25

plot type (

"

), 12

.

12,

.

31

Sci

(scientific notation mode), 1

.

10, A

.

25

scientific notation, 1

.

7,1

.

10

screen modes, 1

.

12

second cursor (

2nd

), 1

.

5

second key (

2nd

), 3

. S (continued) .

seconds DMS notation (

"

) , 2

.

23

Select(

, 11

.

12, A

.

25

selecting data points from a plot, 11

.

13

functions from the home screen or a program, 3

.

8

functions in the

Y=

editor, 3

.

7

items from menus, 4 stat plots from the

Y=

editor, 3

.

7

Send(

(send to CBL or CBR), 16

.

21, A

.

26

sending. See transmitting

Seq

(sequence graphing mode), 1 .

11,

A

.

26

seq(

(sequence), 11 .

12, A

.

26

sequence graphing axes format, 6 .

8

CALC (calculate menu), 6 defining and displaying, 6

.

10

.

3

evaluating, 6 .

10

free-moving cursor, 6 .

9

graph format, 6 .

8

Index-11

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 11 of 16

Index (continued)

graph styles, 6 .

4

moving the cursor to a value, 6 .

9

nonrecursive sequences, 6 .

5

phase plots, 6 .

13

recursive sequences, 6 .

6

setting sequence mode, 6 .

3

selecting and deselecting, 6 .

4

TI-82 STATS versus TI.82 table, 6 .

15

tracing, 6 .

9

web plots, 6 .

11

window variables, 6 .

7

Y= editor, 6

.

4

ZOOM (zoom menu), 6

.

10

Sequential

(graphing order mode), 1

.

12,

service information, B

.

12

setting

A

.

26

display contrast, 1

.

3

graph styles, 3

.

9

graph styles from a program, 3

.

10

modes, 1

.

9

modes from a program, 1

.

9

split-screen modes, 9

.

3

split-screen modes from a program, 9

.

6

tables from a program, 7

.

3

. S (continued) .

SetUpEditor

, 12

.

21, A

.

26

shade above (

éééé

) graph style, 3 shade below (

ê

) graph style, 3

.

9

.

10

Shade(

Shade

Û

, 8

Shadec

2

(

.

9, A

, 13

, 13

.

26

.

36, A

.

26

.

36, A

.

27

ShadeNorm(

, 13

.

35, A

.

27

Shade_t(

, 13

.

36, A

.

27

shading graph areas, 3 .

10, 8

.

10

Simul

(simultaneous graphing order mode), 1 .

12, A

.

27

sin(

(sine), 2 .

3, A

sin

M1

(

(arcsine), 2 .

.

27

3, A

.

27

sine (

sin(

), 2 .

3, A

.

27

sine regression formula, A .

50

sinh(

(hyperbolic sine), 15 .

10, A

.

27

sinh M1 (

(hyperbolic arcsine), 15 .

10, A

.

27

SinReg

(sinusoidal regression), 12 .

27,

A

.

28

Smart Graph, 3 .

15

solve(

, 2 .

12, A

.

28

Solver

, 2

.

8

Index-12

solving for variables in the equation solver,

2

.

10, 2 .

11

SortA(

(sort ascending), 11 .

10, 12 .

20,

A

.

28

SortD(

(sort descending), 11 .

10, 12 .

20,

A

.

28

split-screen modes

G.T

(graph-table) mode, 9 .

5

Horiz

(horizontal) mode, 9 .

4

setting, 9 .

3, 9 .

6

split-screen values, 8 square (

2

) , 2

.

3 , A

square root (

‡(

) , 2

.

.

12, 8

36

.

3 , A

.

37

STAT CALC menu, 12

.

24

STAT EDIT

menu, 12

.

20

stat list editor

.

16, 9

.

6

attaching formulas to list names, 12 clearing elements from lists, 12

.

12

creating list names, 12

.

12

detaching formulas from list names,

.

14

12

.

