Texas Instruments TI-80 graphing calculator Guidebook
Pubblicità
Pubblicità
TI-80
GRAPHING CALCULATOR
GUIDEBOOK
TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR,
Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas
Instruments Incorporated.
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Macintosh is a registered trademark of Apple Computer, Inc.
© 1995–1997, 2001 by Texas Instruments Incorporated.
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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 calculator. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
US FCC
Information
Concerning
Radio Frequency
Interference
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
.
80 Graphing Calculator. Getting Started gives a quick overview of its features. The first chapter gives general instructions on operating the TI
.
80. Other chapters describe its interactive features. The applications in Chapter 11 show how to use these features together.
Using this Guidebook Effectively
....................
Glossary
.........................................
TI
-80 Keyboard
...................................
First Steps
.......................................
TI
-80 Menus
......................................
Entering a Calculation: Compound Interest
...........
Continuing a Calculation
...........................
Defining a Function: Box with Lid
...................
Defining a Table of Values
..........................
Zooming In on the Table
...........................
Changing the Viewing Window
......................
Displaying and Tracing the Graph
...................
Zooming In on the Graph
...........................
Other TI
-80 Features
..............................
Turning the TI -80 On and Off
.......................
Setting the Display Contrast
........................
The Display
......................................
Entering Expressions and Instructions
...............
The Edit Keys
....................................
Setting Modes
....................................
TI
-80 Modes
......................................
Variable Names
...................................
Storing and Recalling Variable Values
................
Last Entry
........................................
Last Answer
......................................
TI
-80 Menus
......................................
The
VARS
and
Y VARS
Menus
......................
EOS (Equation Operating System)
..................
Error Conditions
.................................
Introduction iii
Getting Started: Lottery Chances
....................
Using the TI
-80 Functions
..........................
Keyboard Math Operations
.........................
MATH MATH
Operations
...........................
MATH NUM
(Number) Operations
...................
MATH PRB
(Probability) Operations
.................
ANGLE
Operations
................................
TEST
(Relational) Operations
.......................
Getting Started: Working with Fractions
.............
Setting Modes for Fraction Results
..................
Entering and Using Fractions in Calculations
.........
The
FRACTION
Menu
..............................
Getting Started: Graphing a Circle
...................
Defining a Graph
..................................
Setting Graph Modes
..............................
Defining Functions in the
Y=
List
....................
Evaluating
Y=
Functions in Expressions
.............
Selecting Functions
...............................
Defining the Viewing Window
......................
Displaying a Graph
................................
Exploring a Graph with the Free-Moving Cursor
......
Exploring a Graph with
TRACE
.....................
Exploring a Graph with
ZOOM
......................
Setting the Zoom Factors
..........................
Getting Started: Path of a Ball
Exploring a Parametric Graph
......................
Defining and Displaying a Parametric Graph
..........
......................
iv Introduction
Getting Started: Roots of a Function
.................
Defining the Independent Variable
..................
Defining the Dependent Variable
....................
Displaying the Table
...............................
Getting Started: Shading a Graph
....................
DRAW DRAW
Menu
...............................
Drawing Lines
....................................
Drawing Horizontal and Vertical Lines
...............
Drawing a Function
...............................
Shading Areas on a Graph
..........................
Drawing Points
...................................
Clearing a Drawing
................................
Getting Started: Generating a Sequence
..............
About Lists
.......................................
LIST OPS
Operations
..............................
LIST MATH
Operations
............................
Getting Started: Building Height and City Size
.........
Setting Up a Statistical Analysis
.....................
The
STAT
List Editor
..............................
Viewing, Entering, and Editing Lists
.................
Sorting and Clearing Lists
..........................
Statistical Analysis
................................
Types of Statistical Analysis
........................
Statistical Variables
...............................
Statistical Plotting
................................
Statistical Analysis in a Program
....................
Statistical Plotting in a Program
.....................
Introduction v
Getting Started: Rolling a Die
.......................
About TI
-80 Programs
.............................
Creating and Executing Programs
...................
Editing Programs
.................................
PRGM CTL
(Control) Instructions
...................
PRGM I/O
(Input/Output) Instructions
...............
Calling Other Programs
............................
Probability Experiments: Coins, Dice, and Spinners
...
The Unit Circle and Trigonometric Curves
............
Program: Newton’s Numerical Solve Routine
.........
Program: Numerical Integration
.....................
Program: Window Variables Store and Recall
.........
Graphing the Inverse of a Function
..................
Graphing a Piecewise Function
.....................
Graphing Inequalities
..............................
Graphing a Polar Equation
.........................
Program: Guess the Coefficients
....................
Checking Available Memory
........................
Deleting Items from Memory
.......................
Resetting the TI
-80
................................
vi Introduction
Table of TI
-80 Functions and Instructions
............
Menu Map
........................................
TI
-80 Variables
...................................
Battery Information
...............................
Accuracy Information
.............................
In Case of Difficulty
...............................
Service and Support Information
...................
Warranty Information
..............................
Index
Introduction vii
Using this Guidebook Effectively
The structure of the TI
-
80 guidebook and the design of its pages can help you find the information you need quickly. Consistent presentation techniques are used throughout to make the guidebook easy to use.
Structure of the
Guidebook
Page-Design
Conventions
The guidebook is designed to teach you how to use the calculator.
¦
Getting Started is a fast-paced, keystroke-by-keystroke introduction.
¦
Chapter 1 describes general operation and lays the foundation for Chapters 2 through 10, which describe specific functional areas of the TI
-80. Most chapters begin with a brief Getting Started introduction.
¦
Chapter 11 contains application examples that incorporate features from different functional areas of the calculator.
These examples can help you see how different functional areas work together to accomplish meaningful tasks.
¦
Chapter 12 describes memory management.
When possible, units of information are presented on a single page or on two facing pages. Several page-design elements help you find information quickly.
¦
Page headings
—The descriptive heading at the top of the page or two-page unit identifies the subject of the unit.
¦
General text
—Just below the page heading, a short section of bold text provides general information about the subject covered in the unit.
¦
Left-column subheadings
—Each subheading identifies a specific topic or task related to the page or unit subject.
viii Introduction
Information-
Mapping
Conventions
¦
Specific text
—The text to the right of a subheading presents detailed information about that specific topic or task. The information may be presented as paragraphs, numbered procedures, bulleted lists, or illustrations.
¦
Page “footers”
—The bottom of each page shows the chapter name, chapter number, and page number.
Several conventions are used to present information concisely and in an easily referenced format.
¦
Numbered procedures
—A procedure is a sequence of steps that performs a task. In this guidebook, each step is numbered in the order in which it is performed. No other text in the guidebook is numbered; therefore, when you see numbered text, you know you should perform the steps sequentially.
¦
Lists with bullets
—If several items have equal importance, or if you may choose one of several alternative actions, this guidebook precedes each item with a “bullet” (
¦
) to highlight it—like this list.
¦
Tables and charts
—Sets of related information are presented in tables or charts for quick reference.
¦
Keystroke examples
—The Getting Started examples provide keystroke-by-keystroke instructions, as do the numerous short examples and several detailed examples that are identified with a
.
Introduction ix
Reference Aids
Several techniques have been used to help you look up specific information when you need it. These include:
¦
A chapter table of contents on the first page of each chapter, as well as the full table of contents at the front of the guidebook.
¦
A glossary at the end of this section, defining important terms used throughout the guidebook.
¦
An alphabetical table of functions and instructions in
Appendix A, showing their correct formats, how to access them, and page references for more information.
¦
Information about system variables in Appendix A.
¦
A table of error messages in Appendix B, showing the messages and their meanings and giving problem-handling information.
¦
An alphabetical index at the back of the guidebook, listing tasks and topics you may need to look up.
x Introduction
Glossary
This glossary provides definitions for important terms that are used throughout this guidebook.
Argument
Command
Expression
Function
Home Screen
Instruction
List
Menu Items
An argument is an input upon which the value of a function depends.
A command is any entry submitted to the calculator using
¸. There are two types of TI-80 commands: instructions and expressions.
An expression is a complete sequence of numbers, variables, functions, and their arguments that can be evaluated to a single answer. An expression returns the evaluated result to
ANS
.
A function, which may have arguments, returns a value and can be used in an expression.
A function is also the expression entered in the
Y=
editor used in graphing.
The Home screen is the primary screen of the TI
-80, where expressions can be entered and evaluated and instructions can be entered and executed.
An instruction, which may have arguments, initiates an action.
Instructions are not valid in expressions. An instruction does not return a value to
ANS
.
A list is a set of values that the TI
-80 can use for activities such as evaluating a function at multiple values and entering statistical data.
Menu items are shown on full-screen menus.
Introduction xi
Pixel
Real Number
Value
Variable
A pixel (picture element) is a square dot on the TI
-80 display.
The TI
-80 display is 64 pixels wide and 48 pixels high.
On the TI
-80, real numbers are individual decimal or fraction values.
A value is a single decimal or fraction number or a list of decimals or fractions.
A variable is the name given to a location in memory in which a value, an expression, a list, or another named item is stored.
xii Introduction
Getting Started: Do This First!
Getting Started contains two keystroke-by-keystroke examples
an interest rate problem and a volume problem
which introduce you to some principal operating and graphing features of the TI
.
80. You will learn to use the TI
.
80 more quickly by completing both of these examples first.
Contents
TI
-80 Keyboard
...................................
First Steps
.......................................
TI
-80 Menus
......................................
Entering a Calculation: Compound Interest
...........
Continuing a Calculation
...........................
Defining a Function: Box with Lid
...................
Defining a Table of Values
..........................
Zooming In on the Table
...........................
Changing the Viewing Window
......................
Displaying and Tracing the Graph
...................
Zooming In on the Graph
...........................
Other TI -80 Features
..............................
Getting Started 1
TI-80 Keyboard
The keys on the TI
.
80 are grouped by color and physical layout to allow easy location of the key you need. The keys are divided into zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.
The Zones of the
Keyboard
Graphing
Editing
Advanced
Functions
Scientific
Calculator
&
&
&
&
Graphing Keys
Editing Keys
Advanced
Function Keys
Scientific
Calculator Keys
These keys are most frequently used to access the interactive graphing features of the TI
-80.
These keys are most frequently used for editing expressions and values.
These keys are most frequently used to access the advanced functions of the TI -80.
These keys are most frequently used to access the capabilities of a standard scientific calculator.
2 Getting Started
First Steps
Before beginning the two sample problems, follow the steps on this page to reset the TI 80 to its factory settings. (Resetting the TI 80 erases all previously entered data.) This ensures that following the keystrokes in this section produces the same actions.
x
1. Press
´ to turn the calculator on.
If the screen is very dark or blank, adjust the display contrast. Press and release
2, and then press and hold
8 (to make the display lighter) or press and hold
7 (to make the display darker). You can press
M to clear the display.
2. Press and release
2, and then press µ. (Pressing
2 gives you access to the
2nd
operations, which are printed at the upper left of the keys.
MEM
is the
2nd
operation of the
µ key.)
The
MEMORY
menu is displayed.
3. Press
3
to select
RESET...
from the
MEMORY
menu.
The
MEMORY RESET
menu is displayed.
E
4. Press
2
to select
RESET
from the
MEMORY RESET
menu. The calculator is reset, and the
MEM CLEARED
message is displayed.
Getting Started 3
TI-80 Menus
To leave the keyboard uncluttered, the TI
.
80 uses full-screen menus to display many additional operations. The use of specific menus is described in the appropriate chapters.
Displaying a Menu
When you press a key that displays a menu, such as
I, that menu screen temporarily replaces the screen where you are working.
After you make a selection from a menu, you usually are returned to the screen where you were.
Moving from One Menu to Another
A menu key may display more than one menu name. The names appear on the top line. The name of current menu is highlighted, and the items in that menu are displayed.
Use
9 or 6 to display a different menu.
Selecting an Item from a Menu
The number of the current item is highlighted. If there are more than seven items on the menu, a $ appears on the last line in place of the : (colon).
To select from a menu, you can either:
¦
Use
8 and 7 to move the cursor to the item, and then press
¸.
¦
Press the number of the item.
Note:
The tenth item in a menu is number
0
. If there are more than 10 items, they are numbered A, B, C, etc. To select one of these items, press
? and then the letter.
Leaving without Making a Selection
To leave a menu without making a selection:
¦ Press 2 . to return to the Home screen.
¦ Press M to return to the screen where you were.
¦
Press the key for another screen or menu.
4 Getting Started
Entering a Calculation: Compound Interest
The TI
.
80 displays up to 8 16-characters lines so that you see an expression and its solution together. You can store values to variables, enter multiple instructions on one line, and recall previous entries.
Using trial and error, determine when an amount invested at 6% annual compounded interest will double in value.
1. For the first guess, compute the amount available at the end of 10 years. Enter the expression just as you would write it. (Use 1000 for the amount.)
Press
1000
p
1.06
Z
10
.
2. Press
¸ to evaluate the expression.
The answer is shown on the right side of the display.
The cursor is positioned on the next line, ready for you to enter the next expression.
3. The next guess should be greater than 10 years. Make the next guess 12 years. To calculate the amount after
12 years, press
1000
p
1.06
Z
12
, followed by
¸.
Getting Started 5
Continuing a Calculation
To save keystrokes, you can use the Last Entry feature to recall the last expression entered and then edit it for a new calculation. In addition, the next expression can be continued from the previous result.
1. The next guess should be less than, but close to, 12 years. Compute the amount available at the end of
11.9 years, using the Last Entry feature. Press 2, followed by ² (the second function of ¸).
The last calculated expression is shown on the next line of the display. The cursor is positioned at the end of the expression.
2. You can edit the expression. Press
6 to move the cursor over the
2
. Then type
1.9
to change
12
to
11.9
.
Press
¸ to evaluate the expression.
Note:
This process can be continued to obtain a solution with the desired accuracy.
3. You can continue a calculation using the result of the last calculation. For example, if the final amount determined above is to be divided among seven people, how much would each person get?
To divide the last calculation by seven, press e
7
, followed by
¸.
As soon as you press e,
ANS
à is displayed at the beginning of the new expression.
ANS
is a variable that contains the last calculated result. In this case,
ANS
contains 2000.505716.
6 Getting Started
Defining a Function: Box with Lid
Take an 8½"×11" sheet of paper and cut X by X squares from two corners and X by (X+B) rectangles from the other two corners. Now fold the paper into a box with lid. What X would give the maximum volume V of a box made in this way?
Use tables and graphs to determine the solution.
Begin by defining a function that describes the volume of the box.
From the diagram: 2X + A = W
2X + 2B = L
V = A B X
Substituting: V = (W – 2X) (L à 2 – X) X
If necessary, press z † Í to change the
MODE
to
FLOAT
. Then press y . ‘ to return to the Home screen and clear it.
1. Press
8.5
¿ ƒ
W
Í to store the width of the paper.
Press
11
¿ ƒ
L
Í to store the length of the paper.
X
W A
X B
L
X B
2. You define functions for tables and graphs on the
Y=
edit screen.
Press o to access this screen.
3. Enter the function for volume as
Y1
. Press
£ ƒ
W
¹
2
@ ¤ £ ƒ
L
¥
2
¹ @ ¤ @ Í to define function
Y1
in terms of
X
. (
@ lets you enter
X
quickly without pressing
ƒ.)
The
=
sign is highlighted to show that
Y1
is selected.
Getting Started 7
Defining a Table of Values
The table feature of the TI
.
80 provides numeric information about a function.
Use a table of values from the previously defined function to estimate an answer to the problem.
1. Press y # (above p) to display the
TABLE SETUP
screen.
2. Press
Í to accept
TBLMIN=0
.
3. Press
.5
Í to define the table increment @
TBL=.5
.
4. Press y & (above s) to display the table.
Note that the maximum value is around
1.5
, between
1
and
2
.
5. Press and hold
† to scroll the table until the sign change appears. Note that the maximum length of
X
for this problem occurs where the sign of
Y1
(volume) becomes negative.
6. Press y #. Note that
TBLMIN
has changed to reflect the first line of the table you last displayed.
8 Getting Started
Zooming In on the Table
You can adjust the way a table is displayed to get more detailed information about any defined function. By varying the value of @ TBL, you can “zoom in” on the table.
1. Adjust the table setup to get a more accurate estimate of the maximum size of the cutout. Press
1
Í to set
TBLMIN
. Press
.1
to set
@
Tbl
.
2. Press y &.
3. Use
† and } to scroll the table. Note that the maximum value displayed is
33.072
, which occurs at
X=1.6
. The maximum occurs at
1.5<X<1.7
.
Getting Started 9
4. Press y #. Press
1.5
Í to set
TBLMIN
.
Press
.01
Í to set @
TBL
.
5. Press y & and use † and } to scroll the table.
Two “equal” maximum values are shown,
33.074
at
X=1.58
and
X=1.59
.
6. Press
† or } to move the cursor to
1.58
. Press
~ to move the cursor into the
Y1
column. The bottom line of the display shows the value of
Y1
at
1.58
in full precision,
33.073824
.
7. Press
† to display the “other” maximum. The value of
Y1
at
1.59
in full precision is
33.073908
. This would be the maximum volume of the box if you could cut your piece of paper at .01-inch increments.
10 Getting Started
Changing the Viewing Window
The viewing window defines the portion of the coordinate plane that appears in the display. The values of the Window variables determine the size of the viewing window. You can view and change these values.
1. Press p to display the Window variables edit screen. You can view and edit the values of the
Window variables here.
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.
2. Press
0
Í to define
XMIN
.
3. You can enter expressions to define values in the window editor. Press
8.5
¥
2 .
4. Press
Í. The expression is evaluated, and
4.25
is stored in
XMAX
. Press
Í to accept
XSCL
as
1
.
5. Press
0
Í
40
Í
10
Í to define the
Y
Window variables.
XMIN
YMIN
YMAX
XSCL
XMAX
YSCL
Getting Started 11
Displaying and Tracing the Graph
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 with TRACE.
1. Press s to graph the selected function in the viewing window.
The graph of
Y1=(W–2X)(L
à
2–X)X
is shown in the display.
2. Press
~ once to display the free-moving cursor just to the right of the center of the screen. The bottom line of the display shows the X- and Y-coordinate values for the position of the graph cursor.
3. Use
|, ~, }, and † to position the free-moving cursor at the apparent maximum of the function.
As you move the cursor, X- and Y-coordinate values are updated continually to reflect the cursor position.
4. Press r. The Trace cursor appears on the
Y1
function.
1
in the upper right corner of the display shows that the cursor is on
Y1
. As you press
| and
~, you trace along
Y1
, one
X
dot at a time, evaluating
Y1
at each
X
.
5. Press
| and ~ until you are on the maximum Y value. This is the maximum of
Y1(X)
for the X pixels.
(There may be a maximum value “in between” pixels.)
12 Getting Started
Zooming In on the Graph
You can magnify the viewing window around a specific location using the Zoom instructions to help identify maximums, minimums, roots, and intersections of functions.
1. Press q to display the
ZOOM
menu.
This menu is typical of TI -80 menus. To select an item, you may either press the number to the left of the item, or you may press
† until the item number is highlighted and then press
Í.
2. To
ZOOM IN
, press
2
. The graph is displayed again.
The cursor has changed to indicate that you are using a Zoom instruction.
3. Use
|, }, ~, and † to position the cursor near the maximum value on the function, and press
Í.
The new viewing window is displayed. It has been adjusted in both the
X
and
Y
directions by factors of
4, the values for Zoom factors.
4. Press p to display the new window variable values.
Getting Started 13
Other TI
.
80 Features
Getting Started has introduced you to basic calculator operation and the table and function graphing features of the TI 80. The remainder of this Guidebook describes these features in more detail and also covers other capabilities of the
TI 80.
Fractions
Graphing
Tables
Lists
Statistics
Programming
You can enter fractions directly from the keyboard and perform calculations with fractions. You can convert between fractions and their decimal equivalents. In
MANSIMP
mode, you can simplify fractions step-by-step. The TI
-80 tells you when a fraction can be simplified and shows the common factor after simplification (Chapter 3).
You can store, graph, and analyze up to four functions
(Chapter 4) and up to three parametric functions (Chapter 5).
You can use Draw operations to annotate graphs (Chapter 7).
You can create function evaluation tables to analyze multiple functions simultaneously (Chapter 6).
You can enter and save up to six lists for use in statistical analysis. You also can use lists to evaluate expressions at multiple values simultaneously (Chapter 8).
You can perform one-variable and two-variable list-based statistical analysis, including regression analysis, and plot the data as histograms, points, x-y lines, or box-and-whisker plots.
You can define and save three statistical plot definitions
(Chapter 9).
You can enter and save programs that include extensive control and input/output instructions (Chapter 10)
14 Getting Started
Chapter 1: Operating the TI-80
This chapter describes the TI
.
80 and provides general information about its operation.
Chapter
Contents
Turning the TI
.80 On and Off
.......................
Setting the Display Contrast
........................
The Display
......................................
Entering Expressions and Instructions
...............
The Edit Keys
....................................
Setting Modes
....................................
TI
.80 Modes
......................................
Variable Names
...................................
Storing and Recalling Variable Values
................
Last Entry
........................................
Last Answer
......................................
TI
.80 Menus
......................................
The
VARS
and
Y
.
VARS
Menus
......................
EOS (Equation Operating System)
..................
Error Conditions
..................................
Operating the TI-80 1-1
Turning the TI-80 On and Off
To turn the TI
.
80 on, press the
´
key. To turn it off, press and release
y
, and then press
®
. After about five minutes without any activity, the APD™
(Automatic Power Down™) feature turns the TI
.
80 off automatically.
Turning the
Calculator On
Turning the
Calculator Off
APD™
(Automatic
Power Down™)
Batteries
Press
´ to turn the TI-80 on.
¦
If you pressed y ® to turn the calculator off, the display shows the Home screen as it was when you last used it, and errors are cleared.
¦
If APD turned the calculator off, the display returns to the same screen or editor in which you left it. See “APD
(Automatic Power Down)” below.
Press and release
2, and then press ® to turn the TI-80 off.
¦
Any error condition is cleared.
¦
All settings and memory contents are retained by the
Constant Memory
é
feature.
To prolong the life of the batteries, APD turns the TI -80 off automatically after several minutes without any activity. When you press ´, the calculator shows the same screen or editor in which you left it.
¦
If an error message was displayed when APD turned the
TI
-80 off, the error is cleared, and the display returns to a blank line on the Home screen.
¦
If a menu was displayed, the display returns to the screen or editor from which you called the menu.
All settings and memory contents are retained by the Constant
Memory feature.
Note:
APD does not occur if a calculation or program is in progress, unless the program is paused.
The TI
-80 uses two CR2032 lithium batteries. To replace the batteries without losing any information stored in memory, follow the directions in Appendix B.
1-2 Operating the TI-80
Setting the Display Contrast
The brightness and contrast of the display depend on room lighting, battery freshness, viewing angle, and the adjustment of the display contrast. The contrast setting is retained in memory when the TI
.
80 is turned off.
Adjusting the
Display Contrast
When to Replace
Batteries
You can adjust the display contrast to suit your viewing angle and lighting conditions. As you adjust the contrast setting, the display becomes lighter or darker. A highlighted number in the upper right corner changes to indicate the current contrast setting; 0 is the lightest, and 9 is the darkest.
To adjust the display contrast:
1. Press and release the
2 key.
2. Use one of two keys:
¦
To increase the contrast (darken the screen), press and hold
7.
¦
To decrease the contrast (lighten the screen), press and hold
8.
Note:
The display may become completely blank if you adjust the contrast setting too low. If this happens, press and release y, and then press and hold 7 until the display reappears.
As you use the TI
-80, the battery voltage will gradually drop, and the display will dim. You can adjust the contrast to darken the display when this happens. If the display is dim and adjusting the contrast to level 9 does not make it dark enough, you should replace the batteries. Refer to Appendix B for instructions on how to change the batteries.
Note:
After you change batteries, the display contrast may appear very dark. Press and release y, and then press and hold
8 to lighten the display.
Operating the TI-80 1-3
The Display
The TI
.
80 displays both text and graphs. Graphs are described in Chapters 4 and 5.
Home Screen
Displaying
Entries and
Answers
Returning to the
Home Screen
The primary screen of the TI
-80 is the Home screen. You enter instructions to be executed, expressions to be evaluated, and see the results on the Home screen.
When text is displayed, the TI -80 screen can show a maximum of eight lines with 16 characters each.
¦
If all lines of the display are filled, text “scrolls” off the top of the display.
¦
If an expression on the Home screen, the
Y=
editor
(Chapter 4), or the program editor (Chapter 10) is longer than one line, it wraps to the beginning of the next line.
¦
On numeric editors such as the Window screen
(Chapter 4), an expression scrolls to the left and right.
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 (pages 1
-9 through 1-11) control the way the calculator interprets expressions and displays answers.
If an answer is too long to display in its entirety, you can press
9 and 6 to scroll the answer so that you can view all of it. In the second example below, the open brace without a corresponding close brace indicates that the list is too long to be displayed in its entirety.
Entry
Answer
Answer
Answer (scrolled)
To return to the Home screen from any other screen, press y ..
1-4 Operating the TI-80
Display Cursors
In most cases, the appearance of the cursor indicates what will happen when you press the next key.
Cursor
Entry
INS
2nd
(insert)
ALPHA
memory “full”
Appearance
Blinking
0
Blinking
Blinking
Blinking
_
Checkerboard rectangle
Meaning
The next keystroke is entered at the cursor; it types over any character.
The next keystroke is inserted at the cursor.
The next keystroke is a
2nd
operation.
The next keystroke is an alphabetic character.
You have entered the maximum number of characters in a name, or memory is full.
Busy Indicator
Graphs and the screens for viewing and editing tables and lists have different cursors, which are described in the appropriate chapters.
When the TI -80 is calculating or graphing, a vertical line shows in the upper right of the display as a busy indicator.
During a pause in a program, the busy indicator is a dotted line.
Operating the TI-80 1-5
Entering Expressions and Instructions
In most places where a value is required, you can use an expression to enter the value. You can enter instructions, which initiate an action, on the Home screen or in the program editor (Chapter 10).
Expressions
Entering an
Expression
An expression is a complete sequence of numbers, variables, functions, and their arguments that evaluate to a single answer. For example,
p r
ñ is an expression. On the TI-80, you enter an expression in the same order as you would write it.
You can create expressions on the Home screen to calculate an answer. In most places where a value is required, you can use an expression to enter the value.
To create an expression, you enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press
¸, regardless of the cursor location. The entire expression is evaluated according to
Equation Operating System (EOS
TM
) rules, and then the answer is displayed.
Note:
EOS rules determine the order in which operations are completed (page 1
-20).
Most TI -80 functions and operations are symbols with several characters in them. You must enter the symbol from the keyboard or menu. You cannot spell it out. For example, to calculate the log of 45, you must press l
4 5
. You cannot type in the letters
L O G
. (If you type
LOG
, the TI
-80 interprets the entry as implied multiplication of the variables
L
,
O
, and
G
.)
Calculate 3.76 ÷ (
-7.9 + ‡5) + 2 log45.
3.76
e c ·
7.9
« y ]
5 d «
2
l
45
¸
Multiple Entries on a Line
To enter more than one expression or instruction on a line, separate them with a colon (:). They are all stored together in
Last Entry (page 1
-15).
1-6 Operating the TI-80
Entering a
Number in
Scientific
Notation
To enter a number in scientific notation:
1. Type the part of the number that precedes the exponent.
This value can be an expression.
2. Press
2 ^. í is displayed.
3. If the exponent is negative, press
·, and then type the exponent, which can be one or two digits.
Functions
Instructions
Interrupting a
Calculation
Entering a number in scientific notation does not cause the answers to be displayed in scientific notation. The display format is determined by the mode settings (pages 1
-9 through
1
-11) and the size of the number.
A function returns a value. For example,
÷
,
×
,
−
,
+
, ‡, and
LOG
are functions. Some functions take more than one argument, which is indicated by a
(
at the end of the name. MIN( requires two arguments in this example:
MIN(5,8)
.
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. Some instructions take more than one argument, which is indicated by a
(
at the end of the name.
LINE(
requires four arguments in this example:
LINE(1,1,3,3)
.
While the busy indicator is displayed, indicating that a calculation or a graph is in progress, you can press
´ to stop the calculation. (There may be a delay.)
Operating the TI-80 1-7
The Edit Keys
The arrow keys near the upper right of the keyboard control the movement of the cursor. In normal entry, a keystroke types over the character or characters at the position of the cursor. The
4
and
y
/
keys delete or insert characters.