16

displaying, 12

.

10

edit-elements context, 12

.

18

. S (continued) .

stat list editor (continued) editing elements of formula-generated lists, 12

.

16

editing list elements, 12

.

13

enter-names context, 12 entering list names, 12

.

19

.

11

formula-generated list names, 12

.

15

removing lists, 12

.

12

restoring list names

L

1

L

6

, 12

.

12,

12

.

21

switching contexts, 12 .

17

view-elements context, 12 .

18

view-names context, 12 .

19

STAT PLOTS menu, 12 .

34

stat tests and confidence intervals

ANOVA(

(one-way analysis of variance), 13

c

²

.Test

.

25

(chi-square test), 13 .

22

LinRegTTest

(linear regression t test),

13

.

24

1.PropZInt

(one-proportion

z confidence interval), 13 .

20

1.PropZTest

(one-proportion z test),

13

.

14

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 12 of 16

2.PropZInt

(two-proportion

z confidence interval), 13 .

21

2.PropZTest

(two-proportion z test),

13

.

15

(two-sample Û.Test),

13

.

23

2.SampTInt

(two-sample t confidence interval), 13 .

19

2.SampTTest

(two-sample t test),

13

.

13

2.SampZInt

(two-sample z confidence interval), 13

.

18

2.SampZTest

(two-sample z test),

13

.

12

TInterval

(one-sample t confidence interval), 13

.

17

T.Test

(one-sample t test), 13

.

11

ZInterval

(one-sample z confidence interval), 13

.

16

Z.Test

(one-sample z test), 13

Stats input option, 13

.

6, 13

STAT TESTS

menu, 13

.

9

.

7

.

10

statistical distribution functions. See distribution functions

. S (continued) .

statistical plotting, 12

.

31

Boxplot

(regular box plot), 12

.

33

defining, 12

.

34

from a program, 12

Histogram

.

37

, 12

.

32

ModBoxplot

(modified box plot),

12

.

32

NormProbPlot

(normal probability plot), 12

.

33

Scatter

, 12 tracing, 12

.

31

.

36

turning on/off stat plots, 3

.

7, 12

.

35

viewing window, 12

.

36

xyLine

, 12

.

31

statistical variables table, 12

.

29

stdDev(

(standard deviation), 11 .

18, A

.

28

Stop

, 16 .

15, A

Store (

!

), 1 .

.

28

14, A

.

28

StoreGDB

, 8 .

19, A

.

28

StorePic

, 8 .

17, A

.

29

storing graph databases ( GDB s), 8 .

19

graph pictures, 8 .

17

variable values, 1 .

14

String4Equ(

(string-to-equation conversions), 15 .

8, A

.

29

strings, 15 .

315 .

9

concatenation (

+

), 15 .

6, A .

38

converting, 15

.

7, 15

.

8

defined, 15

.

3

displaying contents, 15

.

5

entering, 15

.

3

functions in

CATALOG

, 15

.

6

indicator (

"

), 15

.

3

length (

length(

), 15

.

8, A

.

13

storing, 15

.

5

variables, 15

.

4

student-t distribution probability (

tcdf(

), 13

.

31, A

.

29

probability density function (

tpdf(

),

13

.

30, A

.

30

sub(

(substring), 15 subroutines, 16

.

9, A

.

29

.

15, 16

.

22

subtraction (

N

), 2

.

3, A

.

38

sum(

(summation), 11 system variables, A

.

49

.

18, A

.

29

Index-13

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 13 of 16

Index (continued)

. T .

TABLE SETUP

screen, 7

.

3

tables, 7

.

1 – 7

.

6

description, 7

.

5

variables, 7

.

3 – 7

.

5

tan(

(tangent), 2

.

3, A

.

29

tan

M1

(

(arctangent), 2

.

3, A

.

29

tangent (

tan(

), 2

.

3, A

.

29

Tangent(

(draw line), 8 tangent lines, drawing, 8

.