Key(s)
9 or 6
7 or 8
2 6
2 9
¸
M
4 y / y
?
y <
@
Action(s)
Moves the cursor within an expression. These keys repeat when you hold them down.
Moves the cursor between lines within an expression. These keys repeat when you hold them down.
¦
On the top line of an expression on the Home screen,
7 moves the cursor to the beginning of the expression.
¦
On the bottom line of an expression on the Home screen,
8 moves the cursor to the end of the expression.
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 (blanks) the current line.
¦
On a blank line on the Home screen, clears everything on the Home screen.
¦
In an editor, clears (blanks) the expression or value where the cursor is located; it does not store a zero.
Deletes the character at the cursor. This key repeats.
Lets you insert characters at the underline cursor. To end insertion, press y / or a cursor key.
Next key press is a
2nd
operation (the gold-colored label printed to the left above a key). The cursor changes to
. To cancel
2nd
, press y again.
Next key press is an
ALPHA
character (the light gray character to the right above a key). The cursor changes to
A
.
To cancel
ALPHA
, press
? or a cursor key.
Sets
ALPHA-LOCK
; each subsequent key press results in an
ALPHA
character. The cursor changes to . To cancel
ALPHA-LOCK
, press
?.
Allows you to enter an
X
in
FUNC
mode or a
T
in
PARAM
mode without pressing
? first.
1-8 Operating the TI-80
Setting Modes
Modes control how numbers and graphs are displayed and interpreted by the calculator. Mode settings are retained by the Constant Memory feature when the
TI
.
80 is turned off.
Checking MODE
Settings
Press
3 to display the
MODE
screen. The current settings are highlighted. The settings are described on the following pages.
NORMAL SCI
Numeric display format.
FLOAT 0123456789
Number of decimal places.
RADIAN DEGREE a
Àbºc bºc
Unit of angle measure.
Type of fraction display.
AUTOSIMP MANSIMP
Whether to simplify fractions.
FUNC PARAM
CONNECTED DOT
Type of graphing.
Whether to connect graph points.
SEQUENTIAL SIMUL
Whether to plot simultaneously.
Changing MODE
Settings
Leaving the
MODE Screen
Setting a Mode from a Program
To change the mode setting:
1. Press
8 or 7 to move the cursor to the line of the setting that you want to change. The setting that the cursor is on blinks.
2. Press 9 or 6 to move the cursor to the setting that you want.
3. Press
¸.
To leave the
MODE
screen:
¦
Press the appropriate keys to go to another screen.
¦
Press y . or M to return to the Home screen.
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 line in the program editor (Chapter 10), press
3 to display a menu of the mode names, and then select the name. The name is copied to the cursor location.
Operating the TI-80 1-9
TI-80 Modes
The TI
.
80 has eight mode settings. They control how numeric entries are interpreted, how answers are calculated or displayed, and how graphs appear in the display. Modes are set on the MODE screen (page 1
.
9).
NORMAL
SCI
FLOAT
Fixed Decimal
Notation formats affect only how 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
display format is the way in which we usually express decimal numbers, with digits to the left and right of the decimal, as in
12345.67
.
SCI
(scientific) notation expresses numbers in two parts. The significant digits can be displayed with one digit to the left of the decimal. The appropriate power of 10 displays to the right of í, as in
1.234567
í
4
.
Note
: If you select normal display format, but the answer cannot be displayed in 10 digits or the absolute value is less than .001, the TI
-80 displays the answer in scientific notation.
Decimal settings affect only how an answer is displayed on the Home screen. You can enter a number in any format. The decimal settings apply to both notation formats.
FLOAT
(floating) decimal setting displays up to 10 digits, plus the sign and decimal.
The fixed decimal setting lets you select the number of digits
(
0
to
9
) to be displayed to the right of the decimal. The displayed value is rounded based on the number of digits you selected. The actual value is stored and used in calculations.
Place the cursor on the number of decimal digits you want, and press
¸.
Note:
In the program editor, the format for fixed decimal settings is
FIX
n. Enter n as an integer from
0
to
9
. The mode is changed to fixed decimal when the program is executed.
1-10 Operating the TI-80
RADIAN
DEGREE a
À
b
º
c b
º
c
AUTOSIMP
MANSIMP
FUNC
PARAM
CONNECTED
DOT
SEQUENTIAL
SIMUL
The angle mode controls:
¦
How the calculator interprets angle arguments in
SIN
,
COS
,
TAN
, and polar-to-rectangular conversions.
¦
How the calculator returns angle answers to
SIN
ê,
COS
ê,
TAN
ê, and rectangular-to-polar conversions.
RADIAN
mode interprets angle arguments as radians and returns angle answers in radians.
DEGREE
mode interprets angle arguments as degrees and returns angle answers in degrees.
a
À
b
º
c
displays fraction results as mixed numbers; for example, the result of
1
º
3 + 4
º
3
is displayed as
1
À
2
º 3.
b
º
c
displays fraction results as simple fractions; for example, the result of
1
º
3 + 4
º
3
is displayed as
5
º
3
.
AUTOSIMP
automatically simplifies fraction results to their lowest terms before displaying them; for example, the result of
2
º
6 + 2
º
6
is displayed as
2
º
3
.
MANSIMP
displays fraction results without automatic simplification; for example, the result of
2
º
6 + 2
º
6
is displayed as
4
º
6
.
FUNC
(function) graphing plots functions where
Y
is expressed in terms of
X
(Chapter 4).
PARAM
(parametric) graphing plots relations where
X
and
Y
are each expressed in terms of
T
(Chapter 5).
CONNECTED
draws line segments between the calculated points of the selected functions.
DOT
plots only the calculated points of the selected functions.
SEQUENTIAL
graphing evaluates and plots one function completely before the next function is evaluated and plotted.
SIMUL
(simultaneous) graphing evaluates and plots all selected functions for a single value of
X
, one at a time. In
Parametric mode,
X
and
Y
are selected pairs. They are evaluated and plotted a
T
value at a time.
Operating the TI-80 1-11
Variable Names
On the TI
.
80 you can enter, name, and use several types of data: numeric values
(including fractions), lists, functions, and statistical plots.
Variables and
Defined Items
The TI
-80 uses both user-assigned and pre-assigned names for variables and other items saved in memory.
Variable Type
Numeric values
(including fractions)
Lists
Names
A
,
B
, ...,
Z
, q (single character only).
Functions
Parametric equations
Statistical plots
System variables
L1
,
L2
,
L3
,
L4
,
L5
,
L6
(on the keyboard).
Y1
,
Y2
,
Y3
,
Y4
(on the
Y=
editor in
FUNC
mode).
X1
î
/Y1
î
X2
î
/Y2
î,
X3
î
/Y3
î (on the
Y=
editor in
PARAM
mode).
PLOT1
,
PLOT2
, PLOT3 (on the
STAT PLOTS
menu).
XMIN
,
XMAX
, and others (on various menus).
Programs have user-defined names also and share memory with variables. Program names can be up to seven characters long. Programs are entered and edited from the program editor (Chapter 10).
You can store to lists (Chapter 8), system variables such as
XMAX (Chapter 4) or TBLMIN (Chapter 6), and all
Y=
functions (Chapters 4 and 5) from the Home screen or from a program. You can store to lists (Chapters 8 and 9) and functions (Chapters 4 and 5) from editors. You can also store to a list element (Chapter 8).
For more information about system variables, see Appendix A.
1-12 Operating the TI-80
Storing and Recalling Variable Values
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.
Storing Values in a Variable
You can store a value to a variable from the Home screen or a program using the § key. Begin on a blank line.
1. Enter the value that you want to store (this can be an expression).
2. Press
§. The symbol ! is copied to the cursor location.
3. Press
? and then the single letter of the variable to which you want to store the value.
4. Press
¸. If you entered an expression, it is evaluated.
The value is stored in the variable.
Displaying a
Variable Value
Using a Variable in an Expression
To display the value of a variable, enter the variable name on a blank line on the Home screen, and then press
¸. You can enter the name of the variable in one of the following ways:
¦
Press ? and the letter of the variable (for user-defined variables).
¦
Press
2 and the name of the list.
¦
Press
L and select the type and name of the variable
(for system variables).
¦
Press
2 G and select the type and name of the function.
To use the current value of a variable in an expression, just enter the variable name in the expression.
Operating the TI-80 1-13
Last Entry
When you press
¸
on the Home screen to evaluate an expression or execute an instruction, the expression or instruction is stored in an area called Last
Entry, which you can recall. When you turn the TI
.
80 off, Last Entry is retained in memory.
Using Last Entry
You can recall Last Entry and edit it from the Home screen.
Press y ². The current line is cleared, and the Last
Entry is copied to the line. The cursor is positioned at the end of the entry. Because the TI
-80 updates the Last Entry storage area only when you press
¸, you can recall the previous entry even if you have begun entering the next expression.
However, when you recall Last Entry, it replaces what you have typed.
5
«
7
¸ y ²
Displaying a
Previous Entry
The TI
-80 keeps previous entries (up to a total of 80 bytes) in
Last Entry. You can display and edit those entries by continuing to press
2 ². Last Entry displays previous entries in a loop, beginning with newest entry and moving to the oldest entry. Once the oldest item is displayed,
2 ² displays the newest item again.
1
§ ?
A
¸
2
§ ?
B
¸
3
§ ?
C
¸ y ²
When you press y ² again, the previous item replaces the item on the current line.
2 ²
1-14 Operating the TI-80
Re
.
executing the
Previous Entry
To execute Last Entry, press
¸ on a blank line on the
Home screen. The entry is executed, but it does not display again.
0
§ ?
N
¸
?
N
«
1
§ ?
N
¸
¸
¸
Multiple Entries on a Line
To enter more than one expression or instruction on a line, separate them with a colon (
:
). They are all stored together in
Last Entry.
If the previous entry contained more than one expression or instruction, separated with a colon (page 1
-6), they all are recalled. You can recall all entries on a line, edit any of them, and then execute all of them.
Using 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
§ ?
R
y ° y T ?
R
a
¸ y ²
Now try this.
y 6
7
y /
.95
¸
Continue until the answer is as accurate as you want.
Operating the TI-80 1-15
Last Answer
When an expression is evaluated successfully from the Home screen or from a program, the TI .
80 stores the answer to a variable, ANS (Last Answer). ANS may be a decimal number, a fraction, or a list. When you turn the TI
.
80 off, the value in ANS is retained in memory.
Using Last
Answer (ANS) in an Expression
You can use the variable
ANS
to represent the last answer in most places. When you press y ±, the variable name
ANS
is copied to the cursor location. When the expression is evaluated, the TI
-80 uses the value of
ANS
in the calculation.
Calculate the area of a garden plot that is 1.7 meters by 4.2
meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.
1.7
p
4.2
¸
147
e y ±
¸
Continuing an
Expression
You can use the value in
ANS
as the first entry in the next expression without entering the value again or pressing y
±. On a blank line on the Home screen, enter the function.
The TI
-80 “types” the variable name
ANS followed by the function.
5
e
2
¸ p
9.9
¸
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. Then calculate the volume of a cylinder of radius 5 meters and height 3.3 meters. Store the result in the variable
V
.
y T
5
a
¸ p
3.3
¸
§ ?
V
¸
1-16 Operating the TI-80
TI-80 Menus
To leave the keyboard uncluttered, the TI
.
80 uses full
.
screen menus to give you access to many additional operations. The use of specific menus is described in the appropriate chapters.
Moving from One
Menu to Another
Some menu keys, such as
I, display more than one menu.
The names of the menus appear on the top line. The current menu is highlighted and the items in that menu are displayed.
Selecting an Item from a Menu
Press
9 or 6 to move the cursor to a different menu.
The number of the current item is highlighted. If there are more than seven items on the menu, a
$ appears on the last line in place of the
:
(colon) between the menu number and name. Menu items, such as
VARS WINDOW
, that end in ...
(ellipsis marks) display another menu.
There are two methods of selecting from a menu.
¦
Press the number of the item you want to select.
¦
Press
8 and 7 to move the cursor to the item you want to select, and then press
¸.
Calculate
ò‡27 .
1. Press
I to display the
MATH
menu.
2. To select
ò‡ , you may either press
4
or press
8 8 8
¸.
3. Enter 27, and then press
¸ to evaluate the expression.
Operating the TI-80 1-17
Leaving a Menu without Making a
Selection
There are several ways to leave a menu without making a selection from the menu.
¦
To return to the Home screen, press
2 ..
¦
To return to the screen where you were, press
M.
¦
To display a different menu, press the appropriate key, such as
*.
¦
To select another screen, press the appropriate key, such as
).
1-18 Operating the TI-80
The VARS and Y
.
VARS Menus
You may want to use the names of system variables (such as XMIN) and functions (such as Y1) in an expression. You may also want to store values directly to those variables. Use the VARS or Y
.
VARS menus to access the names.
VARS Menu
Y .
VARS Menu
The
VARS
menu displays the names of window variables such as
XMIN
and
TSTEP
, statistics variables such as v and Q1 , and table variables such as
TBLMIN
.
Press
L to display the
VARS
menu. Some of the items display more than one menu of variable names.
VARS
1: WINDOW
...
Names of
X, Y,
and
T
variables.
2: STATISTICS
...
X/Y, G,
EQ
, and
BOX
variables.
3: TABLE
...
TBLMIN
and
@
TBL
variables.
4: SIMPFACTOR
... Factor last used by
ú
SIMP
function.
The
Y .
VARS
menus display the names of functions and the instructions to select or deselect functions from a program or the Home screen.
Press
2 G to display the
Y .
VARS
menu. Then press
9 or
6 to select the type of variable you want.
Y
Displays a menu of names of Yn functions.
XT
à
YT
Displays a menu of names of XnT àYnT equations.
ON
à
OFF
Lets you select/deselect functions.
Copying a Name from a VARS or
Y .
VARS Menu
To copy a variable name from a
VARS
or
Y .
VARS
menu:
1. Press
L or 2 G. The
VARS
or
Y .
VARS
menu is displayed.
2. Select the type of variable you want.
3. Press ¸ to select the name you want from the menu. It is copied to the cursor location.
Operating the TI-80 1-19
EOS (Equation Operating System)
The Equation Operating System (EOS™) defines the order of operations for the calculator
that is, the order in which the TI .
80 evaluates functions in expressions. EOS lets you enter numbers and functions in a simple, straightforward sequence.
Order of
Evaluation
A function returns a value. EOS evaluates the functions in an expression in the following order.
1
Functions that are entered after the argument, such as
A
ñ,
2
ê,
22!
,
45
¡,
2 p
ô, and ú
SIMP
.
2
Powers and roots, such as
2^5
or
5
õ‡
32
.
3
Implied multiplication where the second argument is a number, variable name, or list, or begins with an open parenthesis, such as
4A
,
(A+B)4
, or
4(A+B)
.
4
Single-argument functions that precede the argument, such as
L A
,
‡ 63
,
SIN B
, or
LOG 3
.
5
Implied multiplication where the second argument is a multi-argument function or a single-argument function that precedes the argument, such as
2NDERIV(A
ñ
,A,6)
or
ASIN 2
.
6
Permutations (
nPr
) and combinations (
nCr
).
7
Multiplication and division (including
INT÷
).
8
Addition and subtraction.
9
Test functions, such as
>
or .
10
Conversion functions:
8 FRAC
,
8 DEC
,
8 a
À
b
º
c
, and
8 b
º
c
.
Within a priority group, EOS evaluates functions from left to right. However, two or more single-argument functions that precede the same argument are evaluated from right to left.
For example,
SIN FPART LN 8
is evaluated as
SIN(FPART(LN 8))
.
Calculations within a pair of parentheses are evaluated first.
Multi-argument functions, such as
NDERIV(A
ñ
,A,6)
, are evaluated as they are encountered.
The conversion functions
8 FRAC
,
8 DEC
,
8 a
À
b
º
c
, and
8 b
º
c
can be used only at the end of a command line with one exception: they can be followed by a store instruction.
1-20 Operating the TI-80
Implied
Multiplication
Parentheses
Negation
The TI
-80 recognizes implied multiplication. For example, it understands
2
p,
4SIN 45
,
5(1+2)
, and
(2
×
5)7
as implied multiplication.
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
.
You can omit any right (closing) parenthesis at the end of an expression. All “open” parenthetical elements are closed automatically at the end of an expression and preceding the
!
(store) or display-conversion instructions.
Note:
Parentheses are also used to enclose the arguments for certain functions, for example,
NDERIV(A
ñ
,A,6)
. In these cases, parentheses do not indicate implied multiplication.
To enter a negative number, use the negation function. Press
·, and then enter the number. On the TI-80, negation is in the fourth group in the EOS hierarchy. Functions in the first group, such as squaring, are evaluated before negation.
For example,
L
X
ñ is a negative number (or 0); L
9
ñ is L
81
. Use parentheses to square a negative number:
( L 9)
ñ.
Note:
Use the | key for subtraction and the · key for negation. If you press | to enter a negative number, as in
9
p
|
7
, or if you press · to indicate subtraction, as in
9
·
7
, it is an error. If you press
?
A
· ?
B
, it is interpreted as implied multiplication (
A
QL
B
).
Operating the TI-80 1-21
Error Conditions
The TI
.
80 detects any errors at the time it evaluates an expression, executes an instruction, plots a graph, or stores a value. Calculations stop and an error message with a menu is displayed immediately. Error codes and conditions are described in detail in Appendix B.
Diagnosing an
Error
If the TI
-80 detects an error, it displays the error screen.
Correcting an
Error
The top line indicates the general type of error, such as
SYNTAX
or
DOMAIN
. For additional information about each error message, see Appendix B.
¦
If you select
GOTO
, the cursor is displayed at the location where the error was detected.
Note
: If a syntax error was detected in the contents of a
Y=
function during program execution,
GOTO
returns the user to the
Y=
editor, not to the program.
¦
If you select QUIT, or press y . or M, you return to the Home screen.
To correct an error:
1. Note the type of the error.
2. Select
GOTO
, if that option is available; and look at the expression for syntax errors, especially at and before the cursor location.
3. If the error in the expression is not readily apparent, turn to Appendix B, and read the information about the error message.
4. Correct the expression.
1-22 Operating the TI-80
Chapter 2: Math, Angle, and Test Operations
This chapter describes the math, angle, and relational operations that are available on the TI .
80. The most commonly used functions are accessed from the keyboard; others are accessed through menus.
Chapter
Contents
Getting Started: Lottery Chances
....................
Using the TI -80 Functions
..........................
Keyboard Math Operations
.........................
MATH MATH
Operations
...........................
MATH NUM
(Number) Operations
...................
MATH PRB
(Probability) Operations
.................
ANGLE
Operations
................................
TEST
(Relational) Operations
.......................
Math, Angle, and Test Operations 2-1
Getting Started: Lottery Chances
Getting Started is a fast-paced introduction. Read the chapter for details.
Suppose you want to enter a lottery where six numbers will be drawn out of 50.
To win, you must pick all six numbers (in any order). What is the probability of winning if you buy one ticket? What is the probability of winning if you buy five tickets?
1. Determine the number of combinations possible. On the Home screen, press
50
to enter the total number of items. Press
I 6 to display the
MATH PRB
menu .
Press
3
to select
nCr
. Press
6
to enter the number of items selected.
2. Press
¸ to evaluate the expression. This is the total number of possible combinations of 6 numbers drawn from a set of 50 numbers. With one ticket, you have one chance in 15,890,700 of winning.
3. To calculate the probability of winning with one ticket, press
1
e 2 ± ¸. The answer is too large to display in fixed notation; therefore, it is shown in scientific notation. 0.00000006292988981 is the decimal equivalent.
4. To calculate the probability of winning with five tickets, press p
5
¸. Again, the answer is too small to display in fixed notation. The decimal equivalent is 0.000000314649449.
2-2 Math, Angle, and Test Operations
Using the TI-80 Functions
This page contains some general information you should know about the TI
.
80 functions described in Chapter 1.
Using Lists with
Functions
Functions that are valid for lists return a list calculated on an element-by-element basis. If two lists are used in the same expression, they must be the same length. For more information about lists, see Chapter 8.
Using Fractions with Functions
Some math functions (
+
,
–
,
×
, à, x
ñ, ú
b
º
c
,
ú
a
À
b
º
c
,
ú
DEC
) accept fractions as input values.
All other functions convert fractions to decimals before operating on them. For more information about fractions, see Chapter 3.
Math, Angle, and Test Operations 2-3
Keyboard Math Operations
The most commonly used math functions are on the keyboard. The keyboard math operations can be used with decimal numbers, fractions (except as noted), expressions, and lists.
+ (Add)
– (Subtract)
×
(Multiply)
à
(Divide)
The basic arithmetic functions are: addition
«, subtraction |, multiplication p, and division e. Each argument for these functions can be a list.
valueA
+
valueB
, valueA
ìvalueB,
valueA
×
valueB
, valueA
àvalueB
Trig Functions
The trigonometric functions are interpreted according to the current
RADIAN
/
DEGREE
mode setting. (Refer to page 1 -9 for instructions on changing the mode setting.) For example,
SIN 30
in
RADIAN
mode returns
L
.9880316241
; in
DEGREE
mode, it returns
.5
. Each argument for the trigonometric functions may be a list.
SIN
value,
COS
value,
TAN
value
SIN
ê,
COS
ê, and
TAN
ê are the inverse trig functions (arcsine, arccosine, and arctangent).
SIN
ê value,
COS
ê value,
TAN
ê value
RADIAN Mode
ê
(Inverse)
ê (inverse,
V) may be used with numbers, expressions, or lists. The multiplicative inverse is the equivalent of the reciprocal, 1 àx.
value
ê
2-4 Math, Angle, and Test Operations
^
(Power)
2
(Square)
‡ (Square Root)
^
(power,
Z),
2
(square, a), and ‡ (square root, 2 ]) may be used with decimal numbers, fractions, expressions, or lists.
When used with a fraction, ‡ returns a decimal number.
value
^
power
, value
2
, ‡value
Note:
Raising a negative number to a noninteger power can result in a complex number, which returns an error.
LOG
10^
LN
These functions find the logarithm l, power of ten 2 h, and natural log x of the specified value or list of values.
LOG
value,
10^
power
,
LN
value
e^ e^
( 2 s) returns the constant e raised to a power or list of powers.
e^1
returns the value of the constant e.
e^
power
Math, Angle, and Test Operations 2-5
L
(Negation)
L (negation, ·) returns the negative of a number, expression, or list. The narrow negation symbol (
L) distinguishes negation from the subtraction or minus (
–
).
Lvalue
EOS rules (Chapter 1) determine when negation is evaluated.
For example,
L A 2
returns a negative number because squaring is evaluated before negation. Use parentheses to square a negated number,
( L A) 2
.
ABS
ABS
(absolute value,
2 P) returns the absolute value of a number, expression, or list.
ABS
value
p (Pi)
Pi (
2 T) is stored as a constant in the TI-80. Press 2 T to copy the symbol p to the cursor location. The number
3.141592654
is displayed for p, but 3.1415926535898 is used internally in calculations.
2-6 Math, Angle, and Test Operations
MATH MATH Operations
To display the MATH MATH menu, press
I
. When you select a menu item, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.
MATH MATH
Menu
INT ÷
MATH NUM PRB
1: INT÷
Displays quotient and remainder.
2: 8DEC
3:
3
4:
5:
3
‡ x
‡
6: NDERIV(
Displays answer in decimal form.
Cube.
Cube root.
n th
root.
Numerical derivative.
On the Home screen or from a program, INT÷ (integer divide,
MATH MATH
, item 1) returns the quotient (or quotient and remainder) resulting from the division of two integers. Each argument can be a list.
integerA
INT÷
integerB
When
INT÷
is executed on the Home screen, it displays the symbols
Q=
for the quotient and
R=
for the remainder.
Note:
If
INT÷
is embedded in an expression,
Q=
and
R=
may not be displayed.
When used with lists, INT÷ returns a list of quotients only.
If the result of
INT÷
is used in subsequent calculations, the remainder is dropped, and only the quotient is used.
The quotient from
INT÷
is returned to
ANS
.
Math, Angle, and Test Operations 2-7
8
DEC
8
DEC
(convert to decimal,
MATH MATH
, item 2) displays an answer in decimal form.
8
DEC
can only be used after a value and at the end of an expression. value can be a list.
value
8
DEC
expression
8
DEC
3
(Cube)
3
(cube,
MATH MATH
, item 3) returns the cube of a number, expression, or list.
value
3
3
‡
(Cube Root)
3
‡ (cube root,
MATH MATH
, item 4) returns the cube root of a number, expression, or list.
3
‡value
x
‡
(Root) x
‡
(root,
MATH MATH
, item 5) returns the n
th
real root of a number, expression, or list.
n th root
x
‡value
2-8 Math, Angle, and Test Operations
NDERIV( NDERIV(
(numerical derivative,
MATH MATH
, item 6) returns an approximate derivative of an expression with respect to a specified variable, given the value at which to calculate the derivative, and
H (optional; if none is specified, 1í-3 is used).
NDERIV(
expression
,
variable
,
value
)
or
NDERIV(
expression
,
variable
,
value
,
H
)
NDERIV(
uses the symmetric difference quotient method (as shown in the formula below), which approximates the numerical derivative value as the slope of the secant line through the points: f( X +
H)–f(
X –
H) f ¢( x
) =
2
H
As H gets smaller, the approximation usually gets more accurate.
Because of the method used,
NDERIV(
can return a false derivative value at a nondifferentiable point.
Math, Angle, and Test Operations 2-9
MATH NUM (Number) Operations
To display the MATH NUM menu, press
I 9
. When you select a menu item, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.
MATH NUM
Menu
ROUND(
MATH NUM PRB
1: ROUND(
2: IPART
3: FPART
Round.
Integer part.
Fractional part.
4: INT
5: MIN(
Greatest integer.
Minimum value.
6: MAX(
Maximum value.
7: REMAINDER(
Remainder of a division result.
ROUND(
(
MATH NUM
, item 1) returns a number, expression, or list rounded to a specified number of decimals (
9). If the number of decimals is omitted, the number is rounded to the digits that are displayed, a maximum of 10 digits.
Round(
value
,
#decimals
) Round(
value
)
Z PART
FPART
Z
PART
(integer part,
MATH NUM
, item 2) returns the integer part or parts of a number, expression, or list.
FPART
(fractional part,
MATH NUM
, item 3) returns the fractional part or parts of a number, expression, or list.
Z
PART
value
FPART
value
INT INT
(greatest integer,
MATH NUM
, item 4) returns the largest integer less than or equal to a number, expression, or list. The value is the same as
Z
PART for nonnegative numbers and negative integers, but one integer less than
Z
PART for negative noninteger numbers.
INT
value
2-10 Math, Angle, and Test Operations
MIN(
MAX(
MIN(
(minimum value,
MATH NUM
, item 5) returns the smaller of two values or the smallest element in a list. If two lists are compared, it returns a list of the smaller of each pair of elements. If a list and a value are compared, it compares each element in the list to the value.
MAX(
(maximum value,
MATH NUM
, item 6) returns the larger of two values or the largest element in a list. If two lists are compared, it returns a list of the larger of each pair of elements. If a list and a value are compared, it compares each element in the list to the value.
MIN(
valueA
,
valueB
)
MIN(
list
)
MIN(
listA
,
listB
)
MIN(
value
,
list
)
MIN(
list
,
value
)
MAX(
valueA
,
valueB
)
MAX(
list
)
MAX(
listA
,
listB
)
MAX(
value
,
list
)
MAX(
list
,
value
)
REMAINDER(
Note: MIN(
and
MAX(
are also available on the
LIST MATH
menu.
REMAINDER(
(
MATH NUM
, item 7) returns the remainder resulting from the division of two integers, each of which can be a list. (See
INT÷
, page 2–7.)
REMAINDER(
valueA
,
valueB
) REMAINDER(
listA
,
listB
)
REMAINDER(
value
,
list
) REMAINDER(
list
,
value
)
If a list is used as one or both arguments, the result is a list of remainders.
Math, Angle, and Test Operations 2-11
MATH PRB (Probability) Operations
To display the MATH PRB menu, press
I 6
. When you select a menu item, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.
MATH PRB
Menu
RAND
MATH NUM PRB
1: RAND
2: nPr
3: nCr
4: !
5: RANDINT(
Random number generator.
Number of permutations.
Number of combinations.
Factorial.
Random integer generator.
RAND
(random number,
MATH PRB
, item 1) generates and returns a random number greater than 0 and less than 1 (as in the first example below). A random number is generated from a seed value. To control a random number sequence, first store an integer seed value in
RAND
. In the second example below,
1
is stored to
RAND
so that the TI
-80 uses 1 as the seed value for generating random numbers.
Note:
When you reset the TI -80,
RAND
is set to the factory seed value, which is 0.
2-12 Math, Angle, and Test Operations
nPr nCr nPr
(number of permutations,
MATH PRB
, item 2) 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.
nCr
(number of combinations,
MATH PRB
, item 3) 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
nPr
number
items
nCr
number
!
(Factorial)
! (factorial,
MATH PRB
, item 4) returns the factorial of a positive integer or list of integers between 0 and 69.
value
!
RANDINT( RANDINT(
(random integer,
MATH PRB
, item 5) generates a random integer within a specified range. It requires two arguments: the lower and upper boundaries of the range (in any order). Both arguments must be integers. Both arguments can be negative. Both arguments can be lists.
RANDINT(
lower
,
upper
)
Math, Angle, and Test Operations 2-13
ANGLE Operations
To display the ANGLE menu, press
2 E
. The ANGLE menu displays angle indicators and instructions. When you select an item from the menu, the name is copied to the cursor location.
ANGLE
Menu
°
(Degree)
ANGLE
1: ¡
2: r
Degree notation.
Radian notation.
3: R 8Pr(
Returns
r
, given
X
and
Y
.
4: R 8Pq(
Returns q, given
X
and
Y
.
5: P
8Rx(
Returns
x
, given
R
and
q.
6: P 8Ry(
Returns
y
, given
R
and q.
¡
(degree,
ANGLE
, item 1) lets you designate an angle or list of angles as degrees, regardless of the current angle mode setting. In
RADIAN
mode, ¡ can also be used to convert degrees to radians.
value
¡
RADIAN
Mode
r (Radians) r
(radians,
ANGLE
, item 2) lets you designate an angle or list of angles as radians, regardless of the current angle mode setting. In
DEGREE
mode,
r
can also be used to convert radians to degrees.
value
r
DEGREE
Mode
2-14 Math, Angle, and Test Operations
R
8
Pr (
R
8
P q
(
P
8
Rx(
P
8
Ry(
Note:
When converting from one coordinate system to the other, be sure that the angle mode setting,
DEGREE
or
RADIAN
, is appropriate for your angle measurements. (Press
3 to check the current setting.)
R
8
Pr(
(
ANGLE
, item 3) converts the given rectangular coordinates to polar coordinates and returns
r
.
R
8
P q (
(
ANGLE
, item 4) converts the given rectangular coordinates to polar coordinates and returns q.
Both X and Y can be lists.
R 8 Pr(
X
,
Y
)
R 8 P q (
X
,
Y
)
RADIAN
Mode
P 8
Rx( (
ANGLE
, item 5) converts the given polar coordinates to rectangular coordinates and returns
x
.
P 8 Ry(
(
ANGLE
, item 6) converts the given polar coordinates to rectangular coordinates and returns
y
.
Both R and q can be lists.
P
8
Rx(
R
,
q
)
P
8
Ry(
R
,
q
)
RADIAN
Mode
Math, Angle, and Test Operations 2-15
>
‚
=
ƒ
<
TEST (Relational) Operations
To display the TEST menu, press
2 D
. When you select from the menu, the name is copied to the cursor location. These functions are valid for lists; they return a list calculated on an element-by-element basis.
TEST Menu
TEST True if:
1:=
Equal.
2: ƒ
3:>
4:
‚
5:<
6:
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 numbers, expressions, or lists.
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
ƒvalueB
valueA
>
valueB valueA
‚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
-80 does the addition first because of EOS rules, and then it compares 4 to 5.
¦
The expression
2+(2=2)+3
returns
6
. The TI
-80 first performs the relational test because it is in parentheses; then it adds 2, 1, and 3.
2-16 Math, Angle, and Test Operations
Chapter 3: Fractions
This chapter describes how to use the fraction operations on the TI
.
80.
Chapter
Contents
Getting Started: Working with Fractions
.............
Setting Modes for Fraction Results
..................
Entering and Using Fractions in Calculations
.........
The
FRACTION
Menu
..............................
Fractions 3-1
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 1 of 10
Getting Started: Working with Fractions
Getting Started is a fast-paced introduction. Read the chapter for details.
Enter the expression 1
6/27
+ 1
1/9.
Evaluate the expression, simplify the result, and then use the conversion options on the FRACTION menu to convert the result.
This example is performed in
MANSIMP
(manual simplification) mode.
MANSIMP
mode is especially useful for students when they are learning fraction concepts.
When
MANSIMP
mode is selected, the
ú
SIMP
function (from the
FRACTION
menu) can be used to simplify fractions step-by-step.
1. Select
MANSIMP
mode.
2. From the Home screen, press
1
2 ¥
6
2 _
27
«
1
2 ¥
1
2 _
9
to enter the mixedfraction expression,
1
6/27
+ 1
1/9
.
3. Press
¸ to evaluate the expression. The ï indicates that the fraction can be simplified.
4. Press
J
1
to select ú SIMP ( simplify).
ANS
ú
SIMP
is copied to the cursor location.
5. Press
¸ to simplify the fraction.
In
MANSIMP
mode, the TI -80 uses the lowest common factor for simplification. The simplification factor is displayed. The ï preceding the result indicates that the fraction can be simplified further.
Continue pressing
¸ until ï is no longer displayed.
3-2 Fractions
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 2 of 10
The TI
.
80 uses the lowest common factor for simplification. If you want to choose the simplification factor yourself, you can enter it as part of the expression.
6. Press
M to clear the screen. Reenter the expression, or press 2 ² until you see the expression
1
À
6
º
27
+ 1
À
1
º
9
.
7. Press
2 6 2 / c 2 9 b
9
d. This adds the simplification factor 9 and places the expression in parentheses.
8. Press
J
1
to copy ú SIMP to the cursor location.
9. Press ¸ to simplify the fraction result. The simplification factor is displayed.
10. Press
2 ± J
2
¸ to convert the mixed fraction result to a simple fraction.
11. Press
2 ± J
5
¸ to convert the fraction result to its decimal equivalent.
Fractions 3-3
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 3 of 10
Setting Modes for Fraction Results
From the MODE screen, you can select simplification and display format options for fraction results.
AUTOSIMP Mode with b
º
c and a
À
b
º
c Modes
AUTOSIMP
mode simplifies fractions automatically.
Simplification takes place before the expression is evaluated.
Then the result is simplified to its lowest terms. For example,
12 à 16
is simplified to
3 à 4
when you press
¸.
There are two formats for displaying fractions results.
¦
b
º
c
mode displays fraction results in simple-fraction (a fraction without a whole number) format; for example,
25 à 4
.
¦
a
À
b
º
c
displays fraction results in mixed-fraction (a whole number with a fraction) format; for example
5
3/4
.
3-4 Fractions
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 4 of 10
MANSIMP Mode with a
À
b
º
c Mode
MANSIMP
mode lets you simplify fractions manually.
MANSIMP
was designed for teaching and learning fractions concepts. In
MANSIMP
mode, you can simplify fractions and the results of expressions using fractions, step-by-step.
When a fraction result is not expressed in its lowest terms, a down arrow ( ï) is displayed to remind you that you can simplify the result. Use ú
SIMP
from the
FRACTION
menu to simplify the fraction. You can then use ú
b
º
c
or ú
a
À
b
º
c
to change the display format of the fraction result.
Typically, you use the
MANSIMP
simplification mode with the
ú
a
À
b
º
c
display format mode for teaching or learning fraction concepts. The display format of fraction results can vary when you are using
MANSIMP
and ú
a
À
b
º
c
.
¦
When you simply enter a fraction and press
¸, the format in which you entered the fraction is preserved.
¦
When you add or subtract using a mixed fraction, calculation takes place on the whole-number and fractional part of the mixed-fraction separately. The result is displayed as a mixed fraction.
¦
When you multiply or divide using a mixed fraction, the result is displayed as a simple fraction.
Fractions 3-5
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 5 of 10
Entering and Using Fractions in Calculations
The TI
.
80 lets you enter fractions directly from the keyboard.
Entering Simple
Fractions
Entering Mixed
Fractions
A simple fraction is a fraction with no whole-number part; for example,
3 à 4
or
4 à 3
.
To enter a simple fraction:
1. Enter the numerator (up to six digits), and then press 2
_.
2. Enter the denominator (up to and including 1000).
For example, press
2
2 _
3
to enter
2
à
3
.
A mixed fraction is fraction that has both a whole-number and a fractional part; for example
1
1 à 3
.
To enter a mixed fraction:
1. Enter the units (up to three digits), and then press 2
¥.
2. Enter the numerator (up to three digits), and then press
2 _.
3. Enter the denominator (up to and including 1000).
For example, press
5
2 ¥
2
2 _
3
to enter
5
2
à
3
.
3-6 Fractions
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 6 of 10
In general, you can use fractions in expressions just as you would use other numbers. The results of the expressions, however, may or may not be fractions.
Using Fractions in Expressions
The absolute value of a fraction on the TI
-80 cannot be
≥
1000.
«, |, p, e, V, a, ·, and 2 P accept fraction entries and return fraction results. If the absolute value of a fraction result is
≥
1000, or if the results of operations with these functions are not within the limits shown on page 3
-6, the results are given in decimal form.
Other functions accept fraction entries, but convert them to decimal form before operating on them. The results are given in decimal form. For example,
‡ 4 à 9
returns
.6666666667
, not
2
à
3
.
If you use ú
SIMP
with a fraction that has been converted to a decimal, an error occurs.
If an expression contains both a fraction and a decimal number, the result is displayed as a decimal number.
You can also enter fractions in a list, but the results are returned as decimal values.
Fractions 3-7
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 7 of 10
The FRACTION Menu
To display the FRACTION menu, press
J
. The menu items let you simplify and convert fractions. When you select a menu item, the name is copied to the cursor location.
FRACTION Menu
Simplifying
Fractions
ú
SIMP
FRACTION
1:
8SIMP Simplifies the fraction.
2:
8bºc Converts to a simple fraction.
3:
8aÀbºc Converts to a mixed fraction.
4:
8FRAC Converts a decimal to a fraction based on mode.
5:
8DEC
Converts a fraction to a decimal.
ú
SIMP
(simplify fraction,
FRACTION
, item 1) simplifies the specified fraction and displays it, along with the simplification factor.
Note:
ú
SIMP
can only be used in
MANSIMP
mode.
You have two options for simplifying fractions.
¦
You can let the calculator simplify the fraction, step-bystep, using the lowest common factor (LCF).
fraction
ú
SIMP
¦
You can choose a factor (an integer) for simplifying the fraction.
(
fraction
,
factor
)
ú
SIMP
Both simplification options update the variable
FACTOR
.
3-8 Fractions
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 8 of 10
Converting
Simple and
Mixed Fractions
ú
b
º
c
8 a
À
b
º
c
8 b
º
c
(convert to simple fraction,
FRACTION
, item 2) converts
value
to a simple fraction.
8 a
À
b
º
c
(convert to mixed fraction, item 3) converts value to a mixed fraction.
value
8 b
º
c
value
8 a
À
b
º
c
Both
8 b
º
c
and
8 a
À
b
º
c
can be used only at the end of an expression. A ! (§) instruction, however, can follow them.
Fractions 3-9
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 9 of 10
Converting
Decimals and
Fractions
ú
FRAC
8 DEC
8
FRAC
(convert to fraction,
FRACTION
, item 4) converts a
decimal
value to its fraction equivalent and displays it. The
decimal
may be a number, expression, or list.
In
MANSIMP
mode,
8 FRAC
first attempts to return a fraction in terms of 10ths, 100ths, or 1000ths. If this is not possible,
8 FRAC
converts the decimal to its fraction equivalent as it would in
AUTOSIMP
mode. If the value cannot be converted or if the denominator of the equivalent fraction is greater than
1000, the decimal equivalent is returned.
The form of the
8 FRAC
result depends on the current fraction display format. For example, 1.25
8 FRAC
returns
1
1 à 4
if
a
À
b
º
c
is selected or
5 à 4
if
b
º
c
is selected.
If the decimal value for
8 FRAC
is a list, the list is displayed as fractions, but it is still stored internally in decimal form.
8
DEC
(convert to decimal,
FRACTION
, item 5) converts a
fraction
value to its decimal form and displays it.
decimal
8
FRAC
fraction
8
DEC
AUTOSIMP & a
À
b
º
c AUTOSIMP & b
º
c
MANSIMP & a
À
b
º
c MANSIMP & b
º
c
Both
8 FRAC
and
8 DEC
are valid only at the end of an expression. A ! (
§) instruction, however, can follow them.
3-10 Fractions
8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01
9:53 AM Page 10 of 10
Chapter 4: Function Graphing
This chapter describes function graphing on the TI
.
80 in detail. It also lays the foundation for using the parametric graphing features described in Chapter 5.
Chapter
Contents
Getting Started: Graphing a Circle
...................
Defining a Graph
..................................
Setting Graph Modes
..............................
Defining Functions in the
Y=
List
....................
Evaluating
Y=
Functions in Expressions
.............
Selecting Functions
...............................
Defining the Viewing Window
......................
Displaying a Graph
................................
Exploring a Graph with the Free-Moving Cursor
......
Exploring a Graph with
TRACE
.....................
Exploring a Graph with
ZOOM
......................
Setting the Zoom Factors
..........................
Function Graphing 4-1
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 a circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSQUARE to adjust the display to make the functions appear as a circle.
Make sure that your TI
-80 is in
FUNC
mode and all
STAT PLOTS
are turned off.
1. Press
( to display the
Y=
edit screen. Press
2 ] c
100
| @ a d ¸ to enter the expression
Y1=
‡
(100–X
2
)
, which defines the top half of the circle.
The bottom half of the circle is defined by
Y2=
‡
(100–X
2
)
. However, you can also define one function in terms of another; so to define
Y2=
L
Y1
, press
· 2 G (to display the
Y=
variables menu) 1 (to select
Y1
).
2. Press
*
6
to select
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
,.
Notice that the functions appear as an ellipse in the standard viewing window.
3. To adjust the display so each “dot” represents an equal width and height, press
*, and then
5
to select
ZSQUARE
. The functions are replotted and now appear as a circle on the display.
4. To see the
ZSQUARE
Window variables, press
) and notice the values for
XMIN
,
XMAX
,
YMIN
, and
YMAX
.
5. If you want to see the graph again, press
,.
4-2 Function Graphing
Defining a Graph
To define a graph, you set the modes, enter and select the functions to graph, and define the viewing window and the graphing format. Once you have defined a graph, you can plot it, display it, and explore it.
Steps in Defining a Graph
There are six basic steps to defining a graph, although you may not need to do all of the steps each time you define a graph. The procedures are described in detail on the following pages.
Exploring a
Graph
1. Set the mode to
FUNC
graphing (Chapter 1).
2. Enter or edit a function in the
Y=
list (page 4
-5).
3. Select the
Y=
function you want to graph (page 4
-8).
4. Define the viewing window (page 4
-9).
5. Set the graphing format (page 4
-11).
6. Deselect
STAT PLOTS
, if appropriate (Chapter 9).
Once you have defined a graph, you can display it and use several tools on the TI -80 to explore the behavior of the function or functions. These tools are described later in this chapter.
Function Graphing 4-3
Setting Graph Modes
Pressing
3
displays the current mode settings, as described in Chapter 1. For function graphing, the graphing mode must be set to FUNC. Before you graph a function, check to be sure that the mode settings are appropriate.
Checking and
Changing
Graphing Modes
Setting Modes from a Program
Press
3 to display the mode settings. The current settings are highlighted.
The TI
-80 has two graphing modes.
¦
FUNC
(function graphing)
¦
PARAM
(parametric graphing)
To graph functions, you must select
FUNC
(function graphing).
The basics of graphing on the TI
-80 are described in this chapter. Differences in parametric graphing are described in
Chapter 5.
The mode settings can affect how functions are graphed.
¦
RADIAN
or
DEGREE
mode may affect how some functions are interpreted.
¦
CONNECTED
or
DOT
affects how the selected functions are plotted.
¦
SEQUENTIAL
or
SIMUL
affects how functions are plotted if you have more than one function selected.
You can set the graphing mode and other modes from a program.
Begin on a blank line in the program editor. Press
3 to display the
MODE
screen. Press
8 and 7 to place the cursor on the mode that you want to select, and then press
¸.
The name of the mode is copied to the cursor location.
4-4 Function Graphing
Defining Functions in the Y= List
Pressing
(
displays the Y= edit screen. This is where you enter the functions to graph. You can store up to four functions in memory at one time. You can graph one or more of these functions at a time.
Displaying the
Functions in the
Y= List
Press
( to display the
Y=
edit screen. In the example below, the
Y1
and
Y2
functions are defined.
Defining a New
Function
To define a new function in the
Y=
list:
1. Press
( to display the
Y=
edit screen.
2. Move the cursor to the function in the
Y=
list you want to define. If necessary, press
M to erase a previously entered function.
3. Enter the expression to define the function.
¦
You may use functions and variables in the expression.
If the expression evaluates to a value that is not a real number, that point is not plotted; an error does not occur.
¦
The independent variable in the function is
X
. You may press
@, rather than pressing ? ã
X
ä, to enter the
X
variable. (
FUNC
mode defines the independent variable as
X
.)
¦
The expression is stored as one of the four user-defined functions in the
Y=
list as you enter it.
Note:
You can use a list within a
Y=
function; however, the function must evaluate to a single value.
4. When you complete the expression, press
¸ to move to the beginning of the next function.
Note:
When you enter a function, it is automatically selected for graphing in the Y= list. This is indicated by the highlighted equal sign. For details on selecting and deselecting functions, see page 4
-8.
Function Graphing 4-5
Editing a
Function
Clearing a
Function
Defining
Functions from the Home Screen or a Program
To edit a function in the
Y=
list:
1. Press
( to display the
Y=
list, and move the cursor to the function you want to change.
2. Make the changes. You can also press
M to erase the expression, and then enter a new expression.
The expression is stored in the
Y=
list and selected (turned on) as you edit it.
To clear or erase a function on the
Y=
edit screen, position the cursor anywhere on the function, and then press
M.
To define a function from the Home screen or from a program, begin on a blank line.
1. Press ? ã
"
ä, enter the expression, and then press
? ã
"
ä again.
2. Press
§.
3. Press
2 G, and then select the name of the function from the
Y
menu. The name is copied to the cursor location.
4. Press
¸ to complete the instruction.
"
expression
"
!
Y
n
Leaving the Y=
Edit Screen
When the instruction is executed, the TI
-80 stores the expression in the Y= list, selects (turns on) the function, and displays the message
DONE
.
To leave the Y= edit screen:
¦
Select another screen by pressing the appropriate key, such as
, or ).
¦
Press
2 . to return to the Home screen.
4-6 Function Graphing
Evaluating Y= Functions in Expressions
You can the calculate the value of a Y= function at a specified value of X.
Entering the
Functions in the
Y= List
To display the
Y=
list, press
(. Enter these functions for
Y1
,
Y2
, and
Y3
:
X
2
, X+2 , and Y1(Y2(X)) .
@ a
¸
@ «
2
¸
2 G 1 c 2 G 2 c @ d d
Evaluating
Functions
To evaluate the functions, first specify the value of X. Note that X may be a list.
2 .
M 2 G
2 c
3
d
¸
2 G
1
c 2 G
2 c
3
d d
¸
2 G
3
c 2 [
1
, 2 , 3
2 \ d
¸
Evaluating
Functions without
Parentheses
You can also evaluate functions without using parentheses by storing a value to X.
3
§ @ ¸
2 G
1
¸
Function Graphing 4-7
Selecting Functions
Only functions that are selected (turned on) are graphed. All four functions may be selected at one time.
Turning a
Function “On” or
“Off”
You can select and deselect (“turn on” and “turn off”) functions on the
Y=
edit screen. The
=
sign on a selected function is highlighted.
To change the selection status of a function:
1. Display the Y= list, and move the cursor to the function whose status you want to change.
2. Press
6 to place the cursor over the
=
sign of the function.
3. Press
¸ to change the status. If the function was selected, it is now deselected. If it was deselected, it is now selected.
Selecting
Functions from the Home Screen or a Program
Note:
When you enter or edit a function, it is selected automatically. When you clear a function, it is deselected.
To select functions from the Home screen or a program, begin on a blank line.
1. Press
2 G, and then press 6 to select
ON/OFF
. The
ON/OFF
menu is displayed.
2. Select the instruction you want,
FNON
or
FNOFF
. It is copied to the cursor location.
3. To turn specific functions on or off, enter the number(s) of the function(s), separated by commas.
FNON
function#
,
function#
,
. . .
FNOFF
function#
,
function#
,
. . .
For example, in
FUNC
mode,
FNOFF 1,3
turns off functions
Y1
and
Y3
.
4-8 Function Graphing
Defining the Viewing Window
The Window variables determine the boundaries and other attributes of the viewing window. The Window variables are shared by all graphing modes.
The Viewing
Window
The viewing window of the TI
-80 is the portion of the coordinate plane defined by
XMIN
,
XMAX
,
YMIN
, and
YMAX
.
The distance between tick marks is defined by
XSCL
for the
X
axis and
YSCL
for the
Y
axis.
XMIN
YMIN
YMAX
XSCL
YSCL
XMAX
Checking the
Viewing Window
Press
) to display the current Window variable values.
The values shown here are the default values.
Changing a
Window Variable
Value
To change a Window variable value:
1. Press 8 to move to the Window variable you want to change.
2. To enter a real value (which can be an expression), you may do any of the following:
¦
Position the cursor, and then make the changes.
¦
Press
M to clear the value, and then enter a new value.
¦
Begin entering a new value. The original value is cleared automatically when you begin typing.
3. Press
¸, 8, or 7. If you entered an expression, it is evaluated. The new value is stored.
XMIN
must be less than
XMAX
, and
YMIN
must be less than
YMAX
, or you will get an error message when you press
,. To turn off the tick marks, set
XSCL=0
and
YSCL=0
.
Function Graphing 4-9
Leaving the
Window Screen
Storing to a
Window Variable from the Home
Screen or a
Program
To leave the Window screen:
¦
Select another screen by pressing the appropriate key, such as
, or (.
¦
Press
2 . to return to the Home screen.
To store to a Window variable from the Home screen or from a program, begin on a blank line.
1. Enter the value (which can be an expression) that you want to store.
2. Press
§.
3. Press
L to display the
VARS
menu.
4. Select
WINDOW...
to display the Window variables.
5. Select the Window variable. The name of the variable is copied to the cursor location.
6. Press
¸ to complete the instruction.
@ X and @ Y
Note:
You can use a Window variable in an expression by performing steps 3, 4, and 5.
The variables
@ X
and
@ Y
define the distance between the centers of two adjoining pixels on a graph (graphing accuracy).
(XMAX – XMIN)
@
X
=
62
(YMAX – YMIN)
@
Y
=
46
@ X
and
@ Y
are not on the Window screen; however, they are accessible through the
VARS WINDOW...
menu.
@ X
and
@ Y
are calculated from
XMIN
,
XMAX
,
YMIN
, and
YMAX
when a graph is displayed.
You can store values directly to
@
X
and
@
Y
(7 and 8 on the
VARS WINDOW...
menu), in which case
XMAX
and
YMAX
are immediately calculated from
@
X
,
XMIN
,
@
Y
, and
YMIN
.
4-10 Function Graphing
Displaying a Graph
Pressing
,
graphs any functions selected on the Y= edit screen. The current mode settings apply, and the current values of the Window variables define the viewing window.
Turning the Grid
Points On and
Off
Displaying a New
Graph
Smart Graph
Grid points correspond to the axis tick marks. To turn the grid points on and off use
GRIDON
and
GRIDOFF
. The default for the TI -80 is
GRIDOFF
.
1. From the Home screen, press
2 F to display the
DRAW
menu.
2. Press
9
to select
GRIDON
, or press
0
to select
GRIDOFF
.
3. Press
¸. The message
DONE
is displayed.
Press
, to display the graph of the selected function or functions. (Some operations, such as
TRACE
and the Zoom instructions, display the graph automatically.) As a graph is plotted, the busy indicator is on, and
X
and
Y
are updated.
When you press
,, Smart Graph displays the graph screen immediately if nothing has changed that requires the functions to be replotted since the last time the graph was displayed.
Overlaying
Functions on a
Graph
If you have changed any of the following since the graph was last displayed, pressing , replots the graph based on the new values.
¦
Changed a mode setting that affects graphs.
¦
Changed a function in the current picture.
¦
Deselected a function in the current picture.
¦
Changed the value of a variable in a selected function.
¦
Changed a Window variable or format setting.
¦
Cleared drawings by selecting
CLRDRAW
(Chapter 7).
¦
Changed or turned off a
STAT PLOT
definition (Chapter
9).
Note: CLRDRAW
is a fast way to replot a graph.
The TI
-80 lets you graph one function at a time without replotting every function. For example, enter SIN X as Y1 and press
,. Then enter
COS X
as
Y2
and press
, again.
The second function is graphed on top of the original function.
Function Graphing 4-11
Exploring a Graph with the Free-Moving Cursor
While a graph is displayed, you can move the free-moving cursor anywhere on the graph and display the coordinates of any location on the graph.
Free-Moving
Cursor
Graphing
Accuracy
You can press
6, 9, 7, or 8 to move the cursor around the graph. When you first display the graph, no cursor is visible.
As soon as you press
6, 9, 7, or 8, the cursor moves from the center of the viewing window.
As you move the cursor around the graph, the values of the variables
X
and
Y
are updated, and the coordinate values of the cursor location are displayed at the bottom of the screen.
Coordinate values generally appear in floating-decimal format.
The numeric display settings on the
MODE
screen do not affect coordinate display.
To see the graph without the cursor or coordinate values, press , or M. When you press 6, 9, 7, or 8, the cursor begins to move from the same position.
The free-moving cursor moves from dot to dot on the screen.
When you move the cursor to a dot that appears to be “on” the function, it may be near, but not on, the function; therefore, the coordinate value displayed at the bottom of the screen is not necessarily a point on the function. To move the cursor along a function, use
TRACE
(page 4
-13).
The displayed coordinate values of the free-moving cursor approximate actual math coordinates accurate to within the width/height of the dot. As
XMIN
and
XMAX
(and
YMIN
and
YMAX
) get closer together (after a
ZOOM IN
, for example), graphing accuracy increases, and the coordinate values more closely represent the math coordinates.
)
Free-moving cursor “on” the curve
4-12 Function Graphing
Exploring a Graph with TRACE
TRACE moves the cursor from one plotted point to the next along a function.
The cursor coordinates are displayed at the bottom of the screen.
Beginning a
Trace
Moving along a
Function
Press
+ to begin a trace. If the graph is not displayed already, the TI
-80 displays it. The cursor is on the first selected function in the
Y=
list at the middle
X
value on the screen. The number of the function appears at the upper right of the display.
Note:
If any
STAT PLOTS
are turned on, the TI
-80 attempts to trace the first stat plot.
Press
9 and 6 to move the cursor along the function. Each press moves the cursor from one plotted point to the next.
Press
2 9 and 2 6 to move the cursor five plotted points at a time. Tracing updates and displays the values of the variables
X
and
Y
. 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.
Panning to the
Left or Right
QuickZoom
If the
Y
value of a function is above or below the viewing window, the cursor disappears as you move it to that portion of the function. However, the coordinate values at the bottom of the screen indicate the cursor coordinates.
If you trace a function off the left or right edge of the screen, the viewing window automatically pans to the right or left.
XMIN
and
XMAX
are updated to correspond to the new viewing window.
Note:
The screen does not pan if a
STAT PLOT
is on.
While tracing, you can press ¸ to adjust the viewing window so that the cursor location becomes the center of a new viewing window, even if the cursor is above or below the display. This allows “panning” up and down. After
QuickZoom,
TRACE
is still active.
Function Graphing 4-13
Moving from
Function to
Function
Leaving TRACE
Using TRACE in a Program
To trace another selected function on the graph, press
8 or 7 to move the cursor to that function. The cursor moves to the new function at the same
X
value. The function number in the upper right corner of the display changes.
The cursor movement is based on the order of the selected functions in the
Y=
list, not the appearance of the functions as graphed on the screen.