8, A

.

29

.

8

tanh(

(hyperbolic tangent), 15

.

10, A

.

29

tanh

M1

(

(hyperbolic arctangent), 15

.

10,

A

.

29

@Tbl

(table step variable), 7

.

3

TblStart

(table start variable), 7

.

3

tcdf(

(student-t distribution probability),

13

.

31, A

.

29

technical support, B .

12

TEST (relational menu), 2 .

25

TEST LOGIC (Boolean menu), 2 .

26

Text(

instruction, 8 .

12, 9 .

6, A

.

29

placing on a graph, 8 .

12

Then

, 16 .

9, A

.

11

thick (

è

) graph style, 3 .

9

TI.82

link differences, 19 .

9

transmitting to/from, 19 .

4, 19 .

8, 19 .

9

TI-82 STATS features, 17, 18 keyboard, 2, 3 key code diagram, 16

.

20

Link. See linking menu map, A

.

39

TI.GRAPH LINK

, 19

Time

axes format, 6

.

3

.

8, A

.

30

time value of money (

TVM

) calculating, 14

.

6

C/Y

variable (number of compounding periods per year), 14

.

14

formulas, A

.

54

FV

æ

variable (future value), 14

.

14

variable (annual interest rate), 14

.

14

. T (continued) .

time value of money (continued)

variable (number of payment

PMT

P/Y

periods), 14

.

14

variable (payment amount), 14

.

14

PV

variable (present value), 14

.

14

variable (number of payment periods per year), 14

.

14

tvm_FV

(future value), 14

tvm_I% tvm_

Ú

(interest rate), 14

.

.

7, A

.

31

7, A

(# payment periods), 14

.

31

.

7, A

.

31

tvm_Pmt

(payment amount), 14

.

6,

A

.

31

tvm_PV

(present value), 14

.

7, A

.

31

TVM Solver

, 14 variables, 14

.

14

.

4

TInterval

(one-sample t confidence interval), 13 .

17, A

.

30

tpdf(

(student-t distribution probability

TRACE density function), 13 .

30, A

.

30

cursor, 3 .

18

entering numbers during, 3 .

19, 4

.

8,

5

.

6, 6

.

9

expression display, 3 .

14, 3

.

18

Trace

instruction in a program, 3 .

19,

A

.

30

transmitting error conditions, 19 .

6

from a TI.82 to a TI-82 STATS, 19

.

9

items to another unit, 19 lists to a TI.82, 19 stopping, 19

.

6

.

6

.

4, 19

.

8

to an additional TI-82 STATS, 19

T

(transpose matrix), 10 transpose matrix (

T

), 10

T.Test

.

7

.

12, A

.

34

.

12, A

.

34

trigonometric functions, 2

.

3

(one-sample t test), 13

.

11, A

.

30

Index-14

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 14 of 16

. T (continued) .

turning on and off axes, 3

.

14

calculator, 1

.

2

coordinates, 3

.

14

expressions, 3

.

14

functions, 3

.

7

grid, 3

.

14

labels, 3

.

14

pixels, 8

.

16

points, 8

.

14

stat plots, 3

.

7, 12

.

35

tvm_FV

(future value), 14

tvm_I% tvm_

Ú

(interest rate), 14

.

.

7, A

.

31

7, A

(# payment periods), 14

.

.

tvm_Pmt

(payment amount), 14

31

7, A

.

.

6, A

31

.

31

tvm_PV

(present value), 14 .

7, A

.

31

two-proportion z confidence interval

(

2.PropZInt

), 13 .

21, A

.

20

two-proportion z test (

2.PropZTest

),

13

.

15, A

.

20

two-sample Û-Test formula, A .

52

two-sample t test formula, A .

53

two-variable statistics (

2.Var Stats

),

12

.

25, A .

31

. U .

u

sequence function, 6 .

3

user variables, A .

49

uv

/

uvAxes

(axes format), 6 .

8, A .