To leave
TRACE
:
¦
Select another screen by pressing the appropriate key, such as
) or *.
¦
Press
, or M to see the graph without the Trace cursor.
¦
Press 2 . to return to the Home screen.
The Trace cursor remains in the same location if you leave
TRACE
and return, as long as Smart Graph has not caused the graph to be replotted.
On a blank line in the program editor, press
+. The instruction
Trace
is copied 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 function(s), press
¸ to resume program execution.
4-14 Function Graphing
Exploring a Graph with ZOOM
Pressing
*
displays a menu that allows you to adjust the viewing window of the graph quickly in a variety of ways. All of the Zoom instructions are accessible from programs.
ZOOM
Menu
ZBOX
ZOOM
1: ZBOX
Draws box to define viewing window.
2: ZOOM IN
Magnifies graph around cursor.
3: ZOOM OUT
Views more of graph around cursor.
4: ZDECIMAL
Sets .1 as dot size.
5: ZSQUARE
Sets equal sized-dots on
X
and
Y
axes.
6: ZSTANDARD Sets standard Window variables.
7: ZTRIG
Sets built-in trig Window variables.
ZBOX
lets you use the cursor to select opposite corners of a box to define a new viewing window.
1. Select
ZBOX
from the
ZOOM
menu. The different cursor at the center of the screen indicates that you are using a
Zoom instruction.
2. Move the cursor to any corner of the box you want to define, and then press ¸. As you move the cursor away from the point just selected, you see a small square dot, indicating that the first corner is selected.
3. Move the cursor to the diagonal corner of the box you want to define. As you move the cursor, the boundaries of the box change on the screen.
Note:
Before you press
¸, you can cancel
ZBOX
at any time by pressing
M.
4. When the box is defined as you want it, press
¸ to replot the graph.
You can repeat steps 2 through 4 to do another
ZBOX
.
Function Graphing 4-15
ZOOM IN
ZOOM OUT
Leaving ZOOM
IN or ZOOM OUT
ZOOM IN
magnifies the graph around the cursor location. The
XFACT
and
YFACT
settings determine the extent of the zoom
(page 4
-18). The default value for both
XFACT
and
YFACT
is
4.
1. After checking or changing
XFACT
and
YFACT
, select
ZOOM IN
from the
ZOOM
menu.
Notice the different cursor. It indicates that you are using a Zoom instruction.
2. Move the cursor to the point that you want as the center of the new viewing window, and then press
¸.
The TI
-80 adjusts the viewing window by
XFACT
and
YFACT
, updates the Window variables, and replots the selected functions centered on the cursor location.
3.
ZOOM IN
is still turned on. To zoom in on the graph again:
¦
At the same point, press
¸.
¦
At a new point, move the cursor to the point that you want as the center of the new viewing window, and then press
¸.
ZOOM OUT
displays a greater portion of the graph, centered on the cursor location, to provide a more global view. The procedure for
ZOOM OUT
is the same as for
ZOOM IN
.
To leave
ZOOM IN
or
ZOOM OUT
:
¦
Select another screen by pressing the appropriate key, such as
+ or ,.
¦
Press 2 . to return to the Home screen.
4-16 Function Graphing
ZDECIMAL
ZSQUARE
ZSTANDARD
ZTRIG
ZDECIMAL
replots the functions immediately, updates the
Window variables to preset values that set
@
X
and
@
Y
equal to
.1
, and defines the
X
and
Y
value of each pixel as one decimal.
XMIN = L 3 . 1
XMAX = 3.1
XSCL = 1
YMIN = L 2 . 3
YMAX = 2.3
YSCL = 1
ZSQUARE
replots the functions immediately, redefining the window based on the current Window variables, but adjusted in only one direction so that
@ X= @ Y
. This 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.
ZSTANDARD
replots the functions immediately, updating the
Window variables to the standard values:
XMIN =
L
10
XMAX = 10
XSCL = 1
YMIN =
L
10
YMAX = 10
YSCL = 1
ZTRIG
replots the functions immediately, updating the
Window variables to preset values appropriate for plotting trig functions. In
RADIAN
mode, these are:
XMIN = L (31/12) p ( L 8.115781..)
XMAX = (31/12) p (8.1157810..)
XSCL = ( p /2) (1.5707963..)
YMIN = L 2 ( L 2 )
YMAX = 2 ( 2 )
YSCL = 1 (1)
Function Graphing 4-17
Setting the Zoom Factors
The Zoom factors, XFACT and YFACT, determine the extent of the change for the viewing window created by ZOOM IN or ZOOM OUT on a graph.
Zoom Factors
Checking Zoom
Factors
Zoom factors 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.
To review the current values of the Zoom factors (
XFACT
and
YFACT
):
1. Press
L, and then press
1 to select
WINDOW...
.
2. Press
9
to select
XFACT
or
0
to select
YFACT
.
XFACT
or
YFACT
is copied to the cursor location.
3. Press ¸. The Zoom factor is displayed.
Setting Zoom
Factors from the
Home Screen or a Program
To set the Zoom factors
XFACT
and
YFACT
from the Home screen or a program, begin on a blank line.
1. Enter the factor, and then press
§.
2. Press
L, and then press
1
to select
WINDOW...
.
3. Press
9
to select
XFACT
or
0
to select
YFACT
.
XFACT
or
YFACT
is copied to the cursor location on the Home screen.
4. Press
¸ to store the Zoom factor to the variable.
4-18 Function Graphing
Chapter 5: Parametric Graphing
This chapter describes how to graph parametric equations on the TI
.
80. Before doing parametric graphing, you should be familiar with Chapter 4, Function
Graphing.
Chapter
Contents
Getting Started: Path of a Ball
......................
Defining and Displaying a Parametric Graph
..........
Exploring a Parametric Graph
......................
Parametric Graphing 5-1
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 kicked at an angle of 60
¡
with an initial velocity of 15 meters per second. (Ignore air resistance.) What is the maximum height? When does the ball strike the ground?
1. Press
3, and then press 8 8 8 8 8 9 ¸ to select
PARAM
mode.
For initial velocity v
0
and angle q, the horizontal component of the ball as a function of time is
X(t) = t v
Y(t) = t v
0
0
cos q. The vertical component is
sin q -(gà2) t 2
. The gravity constant g is
9.8 m àsec
2
.
2. Press (. Press
15
@ X
60
2 E
1
(to select
¡) ¸ to define the
X
portion of the parametric equation in terms of
T
.
3. Press
15
@ W
60
2 E
1
(to select
¡) | c
9.8
e
2
d @ a ¸ to define the
Y
portion.
4. Press
). Enter the Window variables appropriate for this problem.
TMIN=0
TMAX=3
TSTEP=.2
XMIN=
ë
2
XMAX=25
XSCL=5
YMIN=
ë
2
YMAX=10
YSCL=5
5. Press
+ to graph the position of the ball as a function of time.
Tracing begins at
TMIN
. As you press
9~ 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.
The maximum height is approximately 8.6 meters. The ball strikes the ground in approximately 2.6 seconds.
5-2 Parametric Graphing
Defining and Displaying a Parametric Graph
Parametric equations consist of an X component and a Y component, each expressed in terms of the same independent variable T. They are often used to graph equations over time. Up to three pairs of parametric equations can be defined and graphed at a time.
Defining a
Parametric
Graph
Setting
Parametric
Graph Modes
Displaying
Parametric
Equations
The steps for defining a parametric graph are the same as those for defining a function graph (page 4
-3). Differences are noted below.
Press
3 to display the mode settings. To graph parametric equations, you must select
PARAM
before you enter Window variables or enter the components of parametric equations.
Normally, you should also select
CONNECTED
to obtain a more meaningful parametric graph.
After selecting
PARAM
mode, press ( to display the parametric
Y=
edit screen.
Defining
Parametric
Equations
On this screen, you display and enter both the
X
and
Y
components. The TI
-80 allows three parametric equations, each defined in terms of
T
.
Follow the same procedures as for function graphing (pages
4
-5 to 4-6) to enter the two components that define a new parametric equation.
¦
You must define both the
X
and
Y
components in a pair.
¦
The independent variable in each component is
T
. You may press
@, rather than pressing ? ã
T
ä, to enter the parametric variable
T
. (
PARAM
mode defines the independent variable as
T
.)
Parametric Graphing 5-3
Selecting
Parametric
Equations
Setting Window
Variables
The TI
-80 graphs only the parametric equations you select.
The highlighted
=
sign on both components of an equation indicates that the equation is selected.
You may select any or all of the equations on the parametric
Y=
edit screen.
To change the selection status of a parametric equation, press
6 to move the cursor onto the
=
sign of either the
X
or
Y
component and press
¸. The status on both the
X
and
Y
components changes.
Note:
When you enter both components of an equation or edit either component, that equation is selected automatically.
Press
) to display the current Window variable values.
The Window variables define the viewing window. The values shown are the standard values in
RADIAN mode.
TMIN=0
TMAX=6.283185307
Smallest T value to evaluate.
Largest T value to evaluate.
TSTEP=.1308996938996
T value increment.
XMIN=
L
10
XMAX=10
Smallest X value to be displayed.
Largest X value to be displayed.
XSCL=1
YMIN= L 10
YMAX=10
YSCL=1
Spacing between X tick marks.
Smallest Y value to be displayed.
Largest Y value to be displayed.
Spacing between Y tick marks.
To change a Window variable value, follow the steps given for function graphing (page 4 -8).
Note:
You may want to change the
T
variable values to ensure that sufficient points are plotted.
5-4 Parametric Graphing
Displaying a
Graph
VARS WINDOW and Y-VARS
Menus
When you press
,, the TI-80 plots the selected parametric equations. It evaluates both the
X
and the
Y
component 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 a graph is plotted, the TI
-80 updates
X
,
Y
, and
T
.
Note:
Smart Graph applies to parametric graphs also (page
4
-11).
By means of the
VARS WINDOW...
and
Y-VARS
menus, you can:
¦
Access functions by using the name of the component of the equation as a variable.
¦
Select or deselect parametric equations from a program, using the
FNON
and
FNOFF
commands (page 4 -8).
¦
Store parametric equations.
¦
Store values directly to Window variables.
Parametric Graphing 5-5
Exploring a Parametric Graph
As in function graphing, three tools are available for exploring a graph: the freemoving cursor, tracing, and zooming.
Free-Moving
Cursor
Tracing a
Parametric
Graph
The free
-moving cursor works the same in parametric graphing as in function graphing (page 4-12).
Pressing
+ puts the Trace cursor on the first selected equation, at
TMIN
. You can then trace along the equation.
6 or 9
2 6 or 9 ~
7 or 8
M
Moves the cursor one
Moves the cursor five right of the display.
Cancels tracing.
TSTEP
TSTEP
at a time.
s at a time.
Changes to the previous or next equation.
The equation number shows in the upper
Zooming in on a
Parametric
Graph
For each value of
T
, the calculator displays values for
X
and
Y
.
The values for
X
,
Y
, and
T
are updated as you move the Trace cursor. If the cursor moves off the top or bottom of the screen, the coordinate values continue to change appropriately.
The Trace cursor remains in the same location if you leave
TRACE
and return, unless Smart Graph replots the graph.
QuickZoom is available in parametric graphing, but panning is not (page 4
-13).
Pressing
* works the same in parametric graphing as in function graphing (page 4
-15).
Parametric graphing uses the additional Window variables
TMIN
,
TMAX
, and
TSTEP
. These variables are not affected by zooming unless you select
ZSTANDARD
, where
TMIN
= 0,
TMAX
= 6.283185307 (2 p), and
TSTEP
= .1308996938996
( p/24).
5-6 Parametric Graphing
Chapter 6: Tables
This chapter describes how to use tables on the TI
.
80. A table evaluates the selected functions from the Y= list and displays each value for the independent variable along with the evaluated value for each corresponding dependent variable.
Chapter
Contents
Getting Started: Roots of a Function
.................
Defining the Independent Variable
..................
Defining the Dependent Variable
....................
Displaying the Table
...............................
Tables 6-1
Getting Started: Roots of a Function
Getting Started is a fast-paced introduction. Read the chapter for details.
Evaluate the function Y=X
2
– 4X+3 at each integer between
L
10 and 10. How many sign changes are there, and where do they occur?
1. If necessary, select
FUNC
from the
MODE
menu.
Press
2 # to display the
TABLE SETUP
screen. Press
·
10
to set
TBLMIN= L 10
. Leave
@ TBL=1
.
2. Press
( @ a |
4
@ «
3
to enter the function
Y1=X
2
– 4X+3
.
3. Press
2 & to display the table screen.
4. Press
8 repeatedly to view the changes in the value of
Y1
.
6-2 Tables
Defining the Independent Variable
The independent variable for a table is the independent variable in the current graphing mode (X for FUNC mode and T for PARAM mode). You define the minimum value and the incremental value for the independent variable on the
TABLE SETUP screen.
TABLE SETUP
Screen
To display the
TABLE SETUP
screen, press
2 #. The default values are shown below.
TBLMIN and
@ TBL
Setting Up a
Table from the
Home Screen or a Program
TBLMIN
(table minimum) defines the initial value for the independent variable:
X
(
FUNC
mode) or
T
(
PARAM
mode).
@ TBL
(table step) defines the increment for the independent variable.
To change
TBLMIN
and
@ TBL
, simply enter the values at the blinking cursor. To move between
TBLMIN
and
@ TBL
, press
8 and
7.
You can also store values to
TBLMIN
and
@ TBL
from the
Home screen or a program. The variable names are on the
VARS TABLE...
menu.
To change
TBLMIN
or
@
TBL
from the Home screen or a program, begin on a blank line.
1. Enter the value for
TBLMIN
or
@
TBL
.
2. Press
§.
3. Press
L to display the
VARS
menu.
4. Press
3
to select TABLE....
5. Select the table variable (
TBLMIN
or
@ TBL
). The name of the variable is copied to the cursor location.
6. Press
¸ to store the value for the table variable.
Tables 6-3
Defining the Dependent Variable
The selected functions from the Y= list define the dependent variables. You can have as many dependent variables as there are functions in the current graphing mode (four for FUNC mode and six for PARAM mode).
From the Y=
Editor
Enter the functions to define the dependent variables in the
Y=
editor.
FUNC
Mode
PARAM
Mode
In
PARAM
mode, you must define both components of the parametric equation (Chapter 5).
Only functions that are selected are displayed in the table.
(When
=
is highlighted, the function is selected.) You can select and deselect functions from the
Y=
list, from the Home screen, or from a program. (Refer to page 4
-8 for information on selecting and deselecting.)
6-4 Tables
Displaying the Table
The table displays up to six values for the independent variable, along with the six corresponding values of one dependent variable, at a time. Once the table is displayed, you can press
6
,
7
,
9
, and
8
to move around and scroll the table, displaying other independent and dependent values.
The Table
Press
2 & to display the table screen.
FUNC
Mode
PARAM
Mode
Displaying More
Independent
Values
The top line displays the name of the independent variable (
X
for
FUNC
mode;
T
for
PARAM
mode) and one dependent variable (
Y n
for
FUNC
mode;
X nT
or
Y nT
for
PARAM
mode).
The bottom line displays the full value of the current cell, which is indicated by the rectangular cursor. The center portion is used to display the values of the variables, abbreviated to six digits if necessary.
Press
7 and 8 to display additional values for the independent variable and the values for one corresponding dependent variable.
Note:
You can scroll “back” from the value entered for
TBLMIN
. As you scroll,
TBLMIN
is updated automatically to the value shown on the top line of the table. In the example below,
TBLMIN=0
,
@ TBL=1
, and
Y1=X
ñ
+2
generates and displays values of
X
=0, . . ., 5. You can press
7 to scroll backward and display the table for
X
=1, . . . ,4.
Tables 6-5
Displaying Other
Dependent
Variables
If you have more than one function defined and selected, press
9 to display other dependent variables. In the example below,
TBLMIN=0
,
@
TBL=1
,
Y1=X
2
+2
and
Y2=X
3
–2.
You can press
9 9 to see the values for
Y2
.
6-6 Tables
Chapter 7: Draw Operations
This chapter describes how to use the DRAW operations of the TI
.
80. Before using the DRAW operations, you should be familiar with Chapter 4, Function
Graphing.
Chapter
Contents
Getting Started: Shading a Graph
....................
DRAW DRAW
Menu
...............................
Drawing Lines
....................................
Drawing Horizontal and Vertical Lines
...............
Drawing a Function
...............................
Shading Areas on a Graph
..........................
Drawing Points
...................................
Clearing a Drawing
................................
Draw Operations 7-1
Getting Started: Shading a Graph
Getting Started is a fast-paced introduction. Read the chapter for details.
Shade the area below the function Y=X
ä
N
2 and above the functions Y=X
+
1 and
Y=
-
X.
1. If necessary, select
FUNC
mode. Press
( and enter the functions:
Y1=
@ a |
2
¸
Y2=
@ «
1
¸
Y3=
· @ ¸
(Be sure that
Y4
is cleared or turned off.)
2. Press *
4
to select the
ZDECIMAL
viewing window, clear any existing drawings, and display the viewing window and graph.
3. Press
2 . to return to the Home screen.
4. Press 2 F
7
to select
SHADE_Y<
, which is copied to the Home screen.
5. Press
2 G
1
(to select
Y1
).
6. Press
2 ° to add another instruction to this line.
7. Press
2 F
6
to select
SHADE_Y>
, which is copied to the Home screen.
8. Press
2 G
2
(to select
Y2
) b 2 G
3
(to select
Y3
).
9. Press
¸ to see the functions and shading on the graph.
7-2 Draw Operations
DRAW DRAW Menu
To display the DRAW DRAW menu, press
2 F
. What happens when you select an item from this menu depends on whether or not a graph is displayed when you access the menu, as described under each operation.
DRAW DRAW
Menu
DRAW POINTS
1: CLRDRAW
2: LINE(
Clears all drawn elements.
Draws a line between two points.
3: HORIZONTAL Draws a horizontal line.
4: VERTICAL
Draws a vertical line.
5: DRAWF
Draws a function.
6: SHADE_Y>
Shades an area.
7: SHADE_Y<
Shades an area.
8: SHADE(
Shades an area.
9: GRIDON
0: GRIDOFF
Turns the graph grid on.
Turns the graph grid off.
Before Drawing on a Graph
Drawing on a
Graph
(See page 7
-12 for an explanation of
CLRDRAW
.)
Because Draw operations draw on top of the graph of currently selected functions, you may want to do one or more of the following before drawing on a graph:
¦
Change the mode settings.
¦
Enter or edit functions in the
Y=
list.
¦
Select or deselect functions in the
Y=
list.
¦
Change Window variable values.
¦
Turn
STAT PLOTS
on or off.
¦
Clear existing drawings with
CLRDRAW
(page 7
-12).
Draw operations can draw on
FUNC
and
PARAM
graphs. The coordinates for all Draw instructions are always the
X-coordinate and Y-coordinate values of the display.
You can use most of the operations from the
DRAW DRAW
and
DRAW POINTS
menus to draw directly on a graph, using the cursor to identify coordinates; or you can execute these instructions from the Home screen or a program.
Draw Operations 7-3
Drawing Lines
While a graph is displayed, LINE( lets you use the cursor to define a line on the graph. If a graph is not displayed, the instruction is copied to the Home screen.
Directly on a
Graph
To define a line directly on a graph:
1. When a graph is displayed, select
LINE(
from the
DRAW DRAW
menu (item 2).
2. Position the cursor at the beginning point of the line you want to draw. Press
¸.
3. Move the cursor to the end point of the line you want to draw. The line is displayed as you move the cursor. Press
¸.
From the Home
Screen or a
Program
To continue to draw lines, repeat steps 2 and 3. To cancel
LINE(
, press M.
LINE(
(
DRAW DRAW
, item 2) draws a line between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions.
LINE(
X1
,
Y1
,
X2
,
Y2
)
For example, enter
LINE(0,0,6,9)
on the Home screen, and then press
¸.
7-4 Draw Operations
Drawing Horizontal and Vertical Lines
While a graph is displayed, HORIZONTAL and VERTICAL let you define lines on the graph using the cursor. If a graph is not displayed, the instruction is copied to the Home screen.
Directly on a
Graph
To draw horizontal and vertical lines directly on a graph:
1. When a graph is displayed, select
HORIZONTAL
(item 3) or
VERTICAL
(item 4) from the
DRAW DRAW
menu.
2. A line is displayed that moves as you move the cursor.
Position the cursor where you want to draw the line. Press
¸. The line is drawn on the graph.
From the Home
Screen or a
Program
To continue to draw lines, repeat step 2. To cancel
HORIZONTAL
or
VERTICAL
, press M.
HORIZONTAL
(
DRAW DRAW
, item 3) draws a horizontal line at
Y
=Y (which can be an expression, but not a list).
HORIZONTAL
Y
VERTICAL
(
DRAW DRAW
, item 4) draws a vertical line at
X
=X (which can be an expression, but not a list).
VERTICAL
X
Note:
In the example above, the horizontal line is drawn first, and then the vertical line is drawn.
Draw Operations 7-5
Drawing a Function
DRAWF (draw function) draws a function on the current graph. DRAWF must be entered on the Home screen or in the program editor.
Drawing a
Function
DRAWF
(draw function,
DRAW DRAW
, item 5) is not an interactive operation. It draws the specified expression as a function in terms of
X
on the current graph.
DRAWF
expression
For example, if
Y1=.2X
ò
–2X+6
is the only selected function,
DRAWF Y1–5
plots
Y1
and then draws the function
Y1–5
when you press ¸.
Using GRIDON and GRIDOFF
Note:
You cannot trace on
DRAWF
functions.
GRIDON
(
DRAW DRAW
, item 9) and
GRIDOFF
(
DRAW DRAW
, item 0) set graphs to be drawn with the grid points on or off, respectively. The grid points correspond to the axes tick marks. The default for the TI-80 is
GRIDOFF
.
1. From the Home screen, press
2 F to display the
DRAW
menu.
2. Press
9
to select
GRIDON
, or press
0
to select
GRIDOFF
.
3. Press
¸. The message
DONE
is displayed. The next time the graph is displayed, the grid points will be on if you selected
GRIDON
, or off if you selected
GRIDOFF
.
7-6 Draw Operations
Shading Areas on a Graph
There are three shading instructions on the DRAW DRAW menu: SHADE_Y>,
SHADE_Y<, and SHADE(. These instructions are not interactive; they must be entered on the Home screen or in the program editor.
Shading Areas above a Function
SHADE_Y>
(
DRAW DRAW, item 6) takes up to four arguments (functions of
X
).
SHADE_Y>
function
SHADE_Y>
function1
,
. . .
,
function4
When executed,
SHADE_Y>
plots the specified function(s) on the graph and shades the area above the function with a pattern.
The patterns for shading are automatically assigned in the following order.
Function 1
Function 2
Function 3
Function 4
Vertical pattern.
Diagonal pattern, lower left to upper right.
Diagonal pattern, upper left to lower right.
Horizontal pattern.
When you specify multiple functions, the shading is done sequentially.
Draw Operations 7-7
Shading Areas below a Function
SHADE_Y<
( DRAW DRAW, item 7) takes up to four arguments (functions of
X
).
SHADE_Y<
function
SHADE_Y<
function1
,
. . .
,
function4
When executed,
SHADE_Y<
plots the specified function(s) on the graph and shades the area below the function with a pattern.
The patterns for shading are automatically assigned in the following order.
Function 1
Function 2
Function 3
Function 4
Horizontal pattern.
Diagonal pattern, upper left to lower right.
Diagonal pattern, lower left to upper right.
Vertical pattern.
Note that the patterns are assigned in reverse order from the
SHADE_Y>
patterns.
When you specify multiple functions, the shading is done sequentially.
7-8 Draw Operations
Shading a Graph SHADE(
(
DRAW DRAW
, item 8) shades the area on a graph that is below one specified function and above another, between two X values.
SHADE(
is not an interactive operation.
It 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.
You can specify the shading resolution (an integer between 1 and 9). If none is specified, 1 is used. resolution=1 shades every pixel. resolution=2 shades every second pixel.
resolution
=3 shades every third pixel, and so on.
Optionally, you can specify Xleft (the left boundary) and
Xright
(the right boundary) for the shaded area. If Xleft or
Xright
is not specified,
XMIN
and
XMAX
are used.
SHADE(
lowerfunc
,
upperfunc
)
SHADE(
lowerfunc
,
upperfunc
,
resolution
)
SHADE(
lowerfunc
,
upperfunc
,
resolution
,
Xleft
)
SHADE(
lowerfunc
,
upperfunc
,
resolution
,
Xleft
,
Xright
)
Draw Operations 7-9
Drawing Points
To display the DRAW POINTS menu, press
2 F 9
. What happens when you select an item from this menu depends on whether or not a graph is displayed when you access the menu, as described under each operation.
DRAW POINTS
Menu
Drawing a Point
Directly on a
Graph
DRAW POINTS
1: PT-ON(
2: PT-OFF(
Turn on a point.
Turn off a point.
3: PT-CHANGE(
Toggle a point on or off.
To draw points directly on a graph:
1. When a graph is displayed, select
PT .
ON(
from the
DRAW POINTS
menu (item 1).
2. Position the cursor at the location on the display where you want to draw the point. Press
¸. The point is drawn.
To continue to draw points, repeat step 2. To cancel
PT
.
ON(
, press
M.
7-10 Draw Operations
PT
PT
.
.
OFF(
CHANGE(
From the Home
Screen or a
Program
Procedures for using
PT
.
OFF(
(point off,
DRAW POINTS
, item
2) to turn off (erase) a point and
PT
.
CHANGE(
(point change
,
DRAW POINTS
, item 3) to toggle (reverse) a point on and off are the same as for
PT
.
ON(
.
When you use these instructions from the Home screen or a program, you must specify the X-coordinate and the
Y-coordinate of the point as arguments for the instructions.
PT .
ON(
turns on the point at (
X
=X,
Y
=Y).
PT .
OFF(
turns the point off, and
PT .
CHANGE(
toggles the point between on and off.
PT .
ON(
X
,
Y
)
PT .
OFF(
X
,
Y
)
PT .
CHANGE(
X
,
Y
)
Draw Operations 7-11
Clearing a Drawing
All points, lines, and shading drawn on a graph with DRAW operations are temporary. They remain only until you execute a CLRDRAW (clear drawing) instruction or a change prompts Smart Graph to replot the graph, at which time all drawn elements are erased.
When a Graph Is
Displayed
From the Home
Screen or a
Program
To clear drawings from the currently displayed graph, select
CLRDRAW
from the
DRAW DRAW
menu (item 1). The current graph is plotted and displayed immediately with no drawn elements.
Note that
CLRDRAW
gives you a quick way to replot the current graph, in addition to clearing the current drawings.
Begin on a blank line on the Home screen or in the program editor. Select
CLRDRAW
from the
DRAW DRAW
menu (item
1). The instruction is copied to the cursor location.
When the instruction is executed, it clears all drawings from the current graph and displays the message
DONE
. The next time you display the graph, all drawn points, lines, and shaded areas will be gone.
7-12 Draw Operations
Chapter 8: Lists
This chapter describes the list features of the TI
-
80. The TI
.
80 can store up to six lists. A list, depending on available memory, can have up to 99 elements.
Chapter
Contents
Getting Started: Generating a Sequence
..............
About Lists
.......................................
LIST OPS
Operations
..............................
LIST MATH
Operations
............................
Lists 8-1
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
à
A
ñ
and display them in fraction form.
The
SEQ(
function returns a list of values based on five arguments: an expression, a variable to be incremented, a beginning value, an ending value, and an increment.
For this example, the beginning value is 1, the ending value is 8, and the increment is 1.
1. Begin on a blank line on the Home screen. Press
2
= to display the
LIST OPS
menu.
2. Press
4
to select
SEQ(
. The function name is copied to the cursor location on the Home screen.
3. Press
1
e ?
A
a b ?
A
b
1
b
8
b
1
d
§ 2 ¢. Press ¸ to generate the list and store it in
L1
. The list is displayed on the Home screen.
4. Use
9 to scroll the list to see all of the elements.
5. Press
J
4
(to select
4 FRAC
). On the Home screen,
ANS
is typed automatically, followed by
4 FRAC
.
6. Press
¸ to show the sequence in fraction form.
Use 9 to scroll the list to see all of the elements.
8-2 Lists
About Lists
The TI
-
80 has six list variables: L1, L2, L3, L4, L5, and L6. On the Home screen or in a program, you can use, enter, store, and display lists. The list names are on the keyboard. A list may have a maximum of 99 elements.
Using a List in an Expression
To use a list in an expression, you may:
¦
Use the name of the list (
L1
,
L2
,
L3
,
L4
,
L5
, or
L6
) in the expression.
¦
Enter the list directly in the expression.
Entering a List in an Expression
1. Press
2 [to indicate the beginning of the list.
2. Enter a value (which can be an expression) for each element in the list, separated by commas.
3. Press 2 \ to indicate the end of the list.
Saving a List in
Memory
The expression is evaluated when the entry is executed.
Commas are required on entry to separate elements, but they are not displayed on output.
You can save a list in memory in two ways:
¦
Enter the list in the
STAT
list editor (Chapter 9).
¦
Enter the list on a blank line on the Home screen or in a program, press
§, and then enter the name of the list
(
L1
,
L2
,
L3
,
L4
,
L5
, or
L6
).
Copying One
List to Another
To copy a list, store it to another list.
Lists 8-3
Displaying a List on the Home
Screen
To display the contents of a list on the Home screen, enter the name of the list, and press
¸.
A open brace ({)without a corresponding close brace (}) indicates that a list is too long to be displayed in its entirety.
Press
9 and 6 to display the rest of the list.
Storing to or
Recalling a List
Element
You can store a value to or recall a value from a specific list element. Enter the name of the list, followed by the number of the element in parentheses. You can store to any element within the currently defined list dimensions or one beyond.
listname
(
element
)
Lists in Graphing
You can also edit a list by means of the
STAT
list editor
(Chapter 9).
You can use a list in a
Y=
expression. However, the list must be used in such a way that it resolves to a single value; for example,
Y1=X
…
SUM(1
à
(1.1^{1,2,3}))
.
Note:
Unlike the TI
-82 and TI-85, you cannot use a list to graph a family of curves.
8-4 Lists
Notes about
Using Math
Functions with
Lists
A list can be used to input several values for certain functions.
(Other chapters and Appendix A state when a list is valid.)
The function is evaluated for each element in the list, and a list is returned.
¦
If a list is used with a function, the function must be valid for every element in the list.
)
This returns an error because 1 is divided by 0.
¦
If two lists are used with a two-argument function, the lengths of the lists must be the same. The answer is a list in which each element is calculated by evaluating the function using the corresponding elements in the lists.
¦
If a list and a value are used with a two-argument function, the value is used with each element in the list.
Lists 8-5
LIST OPS Operations
Press
2 =
to display the list operations on the LIST OPS menu.
LIST OPS
Menu
SORTA(
SORTD(
OPS MATH
1: SORTA(
2: SORTD(
3: DIM
4: SEQ(
Sorts lists in ascending order.
Sorts lists in descending order.
Accesses the list dimension.
Creates a sequence.
Note: SORTA(
and
SORTD(
are the same as
SORTA(
and
SORTD(
on the
STAT EDIT
menu.
SORTA(
(sort ascending,
LIST OPS
, item 1) and
SORTD(
(sort descending,
LIST OPS
, item 2) have two uses.
¦
With one list name, they sort the elements of an existing list and update the list in memory.
¦
With two to six list names, they sort the first list and then sort the remaining lists as dependent lists, placing their elements in the same order as their corresponding elements in the first list. This allows you to keep sets of related data in the same order when you sort lists.
All of the lists to be sorted must be the same length. The sorted lists are updated in memory.
Note:
You can reference a specific list only once in these instructions.
SORTA(
listname
)
SORTA(
keylistname
,
dependlist1
,
dependlist2
,
. . .
)
SORTD(
listname
)
SORTD(
keylistname
,
dependlist1
,
dependlist2
,
. . .
)
*
8-6 Lists
Accessing List
Dimensions with
DIM
DIM
(dimension,
LIST OPS
, item 3) returns the length (number of elements) of the specified list.
DIM
list
Creating a List with DIM
DIM
is used with
§ to create a new list with a specified number of elements. The elements of the new list are zeros.
length
!
DIM
listname
Redimensioning a List with DIM
DIM
is also used with
§ to redimension an existing list.
¦
The elements in the old list that are within the new dimension are not changed.
¦
Any elements in the old list that are outside the new dimension are eliminated.
¦
Any additional elements that are created are zeros.
length
!
DIM
listname
Lists 8-7
SEQ( SEQ(
(sequence,
LIST OPS
, item 4) requires five arguments: an expression, a variable to be incremented, a beginning value, an ending value, and an increment.
SEQ(
returns a list in which each element is the result of the evaluation of
expression
with regard to variable for values ranging from
begin
to end at steps of increment.
SEQ(
expression
,
variable
,
begin
,
end
,
increment
)
The variable need not be defined in memory. The increment can be negative.
SEQ(
can be used to generate a list of index numbers. This kind of list can be useful in data analysis.
8-8 Lists
LIST MATH Operations
Pressing
2 = 9
accesses the list math operations on the LIST MATH menu.
LIST MATH
Menu
MIN(
MAX(
OPS MATH
1: MIN(
2: MAX(
Returns minimum element of a list.
Returns maximum element of a list.
3: MEAN(
Returns mean of a list.
4: MEDIAN( Returns median of a list.
5: SUM
Returns sum of all elements in a list.
6: PROD
Returns product of all elements in a list.
Note: MIN(
and
MAX(
are the same as
MIN(
and
MAX(
on the
MATH NUM
menu.
MIN(
(minimum,
LIST MATH
, item 1) or
MAX(
(maximum,
LIST MATH
, item 2) returns the smallest or largest element of the specified list. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in the two lists.
MIN(
list
) MAX(
list
)
MIN(
listA
,
listB
) MAX(
listA
,
listB
)
MEAN(
MEDIAN(
MEAN(
(
LIST MATH
, item 3) returns the mean value of the list.
MEDIAN(
(
LIST MATH
, item 4) returns the median value of the list.
MEAN(
list
)
or
MEDIAN(
list
)
If a second list is given, it is interpreted as the frequency of the elements in the list.
MEAN(
list
,
frequency
)
or
MEDIAN(
list
,
frequency
)
Lists 8-9
SUM SUM
(summation,
LIST MATH
, item 5) returns the sum of the elements in the specified list.
SUM
list
PROD PROD
(product,
LIST MATH
, item 6) returns the product of the elements of the list.
PROD
list
Sums and
Products of
Numeric
Sequences
You can combine
SUM
or
PROD
with
SEQ(
to obtain:
upper upper
G
expression
(x)
∏
expression
(x)
x=lower x=lower
To evaluate
G 2
(N–1)
from N=1 to 4:
8-10 Lists
Chapter 9: Statistics
This chapter describes the tools for analyzing statistical data on the TI
-
80. These include entering lists of data, calculating statistical results, fitting data to a model, and plotting data.
Chapter
Contents
Getting Started: Building Height and City Size
.........
Setting Up a Statistical Analysis
.....................
The
STAT
List Editor
..............................
Viewing, Entering, and Editing Lists
.................
Sorting and Clearing Lists
..........................
Statistical Analysis
................................
Types of Statistical Analysis
........................
Statistical Variables
...............................
Statistical Plotting
................................
Statistical Analysis in a Program
....................
Statistical Plotting in a Program
.....................
Statistics 9-1
Getting Started: Building Height and City Size
Getting Started is a fast-paced introduction. Read the chapter for details.
Determine a linear equation to fit the data below. Enter the data, and perform a linear regression. Then plot the data. Predict how many buildings of more than
12 stories you would expect to find in a city of 300 thousand people.
Population in Thousands
150
500
800
250
550
750
Buildings
>
12 Stories
4
31
42
9
20
55
1. To clear any existing lists, press
A
4
to copy
CLRLIST
to the Home screen.
2. Press
2 ¢ b 2 £ b 2 ¤ b 2 t ¸.
The message
DONE
is displayed.
3. Press
A
1
to display the
STAT
list editor. Enter
150
to represent 150,000 for the population of the first city. As you type, the value is displayed on the bottom line.
4. Press
¸. The value is shown in the first element of
L1
, and the cursor moves to the second element in the same list.
9-2 Statistics
5. Enter the remaining elements of
L1
. Press:
500
¸.
800
¸.
250
¸.
550
¸.
750
¸.
6. Press
9 to move to the first element of list
L2
.
7. Enter the elements (number of buildings with more than 12 stories) of
L2
. Press:
4
¸.
31
¸.
42
¸.
9
¸.
20
¸.
55
¸.
8. You can sort the data by size of city. Press
2 .
M to return to a clear Home screen. Press A
2
to select
SORTA(
, which is copied to the Home screen. Press
2 ¢ to select the independent list and then press b 2 £ to select the dependent list.
Press d ¸. The message
DONE
is displayed. The lists have been updated in memory.
9. Press
A
1
to display the sorted lists in the
STAT
list editor.
Statistics 9-3
After entering and sorting the data, define the STAT PLOTS and Window variables; then perform a linear regression (aX + b).
10. Press y ¸ to display the
STAT PLOTS
screen.
11. Press
1
to display the
PLOT1
screen. Move the cursor to
ON
, if necessary, and press
Í to turn
PLOT1
on. Leave
TYPE
as scatter plot (
¼),
XL
(independent list) as
L1
, YL (dependent list) as
L2
, and
Mark
as
›
.
12. Press ) to display the Window variables.
Enter the following values.
0
for
XMIN
1000
for
XMAX
100
for
XSCL
L 15
for
YMIN
100
for
YMAX
10
for
YSCL
13. Press
A 9 to display the
STAT CALC
menu.
14. Press
3
to select
LINREG(aX+b)
, which is copied to the Home screen. Press 2 ¢ b 2 £ ¸.
The least-squares linear regression is calculated; the display shows the values for
a
(slope),
b
(y-intercept), and
r
(correlation coefficient).
9-4 Statistics
Store the regression equation into the Y= list and graph it.
15. In
FUNC
mode, press
( to display the
Y=
editor.
Press
M to clear
Y1
, if necessary. Turn off all other functions, if necessary.
16. Press
L to display the
VARS
menu.
17. Press
2
to select
STATISTICS...
, and press
9 9 to display the
VARS EQ
menu.
18. Press
5
to select
REGEQ
, which copies the linear regression to the
Y=
editor screen.
Note:
Each time you calculate a regression, the regression equation (
REGEQ
) is updated.
19. Press
,. The data points are plotted (›), and then the regression line is drawn.
20. Press
+ and then ~ to trace the points in
PLOT1
, as indicated by
P1
in the upper right corner of the display.
Press
† to move to
Y1
, and continue tracing the function.
Statistics 9-5
You can enter expressions to define lists in the STAT list editor. For example, you can now define predicted values and residuals (the differences between the observed values and the predicted values) for this problem.
21. Press
…
1
to display the
STAT
list editor. Press
~ ~ } to move the cursor onto the name
L3
.
22. Press y ã
Y-VARS ä
1
to select
Y1
, and then press
£ y ¢
¤. This defines
L
å as the values predicted by the
LINREG
line.
23. Press
Í to store the values in
L3
.
24. To store the residuals in
L4
, press
~ } to move the cursor onto the name
L4
. To enter
L4 = L2
N
L3
, press y £ (the observed) ¹ y ¤ (the predicted)
Í.
25. Press
2 ". Press
1
to select
PLOT1
. Move the cursor to
OFF
, and press
Í to turn the plot off.
26. Press
2 "
2
to select
PLOT2.
Move the cursor to
ON
and press
Í to turn the plot on, if necessary. Press
8 8
Í to define
XL
as
L1
.
Press
8 9 9 9
Í to define
YL
as
L4
. Press
8
9
Í to set
MARK
as
+
.
9-6 Statistics
Plot the residuals, and predict how many buildings of 12 or more stories there are in a city with a population of 300 thousand.
27. Press
( 6 ¸ to turn off
Y1
.
28. Press
), and change the Window variable values to best show the residuals. Use the minimum and maximum values of
L4
(
M10.31862745 and
10.74019608) as guidelines for setting
YMIN
and
YMAX
.
29. Press , to plot the residuals.
+
marks each residual value.
30. Press y ã
QUIT
ä
M to return to a clear Home screen. Press y ã
Y-VARS
ä
1
to select
Y1
. Then press
£
300
d Í.
The value of
Y1
(the linear regression equation) for
X =300 (which represents 300 thousand city population) is shown. Remember to round the number mentally to an integer (13) to represent whole buildings.
Statistics 9-7
Setting Up a Statistical Analysis
The data for statistical analyses is stored in lists. The TI
.
80 has six list variables
(L
ã
through L
è
) that you can use in STAT calculations. Several types of statistical analyses are available.
Steps
Follow these basic steps to perform statistical analyses.
1. Enter the statistical data in lists (pages 9 -9 through 9-13).
2. Select the type of statistical calculations you want to do
(pages 9
-14 through 9-16), and specify the list names for the data.
3. Calculate the statistical variables, or fit the data to a model
(page 9
-17).
4. Plot the data (pages 9
-18 through 9-21).
9-8 Statistics
The STAT List Editor
Pressing
A
accesses the STAT list editor and several instructions for use with lists (L
ã
through L
è
). The instructions are discussed on page 9-13.
STAT EDIT
Menu
EDIT CALC
1: EDIT ...
Displays list editor.
2: SORTA(
Sorts list in ascending order.
3: SORTD(
Sorts list in descending order.
4: CLRLIST
Deletes all elements of list.
Displaying the
STAT List Editor
The
STAT
list editor gives you an easy environment in which to enter or edit lists. You can also create lists directly from the keyboard (Chapter 8), if you prefer.
To display the
STAT
list editor, press
A and then press
1
or
¸ to select
EDIT...
from the
STAT EDIT
menu.
Entering List
Elements in the
STAT List Editor
Leaving the
STAT List Editor
The top line of the
STAT
list editor displays the names of the lists (even if the list is empty). The center portion displays up to six elements of two lists, showing the values of the elements (abbreviated to six digits if necessary). The full value of the current element (indicated by the rectangular cursor) is shown on the bottom line.
To enter a list into the
STAT
list editor:
1. Display the
STAT
list editor.
2. Enter the first value in the list, and press
¸ or 8. The value is entered, and the rectangular cursor moves down to the next position.
3. Continue until you enter all the data in the list.
Press
9 and 6 in the editor to move between lists.
Note:
You may enter an expression, which is evaluated when you press ¸, 8, or 7.
To leave the
STAT
list editor:
¦
Select another screen by pressing the appropriate key.
¦
Press
2 . to return to the Home screen.
Statistics 9-9
Viewing, Entering, and Editing Lists
The STAT list editor has two “contexts,” viewing and editing. The current context determines the result of a key press. In both contexts, the full value of the highlighted element is displayed on the bottom line.
Viewing Context
In the viewing context, you can move quickly from one list element to the next.
6 or 9
8 or 7
¸
M
Any entry character
2
4
/
Moves the rectangular cursor to the previous or next list.
Moves the rectangular cursor within the current column. On row 1, 7 moves the cursor to the list name.
Activates the edit cursor on the bottom line.
Clears the value on the bottom line.
Clears the value on the bottom line; copies the character to the bottom line.
Inserts a list element (value is zero).
Deletes the current list element and closes up the list.
Editing
Context
In the editing context, an edit cursor is active on the bottom line; and you can change the value of the current list element.
You can also move the cursor onto the list name and edit the entire list at once.
6 or 9
8 or 7
¸
M
Any entry character
2 /
4
Moves the edit cursor within the value.
Stores the value on the bottom line to the list element; moves the rectangular cursor within the column. On row 1,
7 moves the cursor to the list name.
Stores the value on the bottom line to the list element; moves the rectangular cursor to the next element.
Clears the value on the bottom line.
Copies the character to the edit-cursor location on the bottom line. If it is the first character typed, the value on the bottom line is cleared.
Activates the insert cursor.
Deletes a character.
9-10 Statistics
Deleting a List
Editing a List
Element
You can delete the contents of a list in several ways:
¦
With the
CLRLIST
instruction (page 9
-13).
¦
Through the
MEMORY
menu (Chapter 12).
¦
In the
STAT
list editor, by pressing
7 to move onto the list name and then pressing
M ¸.
¦
In the
STAT
list editor, by deleting each element.
¦
On a command line, by entering
0
!
DIM
listname
.
To edit a list element:
1. Display the
STAT
list editor.
2. Move the rectangular cursor to the element you want to change.
3. Press
¸ to switch to the editing context. Then:
¦
Change the current value by inserting, deleting, or typing over digits.
¦
Press an entry key, such as a number or letter, to begin an entry. This automatically clears the value.
¦
Press
M to clear the entire value and then enter a new value.
Note:
If you clear a value by mistake, you can immediately press
¸ to restore the value at the rectangular cursor.
4. Press ¸ to store the new value and move to another element.
Note:
You may enter an expression, which is evaluated when you press
¸, 8, or 7.
Statistics 9-11
You can enter or edit an entire list by moving the cursor to a list name on the top line of the STAT list editor and then pressing
¸
. The bottom line displays
L n =Ln
×
1, if there is data already in the list. Type any expression that returns a list, and press
¸
. The new list is displayed.
Entering an
Entire List
To enter an entire list:
1. Press
A ¸. Enter several elements in
L1
.
2. Press
7 and 9 as many times as necessary to move the cursor to the list name
L2
.
3. Press
2 ¢ p
2
. This is the expression that will define the elements in
L2
.
4. Press
¸ to define and display
L2
.
Editing an Entire
List
To replace an existing list:
1. Move the cursor to the list name
L2
.
L2=L2
×
1
is displayed.
2. Enter a new expression to replace the existing values in
L2
,
2 ¢ p
3
, for example. Then press
¸. The values in
L2
are replaced, and the new values are displayed.
9-12 Statistics
Sorting and Clearing Lists
Items 2 through 4 on the STAT EDIT menu
SORTA(, SORTD(, and CLRLIST
let you sort or clear list data. Pressing
A
displays these instructions, and selecting an item copies the name of the instruction to the Home screen. Note that SORTA( and SORTD( are the same as SORTA( and SORTD( on the LIST OPS menu (Chapter 8).
SORTA(
SORTD(
SORTA(
(sort ascending,
STAT EDIT
, item 2) and
SORTA(
(sort descending,
STAT EDIT
, item 3) have two uses.
¦
With one list name, they sort the elements of an existing list and update the list in memory.
¦
With two to six list names, they sort the first list and then sort the remaining lists as dependent lists, placing their elements in the same order as their corresponding elements in the first list. This lets you sort two-variable data on X and keep the data pairs together.
All of the lists to be sorted must be the same length. The sorted lists are updated in memory.
Note:
You can reference a specific list only once in these instructions.
SORTA(
listname
)
SORTA(
keylistname
,
dependlistA
,
dependlistB
,
. . .
)
SORTD(
listname
)
SORTD(
keylistname
,
dependlistA
,
dependlistB
,
. . .
)
CLRLIST CLRLIST
(clear list,
STAT EDIT
, item 4) clears (deletes) the elements of one or more lists.
CLRLIST
listnameA
,
listnameB
,
. . .
Statistics 9-13
Statistical Analysis
Pressing
A 9
accesses the STAT CALC menu, where you select and perform statistical calculations. The TI 80 can analyze one-variable or two-variable statistics. Both can have associated frequency lists.
STAT CALC
Menu
Selecting and
Performing a
Statistical
Calculation
Frequency of
Occurrence for
Data Points
EDIT CALC
1: 1-VAR STATS
Calculates 1-variable statistics.
2: 2-VAR STATS
Calculates 2-variable statistics.
3: LINREG(aX+b) Fits data to linear model.
4: QUADREG
Fits data to quadratic model.
5: LINREG(a+bX) Fits data to linear model.
6: LNREG
Fits data to logarithmic model.
7: EXPREG
8: PWRREG
Fits data to exponential model.
Fits data to power model.
To select and perform statistical calculations:
1. Select a calculation type by pressing its corresponding number on the
STAT CALC
menu. The name of the calculation is copied to the Home screen.
2. Enter the name(s) of the list(s) to be used in the calculation. If you enter more than one list name, separate them by commas.
3. Press
¸ to perform the calculation and display the results.
For all of the calculation types, you can include a list of data occurrences, or frequencies. These indicate how many times the corresponding data points or data pairs occur in the data set you are analyzing.
For example, if
L1={15.5,12.1,9.8,14.7,15}
and
L2={1,4,1,3,3}
, then the instruction
1-VAR STATS L1,L2
would assume that
15.5 occurred one time, 12.1 occurred four times, 9.8 occurred one time, and so on.
Frequencies must be greater than or equal to zero. At least one frequency in the list must be greater than zero.
Noninteger frequencies are valid. This is useful in entering frequencies expressed as percentages or parts that add up to
1. Noninteger frequencies, however, may prevent the calculation of certain variables.
9-14 Statistics
Types of Statistical Analysis
These calculations return statistical results based on the list(s) you reference. If you reference a third list name as an argument for 2-VAR STATS or any of the regression models, the list is interpreted as the frequencies of occurrence for the data pairs in the first two lists.
1-VAR STATS 1-VAR STATS
(one-variable statistics,
STAT CALC
, item 1) analyzes data with one measured variable and calculates statistical results as indicated on page 9
-17.
If you reference two list names, the second list is interpreted as the frequency of occurrence for each data point in the first list.
1-VAR STATS
listname
1-VAR STATS
Xlistname
,
freqlistname
2-VAR STATS
LINREG
(aX+b)
2-VAR STATS
(two-variable statistics,
STAT CALC
, item 2) analyzes paired data between which there is a relationship.
This option calculates statistical results as indicated on page
9-17.
The first list you reference is the independent variable (X list).
The second list is the dependent variable (Y list). If you reference a third list name, it is interpreted as the frequency of occurrence for each data pair in the first two lists.
2-VAR STATS
Xlistname
,
Ylistname
2-VAR STATS
Xlistname
,
Ylistname
,
freqlistname
LINREG (aX+b)
(linear regression,
STAT CALC
, item 3) fits the data to the model y=ax+b using a least-squares fit and
x
and
y
. It displays
a
(slope),
b
(y-intercept), and
r
(correlation coefficient).
LINREG (aX+b)
Xlistname
,
Ylistname
LINREG (aX+b)
Xlistname
,
Ylistname
,
freqlistname
Statistics 9-15
QUADREG
LINREG
(a+bX)
LNREG
EXPREG
PWRREG
QUADREG
(quadratic regression,
STAT CALC
, item 4) fits the data to the second-order polynomial y=ax
2
+bx+c. It displays
a
,
b
, and
c
. For three data points the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required.
QUADREG
Xlistname
,
Ylistname
QUADREG
Xlistname
,
Ylistname
,
freqlistname
LINREG (a+bX)
(linear regression,
STAT CALC
, item 5) fits the data to the model equation y=a+bx using a least-squares fit and
x
and
y
. It displays
a
,
b
, and
r
(correlation coefficient).
LINREG (a+bX)
Xlistname
,
Ylistname
LINREG (a+bX)
Xlistname
,
Ylistname
,
freqlistname
LNREG
(logarithmic regression,
STAT CALC
, item 6) fits the data to the model equation y=a+b ln(x) using a least-squares fit and transformed values
LN(x)
and
y
. It displays
a
,
b
, and
r
(correlation coefficient).
LNREG
Xlistname
,
Ylistname
LNREG
Xlistname
,
Ylistname
,
freqlistname
EXPREG
(exponential regression,
STAT CALC
, item 7) fits the data to the model equation y=ab x
using a least-squares fit and transformed values
x
and
LN(y)
. It displays
a
,
b
, and
r
(correlation coefficient).
EXPREG
Xlistname
,
Ylistname
EXPREG
Xlistname
,
Ylistname
,
freqlistname
PWRREG
(power regression,
STAT CALC
, item 8) fits the data to the model equation y=ax b
using a least-squares fit and transformed values
LN(x)
and
LN(y)
. It displays
a
,
b
, and
r
(correlation coefficient).
PWRREG
Xlistname
,
Ylistname
PWRREG
Xlistname
,
Ylistname
,
freqlistname
Note:
Calculations for
v, G
X
,
G
X
ñ,
SX
,
s
X
,
w
,
G
Y
,
G
Y
ñ,
SY
,
s
Y
, and
G
XY
are calculated using transformed values for
LNREG
,
EXPREG
, and
PWRREG
.
9-16 Statistics
Statistical Variables
The statistical variables are calculated as indicated below. Some are displayed when 1-VAR STATS or 2-VAR STATS are calculated. You can access these variables for use in expressions through the VARS STATISTICS... menus. If you edit a list, all statistical variables are cleared.
Variables
1-VAR
STATS
v (mean of X values)
G
X (sum of X values)
G
X
2
(sum of X
2
values)
SX
(sample standard deviation of X)
Ÿ
Ÿ
Ÿ
Ÿ
s X
(population standard deviation of X)
Ÿ
n
(number of data points)
Ÿ
w (mean of Y values)
G
Y
(sum of Y values)
G
Y
ñ
(sum of Y
2
values)
SY
(sample standard deviation of Y)
s Y
(population standard deviation of Y)
G XY
(sum of X
×
Y)
MINX
(minimum of X values)
MAXX
(maximum of X values)
MINY
(minimum of Y values)
Ÿ
Ÿ
MAXY
(maximum of Y values)
Q1
(1st quartile)
MED
(median)
Q
3
(3rd quartile)
a
,
b
(regression/fit coefficients)
a
,
b
,
c
(quadratic coefficients)
r
(correlation coefficient)
REGEQ
(regression equation)
Ÿ
Ÿ
Ÿ
2-VAR
STATS
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
LIN, LN,
EXP, PWR
REGS
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
QUADREG
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
Ÿ
VARS
Menu
BOX
BOX
EQ
EQ
EQ
EQ
X/Y
G
X/Y
X/Y
X/Y
X/Y
BOX
X/Y
G
G
X/Y
X/Y
X/Y
X/Y
G
G
X/Y
Q1 and Q3
Noninteger
Frequencies
Large
Frequencies
Zero
Frequencies
The quartile
Q1
is the median of the ordinals to the left of
MED
(median). The quartile
Q3
is the median of the ordinals to the right of
MED
.
If a frequency list contains noninteger values,
SX
and
SY
are undefined. No values are displayed for them in the statistical results.
Q1
,
MED
, and
Q3
are also undefined if the frequency list contains noninteger values.
If a frequency list contains a value larger than 99,
Q1
,
MED
, and
Q3
will not be calculated.
If the frequency for an element or data pair is zero, the element or data pair is ignored in the calculation.
Statistics 9-17
Statistical Plotting
You can plot statistical data that you have entered in lists. The types of plots available include scatter plots, x-y lines, box and whisker plots, and histograms.
You can define up to three plots at a time.
Steps
Scatter Plot
¼
To plot statistical data:
1. Enter the statistical data as lists (page 9 -9 and Chapter 8).
2. Select the statistical calculations (pages 9
-14 through 9-16
), and calculate the statistical variables (page 9
-17) or fit the data to a model, if desired.
3. Select or deselect
Y=
equations, as appropriate
(Chapter 4).
4. Define the statistical plot (page 9
-20).
5. Turn the plot(s) on, if necessary (page 9
-21).
6. Define the viewing window (page 9
-21 and Chapter 4).
7. Display and explore the graph by pressing
,, *, or
+.
¼
(scatter plot) plots the data points from
XL
(X list) and
YL
(Y list) as coordinate pairs, showing each point as a box ( Â), cross (
+
), or dot (
¦).
XL
and
YL
must be the same length. They can be the same list.
XYLine
½
½
(XYLine) is a scatter plot in which the data points are plotted and connected in the order in which they appear in
XL
and
YL
. You may want to sort the lists with
SORTA(
or
SORTD(
before plotting.
9-18 Statistics
Box Plot
¾
¾
(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 (
Q1
) and from the third quartile (
Q3
) to the maximum point (
MAXX
). The box is defined by
Q1
, the median (
MED
), and
Q3
(page 9
-17).
Box plots are plotted with respect to
XMIN
and
XMAX
, but ignore
YMIN
and
YMAX
. When two box plots are plotted, the first plots at the top of the screen and the second plots in the middle. When three are plotted, the first plots at the top, the second in the middle, and the third at the bottom.
Histogram
¿
¿
(histogram) plots one-variable data.
XSCL
determines the width of each bar, beginning at
XMIN
. (XMAX – XMIN)
à
XSCL
must be
31. A value occurring on the edge of a bar is counted in the bar to the right.
Frequencies in
Stat Plots
The frequency list specified for a statistical plot works just like the frequency lists specified for other statistical calculations (pages 9-14 through 9-16).