31

uw

/

uwAxes

(axes format), 6 .

8, A .

31

. V .

v

sequence function, 6 .

3

1.Var Stats

(one-variable statistics),

12

.

25, A

.

31

2.Var Stats

(two-variable statistics),

12

.

25, A

.

31

value

operation on a graph, 3

.

25

. V (continued) .

variables complex, 1

.

13

displaying and storing values, 1

.

14

equation solver, 2 graph databases, 1 graph pictures, 1

.

10

.

13

.

13

independent/dependent, 7

.

5

list, 1 real, 1

.

13, 11

.

3

matrix, 1

.

13

.

13, 10

.

3

recalling values, 1

.

15

solver editor, 2

.

9

statistical, 12 string, 15

.

29

.

4, 15

.

5

test and interval output, 13

.

28

types, 1 .

13

user and system, 1 .

13, A

.

49

VARS and Y.VARS

menus, 1 .

21

variance(

(variance of a list), 11 .

18, A .

31

variance of a list (

variance(

), 11 .

18, A .

31

VARS menu

GDB , 1 .

21

Picture , 1 .

21

Statistics , 1 .

21

String , 1 .

21

Table , 1 .

21

Window , 1 .

21

Zoom , 1 .

21

Vertical

(draw line), 8

.

6, A

.

31

viewing window, 3

.

11

vw

/

uvAxes

(axes format), 6

.

8

. W .

w

sequence function, 6

.

3

warranty information, B

.

14

Web

(axes format), 6

.

8, A

.

31

web plots, sequence graphing, 6

.

11

While

, 16

.

11, A

.

window variables

32

function graphing, 3

.

11

parametric graphing, 4

.

5

polar graphing, 5

.

4

sequence graphing, 6

.

7

Index-15

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 15 of 16

Index (continued)

. X .

XFact

zoom factor, 3 x-intercept of a root, 3

xor

(Boolean) exclusive or operator, 2 x th

xyLine

A

root (

(

.

32

x

), 2

Ó

.

6

.

24

.

26

) plot type, 12

.

31

@X

window variable,

3

.

12

.

26,

. Y .

YFact

zoom factor, 3

Y=

editor

.

24

function graphing, 3

.

5

parametric graphing, 4

.

4

polar graphing, 5

.

3

sequence graphing, 6

.

4

Y.VARS

menu

Function

, 1

.

21

Parametri c, 1

.

21

Polar , 1 .

21

On/Off , 1 .

21

@Y

window variable,

3

.

12

. Z .

ZBox

, 3 .

20, A .

32

ZDecimal

, 3 .

21, A .

32

zero

operation on a graph, 3 .

26

ZInteger

, 3 .

22, A .

32

ZInterval

(one-sample z confidence interval), 13 .

16, A .

32

zoom, 3 .

203 .

24

cursor, 3 .

20

factors, 3 .

24

function graphing, 3 .

20

parametric graphing, 4 .

8

polar graphing, 5

.

6

sequence graphing, 6

.

10

ZoomFit

(zoom to fit function), 3

.

22,

A

.

33

Zoom In

(zoom in), 3

.

21, A

.

32

ZOOM

menu, 3

.

20

ZOOM MEMORY

menu, 3

Zoom Out

(zoom out), 3

.

23

.

21, A

.

32

ZoomRcl

(recall stored window), 3

.

23,

A

.

33

ZoomStat

(statistics zoom), 3

.

22, A

.

33

. Z (continued) .

ZoomSto

(store zoom window), 3

.

23,

A

.

33

ZPrevious

(use previous window), 3

.

23,

A

.

33

ZSquare

(set square pixels), 3

.

21, A

ZStandard

(use standard window), 3

.

33

.

22,

Z.Test

ZTrig

A

.

33

(one-sample z test), 13

.

10, A

(trigonometric window), 3

.

34

.

22, A

.

34

Index-16

825915~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22

PM Page 16 of 16

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