If you want to exclude an outlying data point from a plot, enter a zero for that value in the frequency list to prevent having to change the data lists.
Statistics 9-19
Defining the
Plots
To define plots:
1. Press
2 ". The
STAT PLOTS
screen shows the current plot definitions.
2. Select the plot to define (
PLOT1
,
PLOT2
, or
PLOT3
).
3. If you wish to plot the statistical data immediately, select
ON
. You can define a plot at any time and leave it
OFF
.
The definition will be available in the future.
4. Select the type of plot. The options change appropriately.
¦
¦
¦
¦
¼
(scatter plot):
XL
½
(XYLine):
XL
¾
(box plot):
XL
¿
(histogram):
XL
Where:
YL
YL
F
F
MARK
MARK
¦
XL
is the list of independent data.
¦
YL
is the list of dependent data.
¦
F
is the frequency (
1
is used if no list is specified).
¦
MARK
is
›
,
+
, or ¦.
9-20 Statistics
Turning Plots Off or On
PLOTSOFF
and
PLOTSON
allow you to turn statistical plots off or on from the Home screen or a program. Used without
plot#
, they turn all plots off or all plots on. Used with plot#, they turn specific plots off or on.
PLOTSOFF
or
PLOTSON
PLOTSOFF
plot#
,
plot#
,
. . .
PLOTSON
plot#
,
plot#
,
. . .
For example,
PLOTSOFF
followed by
PLOTSON 3
turns all plots off and then turns
PLOT3
on.
Defining the
Viewing Window
Tracing a Stat
Plot
Statistical plots are displayed on the current graph. You may define the viewing window by pressing
) and then entering values for the Window variables.
When you trace a scatter plot or XYLine, tracing begins at the first element in the lists.
When you trace a box plot, tracing begins at
MED
(the median). Press
6 to trace to
Q1
and
MINX
. Press
9 to trace to
Q3
and
MAXX
.
When you trace a histogram, the cursor moves to the top center of each column, starting at the first column.
When you press
7 or 8 to move to another plot or
Y=
function, tracing moves to the current or beginning point on that plot.
Statistics 9-21
Statistical Analysis in a Program
You can enter statistical data, calculate statistical results, and fit data to models from a program.
Entering Stat
Data
Enter the statistical data directly into lists (Chapter 8) in the program.
Statistical
Calculations
To calculate statistical results or fit data to a model from a program:
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, separated by commas, to use in the calculation.
Note:
To display a regression equation and coefficients from a program, the regression function must be the last statement in the program. If it is not the last statement, the regression equation will be evaluated and stored, but the results will not be displayed.
9-22 Statistics
Statistical Plotting in a Program
To display a statistical plot, you may define the plot(s), then turn the plot(s) on, and then display the graph. If you do not define the plot, the current definitions are used.
Defining a Stat
Plot in a
Program
To define a statistical plot in a program:
1. Enter the data into list(s). On a blank line in the program editor, press
2 " to display the
PLOTS
menu.
2. Select the plot to define.
PLOT1(
,
PLOT2(
, or
PLOT3(
is copied to the cursor location.
3. Press
2 " 9 to display the
TYPE
menu. Select the type of plot.
¼
(scatter),
½
(XYLine),
¾
(box), or
¿
(histogram) is copied to the cursor location.
4. Press b. Enter the list names, separated by commas.
5. (This step is for
¼ and ½ only.) Press b. Press 2 mark.
›
, +, or
⋅
MARK
menu. Select the
. is copied to the cursor location.
6. Press d and ¸ to complete the command line.
7. Press
2 "
5
to copy PLOTSON to the command line and the number of the plot (
1
,
2
, or
3
) to turn on. Press
¸ to complete the command line.
Note that
PLOTSOFF
in the example program ensures that all other plots are turned off.
Statistics 9-23
Displaying a Stat
Plot from a
Program
To display a plot, use any of the Zoom instructions (Chapter
4), or use the
DISPGRAPH
instruction (Chapter 10).
9-24 Statistics
Chapter 10: Programming
This chapter describes specific programming instructions and explains how to enter and execute programs on the TI .
80.
Chapter
Contents
Getting Started: Rolling a Die
.......................
About TI
-80 Programs
.............................
Creating and Executing Programs
..................
Editing Programs
.................................
PRGM CTL
(Control) Instructions
..................
PRGM I/O
(Input/Output) Instructions
...............
Calling Other Programs
...........................
Programming 10-1
Getting Started: Rolling a Die
Getting Started is a fast-paced introduction. Read the chapter for details.
A program is a set of commands that can be executed sequentially, as if they had been entered from the keyboard. Write a simple program to simulate the rolling of a single die. It should prompt for the number of rolls and then store the results of the rolls in a list.
1. Press
K 9 9 to display the
PRGM NEW
menu.
2. Press
¸ to select
CREATE NEW.
(The keyboard is now in
ALPHA-LOCK.
) Type
R O L L
as the name of the program, and press
¸. You are now in the program editor. The
:
(colon) in the first column of the second line indicates that this is the beginning of a command line.
3. Press
K 9 to access the
PRGM I/O
menu. Press
4
.
CLRHOME
is copied to cursor location. Press
¸ to complete the instruction and move to the next line.
4. Press
0
§ 2 =
3
2 ¢. This sets the dimension of
L
ã (the list where the results of the rolls will be stored) to 0. Press
¸ to complete the instruction and move to the next line.
5. Press K 9
1
to copy
INPUT
to the cursor location. Press
2 < ã
"
ä
ROLLS
2 D
1
? ã
"
ä b ?
R
to prompt the user to input the number of rolls. Press
¸ to complete the instruction.
6. Press
K
4
to copy
FOR(
to the cursor location.
Press
?
I
b
1
b ?
R
b
1
d. Press ¸ to complete the instruction.
10-2 Programming
7. Press
I 6 to access the
MATH PRB
menu. Press
5
(to copy
RANDINT(
to the cursor location)
1
b
6
d
§ 2 ¢ c ?
I
d to generate random integers from 1 to 6 and store them into element
I
of
L1
. Press
¸ to complete the instruction.
8. Press
K 9
2
to select
DISP
(display), which is copied to the cursor location. Press
2 ¢ c ?
I
d. This instruction displays the value of element
I
(the result of the last roll) in
L1
. Press
¸ to complete the instruction.
9. Press K
6
to select
PAUSE
, which is copied to the cursor location. This pauses the program after displaying the result of the last roll. Press ¸ to complete the instruction.
10. Press
K
5
to select
END
, which is copied to the cursor location.
END
identifies the end of the group of commands in the
FOR(
loop. Press
¸ to complete the instruction.
11. Press
K 9
2
2 ¢ to display the list of all the roll results. Press
¸ to complete the instruction.
12. Press
2 . M K. Move the cursor to the program name
ROLL
. Press
¸. Press ¸ again from the Home screen to execute
PRGM_ROLL
.
Programming 10-3
About TI-80 Programs
Most features of the TI
.
80 are accessible from programs. Programs can access all variables and named items. The number of programs that the TI .
80 can store is limited only by available memory.
Notes about
Programs
"Breaking" a
Program
Memory
Management and
Erasing
Programs
Programs are identified by names of up to seven characters, beginning with a letter.
A program consists of a series of program commands, which begin with a
:
(colon). A program command can be an expression (a command, usually a combination of variables, functions, and numeric values, that returns a value to
ANS
) or an instruction (a command, such as
GRIDON
or
PT-ON(
, that does not return a value to
ANS
).
The TI
-80 checks for errors when you execute the program, not as you enter or edit the program.
Variables and lists saved in memory are global; that is, they can be accessed from all programs. Storing a new value to a variable or list in a program changes the value in memory during program execution.
As calculations are made in programs, the TI
-80 updates
ANS
, just as it would if the calculations were done on the Home screen. Programs do not update Last Entry as each command is executed.
Pressing
´ stops program execution. When you press ´ during program execution, the
ERR: BREAK
menu is displayed.
¦
To go to where the interruption occurred, select
GOTO
.
¦
To return to the Home screen, select
QUIT
.
The size of programs you can store is limited only by available memory. To access the
MEMORY
menu, press
2 ¯ from the Home screen. Memory status is displayed on the
MEMORY
CHECK RAM...
screen. To increase available memory, you can delete items, including other programs, from the
MEMORY DELETE...
screen (Chapter 12).
Note:
Each token in a program takes 1 byte. For example,
SIN 1.23
takes 5 bytes.
10-4 Programming
Creating and Executing Programs
Access the program editor by pressing
K
. Then either choose to create a new program or edit an existing program. In general, anything that can be executed from the Home screen can be included in a program. A program command always begins with a colon (:).
Creating a New
Program
To create a new program:
1. Press
K 9 9 to display the
PRGM NEW
menu. Press
¸ to select
CREATE NEW
.
Entering
Program
Commands
Leaving the
Program Editor
Executing a
Program
2. The keyboard is in
ALPHA-LOCK
. Enter the name you want for the program, followed by
¸. The name may have one to seven characters (
A
–
Z
, q,
0
–
9
) and must begin with a letter.
3. Enter the program commands.
A colon (
:
) indicates the beginning of each program command.
To enter more than one command on a line, separate them with a colon, just as you would on the Home screen. Press
¸ to indicate the end of a command line.
When a command is longer than one line on the screen, it wraps to the next line. 2 6 and 2 9 move the cursor to the beginning and end of a command line.
In the program editor, if you press a key that accesses a menu, the menu screen temporarily replaces the program edit screen. When you make a selection or press
M, you are returned to the program editor.
When you finish entering or editing a program, press
2 .
to return to the Home screen. You must be on the Home screen to execute a program.
To execute a program:
1. From a blank line on the Home screen, press
K to display the
PRGM EXEC
menu. The names of all existing programs are listed in alphabetical order.
2. Select the program.
PRGM_
and the program name are copied to the Home screen; for example,
PRGM_ROLL
.
3. Press
¸ to begin program execution. While the program is executing, the busy indicator is displayed.
Programming 10-5
Editing Programs
The program editor also lets you edit an existing program. As you edit, you can enter commands just as you did when you created the program.
Editing a
Program
To edit a program:
1. Press
K 9 to display the
PRGM EDIT
menu.
Changing
Instructions
Inserting a New
Command Line
Deleting a
Command Line
2. Select the name of an existing program. The program editor and the commands in that program are displayed.
3. Edit the program by changing, inserting, or deleting commands, as needed.
Move the cursor to the command you want to change.
¦
Position the cursor, and then make the changes by typing over the command or using
4 or 2 /.
¦
Press
M to clear (blank) all program commands on the command line (The leading colon is not deleted.), and then enter a new program command.
To insert a new command line, position the cursor where you want to insert the new line, press
2 / to put the TI-80 in insert mode, and then press
¸.
To delete a command line, press
M to clear the line, and then press 4 to delete the colon.
Note:
All programs end with a blank command line; the colon on this line cannot be deleted.
10-6 Programming
PRGM CTL (Control) Instructions
PRGM CTL (program control) instructions are accessed only from within the program editor. They direct the flow within an executing program, making it easy to repeat or skip commands during program execution. While the program editor is displayed, press
K
. The selected menu item is copied to the cursor location.
PRGM CTL
Menu
Controlling
Program Flow
IF
CTL I/O EXEC
1: IF
2: THEN
3: ELSE
4: FOR(
5: END
6: PAUSE
7: LBL
8: GOTO
9: PRGM_
0: RETURN
A: STOP
Creates a conditional test.
Used with
IF
.
Used with
IF-THEN
.
Creates incrementing loop.
Signifies end of loop,
IF-THEN
, or
ELSE
.
Pauses program execution.
Defines a label.
Goes to a label.
Executes a program as a subroutine.
Returns from a subroutine.
Stops program execution.
Program control instructions tell the TI
-80 which command to execute next in a program.
IF
checks a condition that you define to determine what command to execute next. The condition frequently uses relational tests (Chapter 2), such as
IF A<7:A+1
!
A
.
IF
(
PRGM CTL
, item 1) is used for testing and branching. If the condition is false (zero), the command immediately following
IF
is skipped. If the condition is true (nonzero), that command is executed.
IF
instructions can be nested.
:IF
condition
:
command if true
:
command
Programming 10-7
IF-THEN
END
THEN
(
PRGM CTL
, item 2) following an
IF
executes a group of commands if the condition is true (nonzero).
END
(
PRGM CTL
, item 5) identifies the end of the group.
:IF
condition
:THEN
:
command if true
:
...
:END
:
command
IF-THEN-ELSE
END
ELSE
(
PRGM CTL
, item 3) following
IF-THEN
executes a group of commands if the condition is false (zero).
END
(
PRGM CTL
, item 5) identifies the end of the group.
:IF
condition
:THEN
:
command if true
:
...
:ELSE
:
command if false
:
...
:END
:
command
10-8 Programming
FOR(
END
FOR(
(
PRGM CTL
, item 4) is used for looping and incrementing. It increments the variable from the beginning value to the ending value, by the specified increment. The ending value is a maximum or minimum value that is not to be exceeded. The increment is optional (if not specified, 1 is used) and can be negative (ending value < beginning value).
END
identifies the end of the loop.
FOR(
loops can be nested.
:FOR(
variable
,
begin
,
end
,
increment
)
:
command while end not exceeded
:
...
:END
:
command
END
PAUSE
END
(
PRGM CTL
, item 5) identifies the end of a group of commands. Each
FOR(
and each
IF-THEN
or
IF-THEN
-
ELSE
group must have an
END
at the “bottom.”
PAUSE
(
PRGM CTL
, item 6) suspends execution of the program so that you can see answers or graphs. During the pause, the dotted pause indicator is displayed. When
DISP
or
DISPGRAPH
is executed, the appropriate screen is displayed.
Press
¸ to resume program execution.
Programming 10-9
LBL
GOTO
LBL
(label) and
GOTO
(go to) are used together for branching.
LBL
(
PRGM CTL
, item 7) gives a label to a command line in a program. The label is one character (A–Z, 0–9, or q).
LBL
label
GOTO
(
PRGM CTL
, item 8) causes the program to branch to the command line with the same label.
GOTO
label
PRGM_
RETURN
STOP
PRGM_
(
PRGM CTL
, item 9) calls (executes) other programs as subroutines (pages 10 -14). When you select
PRGM_
, it is copied to the cursor location. You may type the letters of an existing program name. You may also enter the name of a program you have not yet created.
When encountered, the command executes the specified program and then returns to the calling program. Execution continues with the command following
PRGM_
programname
.
PRGM_
programname
RETURN
(
PRGM CTL
, item 0) quits the subroutine and returns to the calling program (pages 10
-14), even if it is encountered within nested loops. (Any loops are ended.) There is an implied
RETURN
at the end of any program called as a subroutine. Within the main program,
RETURN
stops program execution and returns to the Home screen.
STOP
(
PRGM CTL
, item A) stops execution of a program and returns you to the Home screen.
STOP
is optional at the end of a program. There is an implied stop at the end of the main program that is being executed.
10-10 Programming
PRGM I/O (Input/Output) Instructions
The PRGM I/O (program input/output) instructions are accessed only from the program editor. They control input to and output from a program, allowing you to enter values and display answers during program execution. While the program editor is displayed, press
K
. The selected menu item is copied to the cursor location.
PRGM I/O
Menu
Displaying a
Graph with
INPUT
CTL I/O EXEC
1: INPUT
Enters a value or displays the current graph.
2: DISP
Displays text, value, or the Home screen.
3: DISPGRAPH Displays the current graph.
4: CLRHOME
Clears the Home screen.
INPUT
without a variable displays the current graph. You can move the free-moving cursor, which updates
X
and
Y
. The dotted pause indicator is displayed. Press
¸ to resume program execution.
For example,
INPUT
during program execution displays:
Programming 10-11
Storing a
Variable Value with INPUT
INPUT
with a variable displays a
?
prompt during program execution. The value for the variable may be a real number, a list, or
Y=
function. During program execution, enter a value
(a real number, an expression, or a list), and press
¸. The value is evaluated and stored to the variable, listname, or
Y=
function, and the program resumes execution.
INPUT
variable
INPUT
listname
INPUT
Yname
You can enter a string of up to 16 characters to prompt for the value to be entered. During program execution, enter a value, and press
¸ after the prompt. The value is stored to the variable, listname, or
Y=
function, and the program resumes execution.
INPUT "
text
",
variable
INPUT "
text
",
listname
INPUT "
text
",
Yname
Note:
When you input lists and expressions during program execution, you must include the braces (
{ }
) around the list elements and quotation marks (
"
) around expressions.
10-12 Programming
Displaying the
Home Screen
Displaying
Values and
Messages
DISP
(display,
PRGM I/O
, item 2) with no value displays the
Home screen. To view the Home screen during program execution, follow the
DISP
instruction with a
PAUSE
.
DISP
(display,
PRGM I/O
, item 2) with one or more values displays the value of each.
DISP
value
DISP
valueA
,
valueB
...
¦
If value is a variable, the current value is displayed.
¦
If value is an expression, it is evaluated and then displayed, according to the current mode settings, on the right of the following line.
¦
If value is text within
"
marks, it displays on the left of the current display line.
For example,
DISP "ANSWER IS", pà
2
displays:
DISPGRAPH
CLRHOME
If
PAUSE
is encountered after
DISP
, the program halts temporarily so that you can examine the screen. Press
¸ to resume program execution.
Note:
A statement that results in a value will display without using
DISP
, if it is the last statement (other than
STOP
,
END
, and
PAUSE
) in the program.
DISPGRAPH
(display graph,
PRGM I/O
, item 3) displays the current graph. If
PAUSE
is encountered after
DISPGRAPH
, the program halts temporarily so you can examine the screen.
Press
¸ to resume execution.
CLRHOME
(clear Home screen,
PRGM I/O
, item 4) clears the
Home screen during execution and places the cursor in the upper left corner; however, program execution does not pause unless
PAUSE
is encountered.
Programming 10-13
Calling Other Programs
On the TI
.
80, any 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.
Calling a
Program from
Another
Program
To call one program from another, begin on a blank line in the program editor and do one of the following.
¦
Press
K 6 to display the
PRGM EXEC
menu, and select the name of the program.
PRGM_
and the name are copied to the cursor location.
¦
Select
PRGM_
from the
PRGM CTL
menu and then type the letters of the programname.
PRGM_
programname
When this instruction is encountered during program execution, the next command that the program executes is the first command in the second program. Execution continues with the subsequent command in the first program when it encounters either a
RETURN
instruction or when the implied
RETURN
at the end of the called program is encountered.
Notes about
Calling
Programs
Variables are global.
A label used with
GOTO
and
LBL
is local to the program in which it is located. A label in one program is not “known” 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 encountered within nested loops.
10-14 Programming
Chapter 11: Applications
This chapter contains application examples that incorporate the TI
.
80 features described in the preceding chapters. Several of the examples use programs.
Chapter
Contents
Probability Experiments: Coins, Dice, and Spinners
...
The Unit Circle and Trigonometric Curves
............
Program: Newton’s Numerical Solve Routine
.........
Program: Numerical Integration
.....................
Program: Window Variables Store and Recall
.........
Graphing the Inverse of a Function
..................
Graphing a Piecewise Function
.....................
Graphing Inequalities
..............................
Graphing a Polar Equation
.........................
Program: Guess the Coefficients
....................
Applications 11-1
Probability Experiments: Coins, Dice, and Spinners
The RANDINT( (random integer) function can be used for probability experiments. RANDINT( takes two arguments that define a set of integers from which to draw for the probability experiments below.
Problem
Procedure
Using
RANDINT(
from the
MATH PRB
menu, devise probability experiments that employ the toss of a coin, the roll of two dice, and the spin of a wheel.
For the coin tossing experiment, enter
RANDINT(0,1)
from the
Home screen. 0 = tails and 1 = heads. Press
¸ repeatedly to generate the coin tosses.
You can also write a simple program to display “heads” or
“tails” for each coin toss.
You can simulate the rolling of two dice by adding together the result from each die after a roll. On the Home screen, enter
RANDINT(1,6)+RANDINT(1,6)
and press
¸ repeatedly.
You can simulate spinning a wheel with the numbers 1 to 100 using the
RANDINT(
function. Enter
RANDINT(1,100)
on the
Home screen and press
¸ repeatedly.
11-2 Applications
The Unit Circle and Trigonometric Curves
You can use the parametric graphing feature of the TI
.
80 to show the relationship between the unit circle and any trigonometric curve.
Problem
Procedure
Graph the unit circle and the sine curve to demonstrate graphically the relationship between them.
Any function that can be plotted in function graphing can be plotted in parametric graphing by defining the X component as T and the Y component as F(T).
Following this procedure to solve the problem.
1. Press
3 and select
RADIAN
,
PARAM
, and
SIMUL
.
2. Press
) and set the Window variables.
TMIN = 0
TMAX = 2 p
TSTEP = .1
XMIN =
.
2
XMAX = 2 p
XSCL = pà
2
YMIN =
.
3
YMAX = 3
YSCL = 1
3. Press
( and enter the expressions to define the unit circle centered at (
L1,0).
X1
î
T=COS T
ì
1 Y1
î
=SIN T
Enter the expressions to define the sine curve.
X2
î
=T Y2
î
=SIN T
Turn off all other functions.
4. Press
, to see the
SIN
function “unwrap” from the unit circle.
Note:
The “unwrapping” can be generalized. Replace
SIN T
in
Y2
î with any other trig function to “unwrap” that function.
Applications 11-3
Program: Newton’s Numerical Solve Routine
This program uses the Newton-Raphson method to find the roots (zeros) of a function numerically.
Problem
Program
Procedure
Find the roots of ex
ì3X.
This program uses the Newton-Raphson method to find a root of
Y1
based on an initial guess. The program prompts for the initial guess. One way to make this initial guess is to graph and trace the function, and then enter X as the guess.
PROGRAM:NEWTON
:INPUT "INITIAL X=",X
:LBL N
:X
ìY1/NDERIV(Y1,X,X)
→
R
:DISP R
:PAUSE
:IF ABS (X
ìR)
≤
ABS (X/1
í10)
:STOP
:R
→
X
:GOTO N
Input initial guess.
Begin loop.
Calculate new root.
Test for convergence.
Estimate with new root.
Follow this procedure to solve the problem.
1. Press
3 and select
FUNC
.
2. Enter the program.
3. Press
(. Enter the expression
e
õì
3X
to define
Y1
.
4. Graph the function using
ZDECIMAL
from the
ZOOM
menu.
11-4 Applications
5. Press
+ and move the cursor close to the left root.
The variables X and Y are updated as you move the cursor.
6. From a blank line on the Home screen, execute the program
NEWTON
.
7. Enter
X
as the initial guess, and press
¸ repeatedly.
The program stops when the relative difference between the new root estimate and the previous root estimate is less than X
íL10.
8. When program execution is complete, evaluate the function at the estimated root.
Repeat the steps in this procedure to find the other root.
Applications 11-5
Program: Numerical Integration
This program uses Simpson’s method to estimate the definite integral of a function.
Problem
Program
Procedure
Estimate the definite integral of
‰
0
1.5
(6
ì6x
5
)dx and graph the area of the integral.
The program estimates the definite integral for
Y1
using
Simpson’s method. It prompts for the lower and upper limits of integration and the number of divisions.
PROGRAM:SIMPSON
:INPUT "LOWER LIMIT=",A
:INPUT "UPPER LIMIT=",B
:INPUT "N DIVISIONS=",D
:0
→
S
:(B
ìA)/(2
×
D)
→
W
:FOR(J,1,D,1)
:A+2(J
ì1)W
→
L
:A+2JW
→
R
:(L+R)/2
→
M
:W(Y1(L)+4Y1(M)+Y1(R))
/3+S
→
S
:END
:DISP "AREA="
:DISP S
Input lower limit.
Input upper limit.
Input # of divisions.
Initialize sum variable.
Calculate division width.
Begin calculation loop.
Calculate left point.
Calculate right point.
Calculate midpoint.
Calculate division sum and add to total.
Display results.
Follow this procedure to solve the problem.
1. Enter the program.
2. Press ( and enter the function in
Y1
. Turn any other functions off.
11-6 Applications
3. Set the Window variables.
4. Execute the program
SIMPSON
from a clear Home screen, entering the limits and divisions as you are prompted.
5. You can display the calculated area graphically, using
SHADE(
from a clear Home screen.
Applications 11-7
Program: Window Variables Store and Recall
The program below lets you store the values for the current Window variables, and it lets you display a graph using previously stored values. It also demonstrates a method for including menus in a program.
Program
PROGRAM:WINMEM
:CLRHOME
:DISP "WINDOW MEMORY"
:DISP "1:STORE WINDOW"
:DISP "2:RECALL WINDOW"
:DISP "3:QUIT"
:DISP " "
:DISP "ENTER 1,2, OR 3"
:INPUT M
:IF M=1
:GOTO S
:IF M=2
:GOTO R
:GOTO Q
:LBL S
:XMIN
→
A
:XMAX
→
B
:XSCL
→
C
:YMIN
→
D
:YMAX
→
E
:YSCL
→
F
:DISP "WINDOW STORED"
:GOTO Q
:LBL R
:A
→
XMIN
:B
→
XMAX
:C
→
XSCL
:D
→
YMIN
:E
→
YMAX
:F
→
YSCL
:DISPGRAPH
:GOTO Q
:LBL Q
:STOP
Present menu of choices.
Evaluate menu selection.
Store current graph
Window variable values.
Display graph with previously stored variable values.
Quit program.
11-8 Applications
Procedure
Follow this procedure to see how the program works.
1. Execute the program
WINMEM
from a blank Home screen.
The program prompts with three options.
¦
Store the Window variables you are currently using.
¦
View a graph using a previously stored set of Window variables.
¦
Quit the program.
2. Press
1
,
2
, or
3
and then
¸ to respond to the prompts.
The Window values are stored in variables A, B, C, D, E, and F.
Applications 11-9
Graphing the Inverse of a Function
You can use the parametric graphing feature of the TI
.
80 to graph the inverse relation of any function by defining the function in X
ã
T
and Y
ã
T
and its inverse in
X
ä
T
and Y
ä
T
.
Problem
Procedure
The function Y=.2X
form as X
T
=T and Y
3
ì2X+6 can be expressed in parametric
T
=.2T
3
ì2T+6.
The inverse relation of the function can be expressed in parametric form as X
T
=F(T) and Y
T
=T. For example,
Y=.2X
3
ì2X+6 would be expressed as X
T
=.2T
3
ì2T+6 and
Y
T
=T.
Graph the function Y=.2X
3
ì2X+6 and its inverse.
Follow this procedure to solve the problem.
1. Select
Param
,
CONNECTED
, and
Simul
modes.
2. Change the Window variable values.
Tmin= L 10
Tmax=10
Tstep=.4
Xmin= L 15
Xmax=15
Xscl=1
Ymin= L 9
Ymax=9
Yscl=5
3. Enter the expressions to define the function in parametric form.
X1
î
=T
Y1
î
=.2T
ò
–2T+6
4. Enter the expressions to define the inverse in parametric form.
X2
î
=.2T
ò
–2T+6
Y2
î
=T
11-10 Applications
5. Enter the expressions to define the line Y=X, about which the graph of the function and the graph of its inverse are symmetric. That is, the reflection of the graph of the function through the line Y=X produces the graph of its inverse.
X3
î
=T
Y3
î
=T
6. Press
, to plot the graph. Press +, and then press
9 several times (until the cursor appears). Next, press
8 and 7 several times to move the cursor from a point on the relation to the reflected point and back again.
Note:
The expressions to define the inverse can be generalized.
X1
î
=Y2
î
Y1
î
=X2
î
Applications 11-11
Graphing a Piecewise Function
The test functions of the TI
.
80 can be used to build piecewise defined functions.
Problem
Define and graph this piecewise defined function.
f(x)= x
ñ
, for x
≤
3
1.5x+1, for 3
< x
<
5
6 ìx, for x
≥
5
The
TEST
functions, which return 1 if true and 0 if false, can be used to build piecewise defined functions. For example, when x is 4 (x
≤
3) is false and will return 0.
Procedure
Follow this procedure to solve the problem.
1. Press
3 and select
FUNC
.
2. Enter the first piece of the function in the
Y=
editor. This piece is f(x)=x
ñ for x
≤
3. It is entered as
(x
ñ
)(x
≤
3)
.
Y
ã is then equivalent to x
ñ
×
1 for x
≤
3 and x
ñ
×
0 for x
>
3.
3. Add the second piece of the function in the
Y=
editor. This piece is f(x)=1.5x+1 for 3
< x
<
5. It is entered as
(1.5x+1)(3
<
x)(x
<
5)
.
When x is less than 3, the test (3
< x) returns 0, and the test
(x
<
5) returns 1. In this case, the second piece of the function is equivalent to (1.5x+1)
×
0
×
1, which is 0. Only when both of these tests are true will the second piece of this function be anything but 0.
11-12 Applications
4. Add the third piece of the function to
Y1
. This piece is f(x)=6
ìx for x
≥
5. It is entered as
(6
ì
x) (x
≥
5)
. When x is greater than or equal to 5, the test (x
≥
5) returns 1. The third piece of the function is then equivalent to (6
ìx)
×
1.
When X is less than 5, the test (x
≥
5) returns 0. The third piece of the function is then equivalent to (6
ìx)
×
0.
5. Enter these Window variable values.
Xmin=
ë
2
Xmax=8
Xscl=2
Ymin=
ë
2
Ymax=10
Yscl=1
6. Graph the piecewise function first in
CONNECTED
and then
DOT
mode. Select
CONNECTED
on the
MODE
screen, and then press
,. Then select
DOT
on the
MODE
screen, and press
,.
CONNECTED DOT
Applications 11-13
Graphing Inequalities
Examine the inequality
.
4X
òì
3X+5<
.
2X+4 graphically. Use the TEST functions to explore the values of X where the inequality is true and where it is false.
Procedure
1. Press
3. Select
DOT
,
SIMUL
, and the default mode settings. Press
2 ", and turn off all stat plots.
2. Press
(, and turn off all functions. Enter the left side of the inequality as
Y1
, the right side as
Y2
, and the statement of the inequality as
Y3
.
Y3
evaluates to 1 if true and 0 if false.
3. Press
), and enter these Window variable values.
Xmin=
ë
10
Xmax=10
Xscl=5
Ymin=
ë
10
Ymax=10
Yscl=5
4. Press
+. Press 8 8 to move to
Y3
. Trace the inequality, observing the value of X.
Y3
is 1 when
Y1
<
Y2
, and
Y3
is 0 when
Y1
≥
Y2
.
5. Press
( and turn off
Y1
and
Y2
. Enter equations to graph only the inequality.
6. Press
+. Notice that the values of
Y3
and
Y4
are zero where the inequality is false.
11-14 Applications
Graphing a Polar Equation
The parametric graphing feature of the TI
.
80 can be used to graph polar equations. Graph the Spiral of Archimedes, the name given to the curve defined by the polar equation r=a q
.
Problem
Procedure
A polar equation r=f( q) can be graphed by applying the conversion formulas, x=f( q) cos(q) and y=f( q) sin(q). Thus, the Spiral of Archimedes can be expressed parametrically as: x = .5 q cos(q) y = .5 q sin(q)
Follow this procedure to solve the problem.
1. Select
PARAM
mode. Choose the defaults for the other mode settings.
2. Enter the expressions to define the parametric equation in terms of T.
3. Set the Window variables to the following values.
Tmin=0
Tmax=25
Tstep=
π⁄
8
Xmin=
Xscl=1
L 10
Xmax=10
Ymin= L 10
Ymax=10
Yscl=1
4. Press , to display the Spiral of Archimedes.
Applications 11-15
Program: Guess the Coefficients
This program generates a function in the form A
×
SIN(BX) with random integer coefficients between 1 and 10. Seven data points from the function are plotted.
You are prompted to guess the coefficients, which are plotted as C
×
SIN(DX). The program continues until your guess is correct. It can be modified for other functions.
Program
PROGRAM:GUESS
:FUNC:RADIAN
:-31( p/12)"XMIN
:31( p/12)"XMAX
: p/2"XSCL
:-10 "YMIN
:10 "YMAX
:1
"YSCL
:"A
×
SIN (BX)" "Y1
:RANDINT(1,10) "A
:RANDINT(1,10) "B
:PLOTSOFF: FNOFF
:DISPGRAPH
:SEQ(XMIN+I
×∆
X,I,0,62,9) "L1
:Y1(L1) "L2
:PLOT1(
¼,L1,L2,›)
:DISPGRAPH
:PAUSE
:"C
×
SIN (DX)" "Y2
:LBL W
:CLRHOME
:DISP "C
×
SIN (DX)"
:INPUT "C=",C
:INPUT "D=",D
:DISPGRAPH
:PAUSE
:IF C=A
:DISP "C IS OK"
:IF C
>
A
:DISP "C IS TOO HIGH"
:IF C
<
A
:DISP "C IS TOO LOW"
:IF D=B
:DISP "D IS OK"
:IF D
>
B
:DISP "D IS TOO HIGH"
:IF D
<
B
:DISP "D IS TOO LOW"
:PAUSE
:IF((C=A)
×
(D=B))=1
:STOP
:GOTO W
Set viewing window.
Initialize coefficients.
Display data points.
Prompt for guesses.
Display results.
Quit if guesses are correct.
11-16 Applications
Chapter 12: Memory Management
This chapter describes how to manage memory on the TI
.
80. To increase the amount of memory available for use, occasionally you may want to delete stored items that you are no longer using. You can also reset the calculator, erasing all data and programs.
Chapter
Contents
Checking Available Memory
........................
Deleting Items from Memory
.......................
Resetting the TI
-80
................................
Memory Management 12-1
Checking Available Memory
The MEMORY CHECK RAM screen displays the total amount of available memory and the amount of memory used by each variable type. This allows you to determine the amount of memory available for new items such as programs and the amount used by old items that you no longer need.
Displaying the
MEM FREE
Screen
To check the amounts of available and used memory:
1. Press
2 ¯ to display the
MEMORY
menu.
2. Press 1 or
¸ to select
CHECK RAM...
.
The amount of available memory and the number of bytes used by each variable type are shown on the right.
3. To leave the
CHECK RAM
display:
¦
Press
2 . to go to the Home screen.
¦ Press 2 ¯ to return to the
MEMORY
menu.
12-2 Memory Management
Deleting Items from Memory
You can delete the contents of any variable (real number, list, or Y= function) or program from memory to increase available memory.
Deleting an Item
To delete an item:
1. Press
2 ¯ to display the
MEMORY
menu.
2. Press 2 to select
DELETE...
A screen showing all variables currently in use and the amount of memory used by each is displayed.
The file names are listed in the following order:
¦
Program names
¦
List names
¦
Y=
equation names
¦
Numeric variable names
3. Use
7 and 8 to position the cursor, which is indicated by
ú in the left column, next to the item you want to delete; and press
¸. The item is deleted immediately.
You can continue to delete individual items from this screen.
To leave the
DELETE
display:
¦
Press
2 . to go to the Home screen.
¦ Press 2 ¯ to return to the
MEMORY
menu.
Note:
Some system variables
ANS
and statistical variables such as
REGEQ
, for example
cannot be deleted. These system variables are not shown on the
DELETE
display.
Memory Management 12-3
Resetting the TI-80
Resetting the TI
.
80 restores memory to the factory settings, including deleting the contents of all variables and programs and resetting all system variables to the original settings. Because you can increase available memory by deleting individual items, you should rarely need to reset the TI .
80.
Resetting
To reset the TI
-80:
1. Press
2 ¯ to display the
MEMORY
menu.
2. Press 3 to select
RESET...
.
3. Make the appropriate menu selection:
¦
To go to the Home screen without resetting memory, select
NO
.
¦
To reset memory, select
RESET
. The Home screen is displayed with the message
MEM CLEARED
.
Note:
If the screen is blank after
RESET
, adjust the display contrast. Press
2 and then press and hold 7 (to make the display darker) or
2 8 (to make the display lighter). You can press
M to clear the message on the display.
12-4 Memory Management
Appendix A: Tables and Reference Information
This appendix provides a list of all TI
-
80 functions that you can use in expressions and instructions that you can use on the Home screen and in programs. It also includes other reference information that can help you.
Appendix
Contents
Table of TI
-80 Functions and Instructions
..........
Menu Map
.......................................
TI
-80 Variables
...................................
Tables and Reference Information A-1
Table of TI-80 Functions and Instructions
A function (F) returns a value or a list and can be used in expressions; an instruction (I) initiates an action. Some, but not all, have arguments. † indicates that the instruction is available for copying only from the program editor.
a
value
ABS
ABS b
À
º
b c
º
value
value
c a
8
À
list
b b
º
º
c
CLRDRAW
CLRHOME c
Addition: valueA+valueB
Addition: value+list
Addition: listA+listB
AUTOSIMP
CLRLIST
listnameA
,
listnameB
,
. . .
Sets the display format for fraction results to
a
À
b
º
c
(mixed fraction) mode.
(I)
Returns a list of absolute values for each element in
list
.
(F)
†
á
3 a
À b
º c
â
Returns value as a mixed fraction.
(F)
Returns the absolute value of value.
(F)
J
á
4 a
À b
º c
â
2 P
2 P
Returns valueA plus
valueB
.
(F)
«
Returns a list in which
value
is added to each list element.
(F)
Returns a list of listA elements plus listB elements.
(F)
Clears the Home screen.
(I)
Deletes
listnameA
,listnameB, . . .
(I)
«
«
Turns on automatic simplification mode for fractions.
(I)
Sets the display format for fraction results to
b
º
c
(simple fraction) mode.
(I)
Returns value as a simple fraction.
(F)
Deletes all drawn elements from a graph or drawing.
(I)
†
á
3
AUTOSIMP
†
3
á b º c
â
J
á
4 b º c
â
â
2 F
DRAW
á
CLRDRAW
â
†
K
I/O
á
CLRHOME
â
A
EDIT
á
CLRLIST
â
A-2 Tables and Reference Information
CONNECTED
COS
COS
COS
COS
value
list
ê value
ê list
Cube: value
Cube: list
Cube Root:
Cube Root:
value list
8
8
ò
DEC
DEC
DEGREE
ò
ò‡value
ò‡list
Degree Notation: value
¡
DIM
list
length
!
DIM
listname
DISP
DISP "
text
"
DISP
valueA
,
valueB
,
. . .
DISP "
text
",
valueA
,
"
text
",
valueB
,
. . .
Sets connected line graphing format.
(I)
Returns the cosine of
value
.
(F)
Returns a list of the cosine for each list element.
(F)
Returns the arccosine of
value
.
(F)
†
á
3
CONNECTED
X
X
2 R
Returns a list of the arccosine for each list element.
(F)
Returns the cube of value.
(F)
Returns a list of the cube for each list element.
(F)
Returns the cube root of
value
.
(F)
Returns a list of the cube root for each list element.
(F)
2 R
I
MATH
á
ò
â
I
MATH
á
ò
â
I
I
á
á
ò‡
ò‡
â
â
MATH
MATH
Returns value in decimal form. form.
Interprets value as an angle in degrees.
(F)
Returns the length of list.
(F)
(I)
Returns list in decimal
(I)
Sets degree mode.
(I)
I
MATH
á
4
DEC
â
I
MATH
á
4
DEC
â
†
3
á
DEGREE
â
2 E
á
ó
â
2 =
OPS
á
DIM
â
2 =
OPS
á
DIM
â
Creates (if necessary) or redimensions list to
length
.
(I)
Displays the Home screen.
(I)
Displays text.
(I)
† K
I/O
á
DISP
â
†
K
I/O
á
DISP
â
Displays valueA,
valueB
, . . .
(I)
Displays text,valueA,text
valueB
, . . .
(I)
†
K
I/O
á
DISP
â
†
K
I/O
á
DISP
â
â
Tables and Reference Information A-3
DISPGRAPH
Division: valueA
Division: list
Division: value
Division: listA
DOT
DRAWF e^ e^
power list
àvalueB
àvalue
àlist
àlistB
expression
Displays the current graph.
(I)
Returns valueA divided by
valueB
.
(F)
†
K
I/O
á
DISPGRAPH
â e e
Returns list elements divided by value.
(F)
Returns value divided by
list
elements.
(F)
e e Returns listA elements divided by listB elements.
(F)
Sets dot graphing format.
(I)
Draws expression (in
X
) on the current graph.
(I)
†
á
á
3
DOT
â
2 F
DRAWF
2 s
â
DRAW
Returns e raised to the value of power.
(F)
Returns a list of e raised to the power of each list element.
(F)
2 s
ELSE
See
IF:THEN:ELSE
END
Equal: valueA=valueB
Equal: listA=listB
Identifies the end of a
FOR(
,
IF-THEN
, or
IF-
THEN-ELSE
structure.
(I)
Returns 1 if valueA =
valueB
. Returns 0 if
valueA
ƒ valueB.
(F)
Applies the = test to each element of listA and listB and returns a list.
(F)
†
K
CTL
á
END
â
2 D
á
=
â
2 D
á
=
â
Equal: list
value
=
Exponent:
=
list value
or
íexponent
Applies the = test to each element of list and value and returns a list.
(F)
Returns 10 to the
exponent
.
(F)
Exponent: value
íexponent
Returns value times 10 to the exponent.
(F)
Exponent: list íexponent Returns list elements times 10 to the exponent.
(F)
2 D
á
=
â
2 ^
2 ^
2 ^
A-4 Tables and Reference Information
EXPREG
Xlistname
EXPREG
,
Ylistname
Xlistname
,
Ylistname
,
freqlistname
Factorial: value
Factorial: list
FIX
n
FLOAT
FNOFF
FNOFF
function#
,
function#
,
. . .
FNON
FNON
function#
,
function#
,
. . .
FOR(
variable
,
begin
,
end
)
:
commands
. . .
:END
FOR(
:
variable
increment
:END
)
commands
,
!
!
begin
. . .
,
end
,
Fits Xlistname and
Ylistname
to the exponential model.
(I)
A
á
CALC
EXPREG
â
Fits Xlistname and
Ylistname
to the exponential model with frequency
freqlistname
.
(I)
A
á
CALC
EXPREG
â
Returns the factorial of
value
(0
integer 69).
(F)
I
á
!
â
PRB
Returns a list containing the factorial for each list element (0
≤
integers
≤
69).
(F)
I
á
!
â
PRB
Sets fixed-decimal display mode for n decimal places.
(I)
Selects all
(I)
Y=
functions.
Selects function#,
function#
, . . .
(I)
†
á
3
FIX
â
Sets floating-decimal display mode.
(I)
Deselects all
Y=
functions.
(I)
Deselects function#,
function#
, . . .
(I)
†
3
á
FLOAT
â
2 G
ON/OFF
á
FNOFF
â
2 G
ON/OFF
á
FNOFF
â
2 G
ON/OFF
á
FNON
â
2 G
ON/OFF
á
FNON
â
†
K
CTL
á
FOR(
â
Executes commands through
END
, incrementing variable from begin by 1 until
variable
> end.
(I)
Executes commands through
END
, incrementing variable from begin by increment until variable > end.
(I)
†
á
K
FOR(
â
CTL
Tables and Reference Information A-5
FPART
FPART
value list
8
8
value
list
FRAC
FRAC
FUNC
GOTO
label
Greater Than:
valueA>valueB
Greater Than:
listA
>
listB
Greater Than:
list
>
value
or
value
>
list
Greater Than or Equal:
valueA ‚valueB
Greater Than or Equal:
listA
‚listB
Greater Than or Equal:
list
‚value or
value
‚list
GRIDOFF
GRIDON
Returns the fractional part of value.
(F)
Returns a list of the fractional parts for each
list
element.
(F)
I
NUM
á
FPART
â
I
NUM
á
FPART
â
Returns value in fraction form, according to the current fraction display format.
(I)
J
á
4 FRAC
â
Displays list in fraction form, according to the current fraction display format.
(I)
J
á
4 FRAC
â
Sets function graphing mode.
(I)
Branches the program to
label
.
(I)
†
3
á
FUNC
â
† K
CTL
á
GOTO
â
2 D
á
>
â
Returns 1 if valueA >
valueB
. Returns 0 if
valueA
valueB.
(F)
Applies the
>
test to each element of listA and listB and returns a list.
(F)
2 D
á
>
â
2 D
á
>
â
Applies the
>
test to each element of list and value and returns a list.
(F)
Returns 1 if valueA
‚
valueB
. Returns 0 if
valueA
<
valueB.
(F)
Applies the
‚ test to each element of listA and listB and returns a list.
(F)
2 D
á
‚
2 D
á
‚
â
â
Applies the
Turns the graph grid on.
(I)
‚ test to each element of list and value and returns a list.
(F)
Turns the graph grid off.
(I)
2 D
á
‚
â
2 F
á
GRIDOFF
â
DRAW
2 F
DRAW
á
GRIDON
â
A-6 Tables and Reference Information
HORIZONTAL
Y
IF
condition
:
commandA
:
commands
IF
condition
:THEN:
commands
:END
IF
condition
:THEN:
commands
:ELSE:
commands
:END
INPUT
INPUT
INPUT
INT
INT
variable
"
text
value
list
integerA
listA
",
INT÷
INT÷
integerB listB
list
INT÷
integer
or
integer
INT÷
list
Inverse: value ê
Inverse: list ê
variable
Draws a horizontal line at value Y.
(I)
If condition = 0 (false), skips commandA.
(I)
2 F
DRAW
á
HORIZONTAL
â
†
K
CTL
á
IF
â
†
K
CTL
á
THEN
â
Executes commands from
THEN
to
END
if condition
= 1 (true).
(I)
Executes commands from
THEN
to
ELSE
if
condition
= 1 (true); from
ELSE
to
END
if condition
= 0 (false).
(I)
†
á
K
ELSE
â
CTL
Displays the current graph with the free-moving cursor.
(I)
†
K
I/O
á
INPUT
â
Prompts for input to store to variable.
(I)
Prompts using text and stores input to variable.
(I)
† K
I/O
á
INPUT
â
†
á
K
INPUT
â
I/O
Returns the largest integer
value.
(F)
I
NUM
á
INT
â
Returns the largest integer
list element.
(F)
I
NUM
á
INT
â
Divides integerA by
integerB
and returns a quotient (
Q
) and remainder (
R
) on the
Home screen, if there are no pending operations.
(F)
I
MATH
á
INT÷
â
Returns a list of quotients from listA and listB.
Returns 1 divided by
value
.
(F)
(F)
Returns list of quotients from integer and list.
(F)
I
MATH
á
INT÷
â
I
MATH
á
INT÷
â
V
Returns 1 divided by each
list
element.
(F)
V
Tables and Reference Information A-7
IPART
IPART
LBL
value
list
label
Returns the integer part of
value
.
(F)
Returns a list of the integer part for each list element.
(F)
Assigns label to the command.
(I)
I
NUM
á
IPART
â
I
NUM
á
IPART
â
†
K
CTL
á
LBL
â
2 D
á
<
â
Less Than: valueA
<
valueB
Returns 1 if valueA <
valueB
. Returns 0 if
valueA
‚ valueB.
(F)
Less Than: listA
<
listB
Applies the < test to each element of listA and listB and returns a list.
(F)
Less Than: list
<
value
or
value
<
list
Less Than or Equal:
valueA valueB
Applies the < test to each element of list and value and returns a list.
(F)
Returns 1 if valueA
valueB
. Returns 0 if
valueA
> valueB.
(F)
2 D
á
<
2 D
á
<
â
2 D
á
â
â
Less Than or Equal:
listA listB
2 D
á
â
Less Than or Equal:
list value or
value list
LINE(
X1
,
Y1
Xlistname
,
,
X2
LINREG(a+bX)
,
Y2
)
Ylistname
LINREG(aX+b)
Xlistname
,
Ylistname
Applies the test to each element of listA and listB and returns a list.
(F)
Applies the test to each element of list and value and returns a list.
(F)
Draws line from (X1,Y1) to (X2,Y2).
(I)
Fits Xlistname and
Ylistname
to the linear model.
(I)
2 D
á
â
2 F
á
LINE(
â
DRAW
A
CALC
á
LINREG(a+bX)
â
á
LINREG(aX+b)
â
LINREG(a+bX)
Xlistname
,
Ylistname
freqlistname
LINREG(aX+b)
Xlistname
,
Ylistname
,
freqlistname
LN
value
,
Fits Xlistname and
Ylistname
to the linear model with frequency
freqlistname
.
(I)
A
CALC
á
LINREG(a+bX)
â
á
LINREG(aX+b)
â x
LN
list
Returns the natural logarithm of value.
(F)
Returns a list of the natural logarithm for each
list
element.
(F)
x
A-8 Tables and Reference Information
LNREG
Xlistname
,
Ylistname
LNREG
Xlistname
,
Ylistname
,
freqlistname
LOG
LOG
MANSIMP
MAX(
MAX(
MAX(
MAX(
MAX(
valueA list listA list
MEAN(
MEAN(
,
)
,
,
valueB listB value value list list
)
,
,
list
)
)
)
or
)
frequency
)
MEDIAN(
list
)
MEDIAN(
list
,
frequency
)
MIN(
MIN(
value
list
valueA list
)
,
valueB
)
Fits Xlistname and
Ylistname
to the logarithmic model.
(I)
Fits Xlistname and
Ylistname
to the logarithmic model with frequency freqlistname.
(I)
Returns the logarithm of
value
.
(F)
Returns a list of the logarithm for each list element.
(F)
Selects manual simplification mode for fractions.
(I)
A
A
LNREG l l
†
á
á
á
CALC
LNREG
â
CALC
3
â
MANSIMP
â
Returns the larger of
valueA
and valueB.
Returns the largest element in list.
(F)
(F)
Returns a list of the larger of each pair of elements in
listA
and listB.
(F)
2 =
MATH
á
MAX(
â
2 =
MATH
á
MAX(
â
2 =
MATH
á
MAX(
â
Returns a list of the larger of each list element compared to value.
(F)
2 =
MATH
á
MAX(
â
Returns the mean of list.
(F)
Returns the mean of list with frequency frequency.
(F)
2 =
MATH
á
MEAN(
â
2 =
MATH
á
MEAN(
â
Returns the median of
list
(F)
.
(F)
Returns the median of list with frequency frequency.
2 =
MATH
á
MEDIAN(
â
2 =
MATH
á
MEDIAN(
â
Returns the smaller of
valueA
and valueB.
Returns the smallest element in list.
(F)
(F)
2 =
MATH
á
MIN(
â
2 =
MATH
á
MIN(
â
Tables and Reference Information A-9
MIN(
MIN(
MIN(
value list
nCr
listA listA list
,
value
nCr
NDERIV(
variable
,
,
listB
)
Multiplication:
valueA
×
valueB
Multiplication:
value
×
list
or list
×
value
Multiplication:
listA
×
listB valueA
nCr
valueB
nCr
value
NDERIV(
value
,
list
list
listB
)
)
or
expression
variable
,
value value
)
expression
,
ε
)
,
,
Returns a list of the smaller of each pair of elements in listA and
listB
.
(F)
Returns a list of the smaller of each list element compared to
value
.
(F)
Returns valueA times
valueB
.
(F)
Returns a list containing each value times each list element.
(F)
Returns a list of listA elements times listB elements.
(F)
Returns the combinations of valueA (integer
‚ 0) taken valueB (integer
‚ 0) at a time.
(F)
Returns a list of the combinations of value
(integer ‚ 0) taken each element in list (integer
‚
0) at a time.
(F)
Returns a list of the combinations of each element (integer ‚ 0) in list taken value (integer ‚ 0) at a time.
(F)
Returns a list of the combinations of each element (integer ‚ 0) in
listA
taken each element in listB (integer ‚0) at a time.
(F)
Returns the approximate numerical derivative of
expression
with respect to variable at value.
ε
is
1 íL3.
(F)
Returns the approximate numerical derivative of
expression
with respect to variable at value, with a specified
ε
.
(F)
2 =
MATH
á
MIN(
â
2 =
MATH
á
MIN(
â p p p
I
PRB
á nCr
â
I
PRB
á nCr
â
I
PRB
á nCr
â
I
PRB
á nCr
â
I
MATH
á
NDERIV(
â
I
MATH
á
NDERIV(
â
A-10 Tables and Reference Information
Negation:
Negation:
list
nPr
ëvalue
ëlist
value
Returns the negative of
value
.
(F)
Returns a list with each
list
element negated.
(F)
·
·
NORMAL
Not Equal: valueA
ƒvalueB
Returns 1 if valueA
ƒ
valueB
. Returns 0 if
valueA
= valueB.
(F)
Not Equal: listA ƒlistB
Sets normal display mode.
(I)
Applies the ƒ test to each element of listA and listB and returns a list.
(F)
Not Equal: list ƒvalue or
value ƒlist
†
3
á
NORMAL
â
2 D
á
ƒ
â
2 D
á
ƒ
â
2 D
á
ƒ
â
valueA value
nPr nPr
valueB
list
Applies the ƒ test to each element of list and value and returns a list.
(F)
Returns a list of the permutations of valueA
(integer
≥
0) taken valueB
(integer
≥
0) at a time.
(F)
Returns a list of the permutations of value
(integer
≥
0) taken each element in list (integer
≥
0) at a time.
(F)
I
á nPr
I
á nPr
â
â
PRB
PRB
I
PRB
á nPr
â
listA
nPr
listB
Returns a list of the permutations of each element (integer
≥
0) in list taken value (integer
≥
0) at a time.
(F)
Returns a list of the permutations of each element (integer
≥
0) in
listA
taken each element in listB (integer
≥
0) at a time.
(F)
I
á nPr
â
PRB
1-VAR STATS
listname
A
CALC
á
1-VAR STATS
â
1-VAR STATS
freqlistname
PARAM
Xlistname
,
Performs one-variable analysis using listname and a frequency of 1.
(I)
Performs one-variable analysis using Xlistname and frequency
freqlistname
.
(I)
Sets parametric graphing mode.
A
†
á
á
CALC
1-VAR STATS
3
PARAM
â
â
Tables and Reference Information A-11
PAUSE
Pi
PLOT
n
(
type
,
Xlist
,
Ylist
)
PLOT
n
(
type
,
Xlist
,
Ylist
,
mark
)
PLOT
n(type
,
Xlist
)
or
PLOT
n
(
type
,
Xlist
,
Flist
)
PLOTSOFF
PLOTSOFF
plot#
,
plot#
. . .
PLOTSON
PLOTSON
plot#
,
plot#
. . .
Power: value
^
power
Power: list
^
power
Power: value
^
list
Power: listA
^
listB
Power of ten:
10^
power
Power of ten:
10^
list
Suspends execution of the program until
¸ is pressed.
(I)
Returns the value of
π rounded to 13 digits.
(F)
†
á
K
PAUSE
2 T
CTL
â
Plots stat plot n (1
-3) of
type
(
¼ or ½) for Xlist and Ylist coordinate pairs.
†
2 "
á
PLOT
n
â
Plots stat plot n (1
-3) of
type
(
¼ or ½) for Xlist and Ylist coordinate pairs with the specified type of
mark
.
(I)
Plots stat plot n (1
-3) of
type
(
¾
or
¿
,) for Xlist with frequency Flist. If
Flist
is omitted, frequency
= 1.
(I)
†
2 "
á
PLOT
n
â
†
2 "
á
PLOT
n
â
Deselects all stat plots.
(I)
2 "
á
PLOTSOFF
â
Deselects stat plot1, plot2, or plot3.
(I)
Selects all stat plots.
(I)
2 "
á
PLOTSOFF
â
2 "
á
PLOTSON
â
Selects stat plot1, plot2, or
plot3.
(I)
Returns value raised to
power
.
(F)
2 "
á
PLOTSON
â
Z
Returns a list of each element raised to the value of power.
(F)
Z
Returns a list of value raised to the power of each list element.
(F)
Returns 10 raised to the value of power.
(F)
Z
Returns a list of each listA element raised to the power of each listB element.
(F)
Z
2 h
Returns a list of 10 raised to the power of each list element.
(F)
2 h
A-12 Tables and Reference Information
PRGM_
programname
PROD
list
P 8 Rx(
R
,
q
)
P
P
P
P
P
P
P
8
8
8
8
8
8
8
PT
Rx(
Rx(
Rx(
Ry(
Ry(
Ry(
Ry(
-
Rlist
R
Rlist
R
R
,
,
,
qlist q
)
Rlist
Rlist
,
,
,
,
q q
)
)
)
qlist qlist qlist
CHANGE(
PT OFF(
X
,
Y
)
PT
-
ON(
X
,
Y
)
)
X
,
)
)
Y
)
Executes the program
programname
.
(I)
Returns the product of elements in list.
(F)
†
K
CTRL
á
PRGM_(
â
2 =
MATH
á
PROD
â
2 E
á
P 4 Ry(
â
Returns the rectangular coordinate
x
, given the polar coordinates R and q.
(F)
Returns a list of
x
coordinates, given the R coordinates in Rlist and a single q.
(F)
2 E
á
P 4 Ry(
â
Returns a list of
x
coordinates, given the single R coordinate and the q coordinates in qlist.
(F)
Returns a list of
x
coordinates, given the R and q coordinates in Rlist and qlist.
(F)
Returns rectangular coordinate
y
, given polar coordinates R and q.
(F)
Returns a list of
y
coordinates, given the R coordinates in Rlist and a single q coordinate.
(F)
Returns a list of
y
coordinates, given a single
R
coordinate and the q coordinates in qlist.
(F)
Returns a list of
y
coordinates, given the R coordinates in Rlist and the q coordinates in qlist.
(F)
Toggles the point at (X,Y).
(I)
Erases the point at (X,Y).
(I)
Draws the point at (X,Y).
(I)
2 E
á
P 4 Ry(
â
2 E
á
P
4
Ry(
â
2 E
á
P
4
Ry(
â
2 E
á
P
4
Ry(
â
2 E
á
P 4 Ry(
â
2 E
á
P 4 Ry(
â
2 F
POINTS
á
PT
-
CHANGE(
â
2 F
POINTS
á
PT
-
OFF(
â
2 F
POINTS
á PT-ON(
â
Tables and Reference Information A-13
PWRREG
PWRREG
Xlistname
Ylistname
Xlistname
Ylistname
QUADREG
Ylistname
QUADREG
Ylistname
,
,
,
freqlistname
Xlistname
Xlistname
,
,
,
freqlistname
Fits Xlistname and
Ylistname
to the power model.
(I)
Fits Xlistname and
Ylistname
to the power model with frequency
freqlistname
.
(I)
Fits Xlistname and
Ylistname
to the quadratic model.
(I)
Fits Xlistname and
Ylistname
to the quadratic model with frequency freqlistname.
(I)
Sets radian mode.
(I)
A
A
á
á
á
PWRREG
CALC
PWRREG
A
QUADREG
A
á
CALC
CALC
CALC
â
â
QUADREG
â
â
RADIAN
Radian Notation: value
RAND r
Interprets value as an angle in radians.
Returns a random number between 0 and 1.
(F)
RANDINT(
upper
)
lower
,
Returns a random integer between lower and upper.
(F)
RANDINT(
lowerlist
,
upper
)
Returns a list of random integers between each element of lowerlist and
upper
.
(F)
RANDINT(
lower
,
upperlist
)
Returns a list of random integers between lower and each element of
upperlist
.
(F)
RANDINT(
lowerlist
,
upperlist
)
Returns a list of random integers between each element of lowerlist and
upperlist
.
(F)
REMAINDER(
valueA
,
valueB
)
Returns the remainder from the division of
valueA
by valueB
REMAINDER(
value
,
list
)
Returns a list of remainders from the division of value by each element in list.
†
3
á
RADIAN
â
2 E
á
r
â
I
PRB
á
RAND
â
I
PRB
á
RANDINT(
â
I
PRB
á
RANDINT(
â
I
PRB
á
RANDINT(
â
I
PRB
á
RANDINT(
â
I
NUM
á
REMAINDER(
â
I
á
NUM
REMAINDER(
â
A-14 Tables and Reference Information
REMAINDER(
value
)
REMAINDER(
listB
)
list
,
listA
,
Return
nthroot
x
‡value
nthroot
x
‡list
list
x
‡value
listA
x
‡listB
ROUND(
value
)
ROUND(
value
,
#decimals
)
ROUND(
list
)
ROUND(
list
,
#decimals
)
R
R
R
8
8
8
Pr(
Pr(
Pr(
X
Xlist
X
,
,
Y
)
,
Y
Ylist
)
)
Returns a list of remainders from the division of each element in list by value.
I
á
NUM
REMAINDER(
Returns a list of remainders from the division of each element in listA by the each element in listB.
I
á
NUM
REMAINDER(
Returns to the calling program.
(F)
(I)
Returns nthroot of value.
Returns a list of nthroot for each list element.
Returns list roots of
value
.
(F)
Returns a list of listA roots of listB.
(F)
(F)
Returns value rounded to
10 digits.
(F)
Returns value rounded to
#decimals (
9).
(F)
Returns list elements rounded to 10 digits.
(F)
Returns list elements rounded to #decimals
(
9).
(F)
Returns the polar coordinate
r
, given the rectangular coordinates X and Y.
(F)
2 E
á
R
4
P q
(
â
Returns a list of
r
coordinates, given the X coordinates in Xlist and a single Y coordinate.
(F)
Returns a list of
r
coordinates, given a single
X
coordinate and the Y coordinates in Ylist.
(F)
2 E
á
R 4 P q (
â
2 E
á
R 4 P q (
â
†
K
CTL
á
RETURN
â
I
MATH
á x ‡â
I
MATH
á x ‡
â
I
MATH
á x
‡
â
I
MATH
á x ‡
â
I
NUM
á
ROUND(
â
I
NUM
á
ROUND(
â
I
NUM
á
ROUND(
â
I
NUM
á
ROUND(
â
â
â
Tables and Reference Information A-15
R
R
R
R
R
8
8
8
8
8
Pr(
P
P
P
P q q q q (
(
(
(
Xleft
Xlist
X
)
,
Y
)
Xlist
X
,
Ylist
Xlist
,
,
,
Ylist lowerfunc
upperfunc
Y
,
)
)
Ylist
)
)
SCI seq(
expression
,
variable
,
begin
,
end
,
increment
) sequential
SHADE(
lowerfunc
,
upperfunc
)
SHADE(
SHADE(
lowerfunc
upperfunc
,
,
resolution
,
resolution
)
,
Returns a list of
r
coordinates, given the X coordinates in Xlist and the Y coordinates in Ylist.
(F)
2 E
á
R
4
P q
(
â
2 E
á
R 4 P q (
â
Returns the polar coordinate
q, given the rectangular coordinates X and Y.
(F)
Returns a list of
q
coordinates, given the X coordinates in Xlist and a single Y coordinate.
(F)
Returns a list of
q
coordinates, given a single
X
coordinate and the Y coordinates in Ylist.
(F)
2 E
á
R 4 P q (
2 E
á
R 4 P q (
â
â
Returns a list of coordinates in Xlist and the Y coordinates in Ylist.
(F) q
coordinates, given the X
2 E
á
R 4 P q (
â
Sets scientific display mode.
(I)
Returns a list created by evaluating expression for
variable
, from begin to
end
by increment.
(F)
†
3
á
SCI
â y ã
LIST
ä
OPS
á seq(
â
Sets sequential graphing mode.
(F)
Shades the area above
lowerfunc
and below
upperfunc
.
(I)
† 3
á sequential
â
2 F
DRAW
á
SHADE(
â
2 F
DRAW
á
SHADE(
â
Shades the area above
lowerfunc
, below
upperfunc
, and with
resolution
(1 through 9).
(I)
Shades the area above
lowerfunc
, below
upperfunc
, to right of
X
=Xleft, and with
resolution
(1 through 9).
(I)
2 F
á
SHADE(
â
DRAW
A-16 Tables and Reference Information
SHADE(
upperfunc
Xleft
,
lowerfunc
,
Xright
)
,
resolution
,
Shades the area above
lowerfunc
, below
upperfunc
, to right of
X
=Xleft, to left of
X
=Xright, and with
resolution
(1 through 9).
(I)
2 F
á
SHADE(
â
DRAW
SHADE_Y>
func1
,
func2
,
. . .
Shades the area above
func1
with vertical pattern and above func2 with diagonal pattern
(lower left to upper right), etc.
(I)
2 F
á
DRAW
SHADE_Y>
â
(
SHADE_Y<
func3
,
func4
,
. . .
Shades the area below
func3
with horizontal pattern and below func4 with diagonal pattern
(upper left to lower right), etc.
(I)
fraction fraction
SIMUL
SIN
ú
value
,
SIMP
factor
)
ú
SIMP
Sets simultaneous graphing mode.
(I)
Returns the sine of value.
(F)
2 F
á
Simplifies fraction by its lowest common factor.
(F)
Simplifies fraction by the specified factor, which must be an integer.
(F)
J
á
SIMP
â
J
á
SIMP
â
†
3
á
SIMUL
â
W
DRAW
SHADE_Y<
â
SIN
list W
SIN
ê value
Returns a list of the sine for each list element.
(F)
Returns the arcsine of
value
.
(F)
2 ã
SIN
– 1
ä
SIN
ê list
2 ã
SIN
– 1
ä
SORTA(
SORTA(
listname
dependlist1
,
)
keylistname
dependlist2
,
. . .
)
,
Returns a list of the arcsine for each list element.
(F)
Sorts listname elements in ascending order.
(I)
Sorts the elements of
keylistname
in ascending order with dependlist1,
dependlist2
. . . as dependent lists.
(I)
2 =
á
SORTA(
OPS
â
2 =
OPS
á
SORTA(
â
Tables and Reference Information A-17
SORTD(
listname
)
SORTD(
keylistname
,
dependlist1
,
dependlist2
,
. . .
)
Square: value ñ
Square: list ñ
Square Root:
‡value
Square Root:
STOP
‡list
Store: value !variable
Store: list !listname
Store:
"
expression
"
!Yn or
"
expression
"
!XnT or
"
expression
"
!YnT
Subtraction:
valueA
ìvalueB
Subtraction:
value ìlist
Subtraction:
list ìvalue
Subtraction:
listA ìlistB
SUM
list
TAN
value
Sorts the elements of
listname
in descending order.
(I)
Sorts the elements of
keylistname
in descending order with
dependlist1
,
dependlist2
. . . as dependent lists.
(I)
2 =
á
SORTD(
2 =
á
SORTD(
OPS
OPS
â
â
Returns value multiplied by itself.
(F)
Returns a list of each list element squared.
(F)
Returns the square root of
value
.
(F)
a a
2 ]
Returns a list of the square roots of each list element.
(F)
2 ]
Stops program execution and returns to the Home screen.
(I)
†
á
K
STOP
Stores value to variable.
(I)
§
Stores list to listname.
(I)
§
Stores expression to Yn
XnT
or YnT function.
(I)
§
â
CTL
Subtracts valueB from
valueA
.
(F)
Subtracts list elements from value and returns a list.
(F)
Subtracts value from list elements and returns a list.
(F)
Subtracts each listB element from each listA element and returns a list.
(F)
Returns the sum of elements in list.
(F)
Returns the tangent of
value
.
(F)
|
|
|
|
2 =
MATH
á
SUM
â
Y
A-18 Tables and Reference Information
TAN
TAN
TAN
list
ê value
ê list
Returns a list of the tangent for each list element.
(F)
Returns the arctangent of
value
.
(F)
Returns a list of the arctangent for each list element.
(F)
Y
2 S
2 S
THEN
See
IF:THEN
TRACE
2-VAR STATS
Xlistname
,
Ylistname
2-VAR STATS
Xlistname
,
Ylistname
,
freqlistname
VERTICAL
ZBOX
ZDECIMAL
ZOOM IN
ZOOM OUT
ZSQUARE
ZSTANDARD
ZTRIG
X
Displays a graph and enters Trace mode.
(I)
Performs two-variable analysis using Xlistname and Ylistname.
(I)
Performs two-variable analysis using Xlistname and Ylistname with frequency freqlistname.
(I)
Draws a vertical line at value X.
(I)
Displays a graph to allow the user to define new viewing window.
(I)
Displays a graph in new viewing window.
(I)
Displays a graph in new viewing window.
(I)
Displays a graph in new viewing window.
(I)
Displays a graph in new viewing window.
(I)
Displays a graph in new viewing window.
(I)
Displays a graph in new viewing window.
(I)
† +
A
CALC
á
2-VAR STATS
â
A
CALC
á
2-VAR STATS
â
2 F
DRAW
á
VERTICAL
â
†
*
á
ZBOX
â
†
*
á
ZDECIMAL
â
†
*
á
ZOOM IN
â
†
*
á
ZOOM OUT
â
†
*
á
ZSQUARE
â
†
*
á
ZSTANDARD
â
†
*
á
ZTRIG
â
Tables and Reference Information A-19
TI-80 Menu Map
Menus begin in the upper left of the keyboard. Default values are shown.
(
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(
FUNC
Y1=
Y2=
Y3=
Y4=
mode) (
PARAM
mode)
X
ã
T
=
Y
ã
T
=
X
ä
T
=
Y
ä
T
=
X
å
T
=
Y
å
T
=
)
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(FUNC mode)
WINDOW
XMIN=
ì10
XMAX=10
XSCL=1
YMIN=
ì10
YMAX=10
YSCL=1
(
PARAM
WINDOW
TMIN=0
mode)
TMAX=2 p
TSTEP= pà24
XMIN=
ì10
XMAX=10
XSCL=1
YMIN=
ì10
YMAX=10
YSCL=1
2 [
TblSet
]
ÚÄÄÙ
TABLE SETUP
TBLMIN=0
@TBL=1
3
ÚÄÙ
NORMAL SCI
FLOAT 0123456789
RADIAN DEGREE a
Àbºc bºc
AUTOSIMP MANSIMP
FUNC PARAM
CONNECTED DOT
SEQUENTIAL SIMUL
*
ÚÄÙ
ZOOM
1:ZBOX
2:ZOOM IN
3:ZOOM OUT
4:ZDECIMAL
5:ZSQUARE
6:ZSTANDARD
7:ZTRIG
3 (in program editor)
ÚÄÙ
MODE
1:NORMAL
2:SCI
3:FLOAT
4:FIX
5:RADIAN
6:DEGREE
7:a
Àbºc
8:bºc
9:AUTOSIMP
0:MANSIMP
A:FUNC
B:PARAM
C:CONNECTED
D:DOT
E:SEQUENTIAL
F:SIMUL
A-20 Tables and Reference Information
2 "
ÚÄÄÄÄÄÙ
STAT PLOTS
1:PLOT1
...
OFF
¼ L1 L2 Â
2:PLOT2
...
OFF
¼ L1 L2 Â
3:PLOT3
...
OFF
¼ L1 L2 Â
4:PLOTSOFF
5:PLOTSON
Screen for
¾ or ¿ plots
(1-variable plots)
PLOTn
ON OFF
TYPE:
¼ ½ ¾ ¿
XL: L1L2L3L4L5L6
F: 1L1L2L3L4L5L6
Screen for
¼ or ½ plots
(2-variable plots)
PLOTn
ON OFF
TYPE:
¼ ½ ¾ ¿
XL: L1L2L3L4L5L6
YL: L1L2L3L4L5L6
MARK:
 + ¦
2 " (in program editor)
ÚÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄ¿
PLOTS
1:PLOT1(
2:PLOT2(
3:PLOT3(
4:PLOTSOFF
5:PLOTSON
TYPE
1:
¼
2:
½
3:
¾
4:
¿
MARK
1:
Â
2:+
3: ¦
A
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄ¿
EDIT
1:EDIT ...
2:SORTA(
3:SORTD(
4:CLRLIST
CALC
1:1-VAR STATS
2:2-VAR STATS
3:LINREG(aX+b)
4:QUADREG
5:LINREG(a+bX)
6:LNREG
7:EXPREG
8:PWRREG
Tables and Reference Information A-21
2 =
ÚÄÄÁÄÄÄÄÄÄÄÄÄ¿
OPS
1:SORTA(
2:SORTD(
3:DIM
4:SEQ(
MATH
1:MIN(
2:MAX(
3:MEAN(
4:MEDIAN(
5:SUM
6:PROD
I
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
MATH
1:INT
÷
2:
4DEC
3:
3
4:
5:
3
X
‡
‡
6:NDERIV(
NUM
1:ROUND(
2:IPART
3:FPART
4:INT
5:MIN(
6:MAX(
7:REMAINDER(
PRB
1:RAND
2:nPr
3:nCr
4:!
5:RANDINT(
J
ÚÙ
FRACTION
1: 4SIMP
2: 4b
ºc
3: 4a
Àbºc
4:
4FRAC
5:
4DEC
2 D
ÚÄÄÄÄÙ
TEST
1:=
2: ƒ
3:>
4:
‚
5:<
6:
2 E
ÚÄÄÄÄÙ
ANGLE
1: ¡
2: r
3:R 4Pr(
4:R
4Pq(
5:P
4Rx(
6:P
4Ry(
A-22 Tables and Reference Information
K
ÚÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄ¿
EXEC
1:name
2:name
3:name
©
EDIT
1:name
2:name
3:name
©
NEW
1:CREATE NEW
K (in program editor)
ÚÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
CTL
1:IF
2:THEN
3:ELSE
4:FOR(
5:END
6:PAUSE
7:LBL
8:GOTO
9:PRGM_
0:RETURN
A:STOP
I/O
1:INPUT
2:DISP
3:DISPGRAPH
4:CLRHOME
EXEC
1:name
2:name
3:name
©
2 F
ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄ¿
DRAW
1:CLRDRAW
2:LINE(
3:HORIZONTAL
4:VERTICAL
5:DRAWF
6:SHADE_Y>
7:SHADE_Y<
POINTS
1:PT-ON(
2:PT-OFF(
3:PT-CHANGE(
8:SHADE(
9:GRIDON
0:GRIDOFF
Tables and Reference Information A-23
L
ÚÄÙ
VARS
1:WINDOW
...
2:STATISTICS
…
3:TABLE…
4:SIMPFACTOR…
L á
WINDOW…
â
ÚÄÄÄÄÄÄÁÄÄÄÄÄ¿
X/Y
1:XMIN
T
1:TMIN
2:XMAX
3:XSCL
4:YMIN
5:YMAX
6:YSCL
7: @X
8: @Y
9:XFACT
0:YFACT
2:TMAX
3:TSTEP
L á
STATISTICS…
â
ÚÄÄÄÄÄÄÁÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄ¿
X/Y
1:n
2: v
3:Sx
4: sx
5: w
6:Sy
G
1: GX
2: GX
ñ
3: GY
4: GY
ñ
5: GXY
EQ
1:a
2:b
3:c
4:r
5:REGEQ
BOX
1:Q
ã
2:MED
3:Q
å
7: sy
8:MINX
9:MAXX
0:MINY
A:MAXY
2 G
ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
Y
1:Y1
2:Y2
3:Y3
4:Y4
XT/YT
1:X
ã
T
2:Y
ã
T
3:X
ä
T
4:Y
ä
T
3:X
å
T
4:Y
å
T
ON/OFF
1:FNON
2:FNOFF
L á
TABLE…
â
ÚÄÄÄÄÄÄÙ
TABLE
1:TBLMIN
2:
@TBL
L á
SIMPFACTOR…
â
ÚÄÄÄÄÙ
SIMPFACTOR
1:FACTOR
A-24 Tables and Reference Information
2 ¯
ÚÄÙ
MEMORY
1:CHECK RAM…
2:DELETE…
3:RESET…
2 ¯ á
CHECK RAM…
â
ÚÄÄÄÄÙ
MEM FREE 7014
REAL 14
LIST 0
Y-VARS 80
PRGM 14
2 ¯ á
DELETE…
â
ÚÄÄÄÄÄÄÙ
DELETE:
úname memory
name memory
name memory
© ©
2 ¯ á
1:NO
2:RESET
RESET…
ÚÄÄÄÄÄÄÙ
â
(names include defined programs, lists,
Y=
equations, and user variables, in that order.)
Resetting memory erases all data and programs.
Tables and Reference Information A-25
TI-80 Variables
The variables listed below are used by the TI
-
80 in various ways. Some have restrictions on their use.
User Variables
System
Variables
The variables
A
through
Z
and q can hold only numbers— either decimals or fractions. You may store to these variables.
The TI
-80 can update
X
,
Y
, and
T
during graphing; therefore, you may wish to reserve those variables for graphing activities.
The variables
L
ã through
L6
are defined as lists. You cannot store another type of data to them.
You can store any string of characters, functions, instructions, or variable names to the functions
Y
n
(in
FUNC
mode) and
X
n
î and
Y
n
î (in
PARAM
mode), by using either
§ or the
Y=
editor. The validity of the string is determined when the function is evaluated.
The values of the Window variables
XMIN
,
XMAX
,
XSCL
,
@
X
,
TSTEP,
etc.
must be real numbers. You may store to them. Since the TI
-80 can update some of them, as the result of a Zoom instruction, for example, you may wish to reserve these variables for graphing activities.
The statistical result variables
n
, v,
MINX
,
G X
,
a
,
r
,
REGEQ
,
X1
,
Y1
,
Q1
,
MED
,
Q3
, etc.
are reserved for use by the TI
-80.
You cannot store to them.
A-26 Tables and Reference Information
Appendix B: Service and Warranty Information
This appendix provides supplemental information that may be helpful as you use the TI .
80. It includes procedures that may help you correct problems with the calculator.
Appendix
Contents
Battery Information
...............................
Accuracy Information
.............................
In Case of Difficulty
...............................
Error Conditions
..................................
Service and Support Information
...................
Warranty Information
..............................
Service and Warranty Information B-1
Battery Information
The TI
.
80 uses two CR2032 lithium 3-volt batteries.
When to Replace the Batteries
Battery
Precautions
As you use the TI
.80, the battery voltage will gradually drop, and the display will dim. You can adjust the contrast to darken the display when this happens. If the display is dim and adjusting the contrast to level 9 does not make it dark enough, you should replace the batteries. Refer to pages B -3 through
B -7 for instructions on how to change the batteries.
Follow these safety guidelines concerning batteries.
¦
Do not mix new and used batteries.
¦
Do not mix different types of batteries.
¦
Follow polarity diagrams carefully.
¦
Do not replace batteries with rechargeable batteries.
¦
Do not place non-rechargeable batteries in a battery charger.
¦
Properly dispose of used batteries immediately. Do not leave them within the reach of small children.
¦
Do not incinerate used batteries.
Retaining Stored
Data
Caution:
The TI
-80 retains stored data when you are changing batteries only if you:
¦
Do not remove both batteries at the same time. (At least one battery must be installed at all times in order to retain memory.)
¦
Turn the unit off and do not turn it back on until you have changed the batteries.
¦
Do not allow the batteries to run down completely before changing them.
Follow the steps on pages B -3 through B-7 when changing batteries.
B-2 Service and Warranty Information
Changing the
Batteries
(Continued)
To change the batteries, first: a. Turn the calculator off. b. Replace the plastic slide cover over the keys.
c. Turn the calculator so that the back is facing you.
Placing your thumb on the ridged area of the plastic battery compartment cover, push down slightly and slide the cover to the right until you can lift off the cover.
Push the red switch up to free the metal battery cover over the lower battery.
Service and Warranty Information B-3
Changing the
Batteries
(Continued)
Slide the metal battery cover away from the battery. The battery pops up.
Remove the old battery. Insert a new battery, positive side (+) up.
Hold the new battery in place and slide the metal battery cover back into position over the battery.
B-4 Service and Warranty Information
Changing the
Batteries
(Continued)
Push the red switch all the way down to free the metal battery cover over the upper battery.
Slide the metal battery cover away from the battery.
Remove the old battery. Insert a new battery, positive side (+) up.
Service and Warranty Information B-5
Changing the
Batteries
(Continued)
Hold the new battery in place and slide the metal battery cover back into position over the battery.
Push the red switch to its center position to lock the metal covers and batteries into place.
Note:
The calculator will not turn on unless the red switch is in the center position.
B-6 Service and Warranty Information
Changing the
Batteries
(Continued)
Replace the plastic battery compartment cover. Turn the calculator on and adjust the contrast display.
To adjust the display contrast, press and release the
2 key.
To increase the contrast (darken the screen), press and hold
7. To decrease the contrast (lighten the screen), press and hold
8.
Service and Warranty Information B-7
Accuracy Information
To maximize accuracy, the TI
.
80 carries more digits internally than it displays.
Computational
Accuracy
Graphing
Accuracy
Values in memory are stored using up to 13 digits with a two-digit exponent.
¦
You can store values in the Window variables using up to
10 digits (13 digits for
XSCL
,
YSCL
, and
TSTEP
).
¦
When a value is displayed, the displayed value is rounded as specified by the
MODE
setting (Chapter 1), with a maximum of 10 digits and a two-digit exponent.
¦
REGEQ
displays up to 13 digits.
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.
¦
@ X
is calculated as
(XMAX–XMIN) à 62
.
¦
If
@ X
is entered from the Home screen or a program, then
XMAX
is calculated as
XMIN+ @ X
×
62
.
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.
¦
@
Y
is calculated as
(YMAX
.
YMIN)
à
46
.
¦
If
@
Y
is entered from the Home screen or a program, then
YMAX
is calculated as
YMIN+
@
Y
×
46
.
Cursor coordinates are displayed as six characters, which may include a negative sign, decimal point, and exponent.
B-8 Service and Warranty Information
Function
Limits
Following is a table of functions and the range of input values for each.
Function
SIN
x, COS x, TAN x
SIN-
1
x, COS-
1
x
LN
x, LOG x e
x
10
x
‡x
x
!
Input Values
0
| x | < 10
10
(degree)
-1 x 1
10-
100
< x < 10
100
-10
100
< x
230.2585092993
-10
100
< x < 100
0
x < 10
100
0
x 69, where x is an integer
Function Results
Following is a table of functions and the range of the result for each.
Function
SIN-
1
x, TAN-
1
x
COS-
1
x
Range of Result
-90¡ to 90¡ or -pà2 to pà2 (radians)
0 ¡ to 180¡ or 0 to p (radians)
Service and Warranty Information B-9
In Case of Difficulty
If you have difficulty operating the calculator, the following suggestions may help you to correct the problem.
Handling a
Difficulty
Follow these procedures if you have difficulties.
1. If you cannot see anything on the display, perhaps the display contrast needs adjusting.
Press and release the
2 key. To increase the contrast
(darken the screen), press and hold
7. To decrease the contrast (lighten the screen), press and hold
8.
You will find additional information on display contrast on page 1
-3.
2. If after adjusting the display contrast, the calculator does not appear to be working at all, be sure the batteries are installed properly and that they are fresh. Refer to “Battery
Information” beginning on page B
-2 for more details.
Note:
Make sure the red switch in the battery compartment is in the center position.
3. If an error occurs, follow the procedure on page 1
-22.
Refer to the more detailed explanations about specific errors beginning on page B
-11, if necessary.
4. If the cursor is a checker-board pattern, memory is full.
Press
2 ¯
DELETE...
and delete some items from memory. See Chapter 12 for additional information about memory management.
5. If the dotted-line busy indicator is displayed, a graph or program is paused, and the TI -80 is waiting for input.
Press ¸ to continue or ´ to break.
B-10 Service and Warranty Information
Error Conditions
When the TI
.
80 detects an error, it displays ERR: message and the error menu.
The general procedure for correcting errors is described on page 1
.
22. The error messages, their possible causes, and suggestions for correction are shown below.
ARGUMENT
BREAK
DATA TYPE
DIM MISMATCH
DOMAIN
A function or instruction does not have the correct number of arguments. See Appendix A and the appropriate chapter.
You have pressed the
´ key to break execution of a program, halt a Draw instruction, or stop evaluation of an expression.
You have entered a value or variable that is the wrong data type.
¦
A function (including implied multiplication) or an instruction has an argument that is an invalid data type; for example, a list where a real number is required. See
Appendix A and the appropriate chapter.
¦
You are attempting to store to an incorrect data type; for example, a list to a real variable.
¦
In function graphing or parametric graphing, you have generated a list result rather than a single value; for example, attempting to graph
Y
ã
={1,2,3}
×
X
.
You are attempting to perform an operation that uses more than one list, but the dimensions do not match.
Typically, this occurs when the value of an argument does not fall within a specified range.
¦
You are attempting to divide by zero.
¦
You are attempting a logarithmic or power regression with a
L
X
or an exponential or power regression with a
L
Y
.
¦
A zero value for
ε
for
NDERIV(
will result in this error.
This error does not occur during graphing because the
TI
-80 allows for undefined values on a graph.
Service and Warranty Information B-11
INCREMENT
INVALID
INVALID DIM
LABEL
MEMORY
MODE
NEST LEVEL
OVERFLOW
¦
The increment in
SEQ(
is
0
or has the wrong sign. This error does not occur during graphing. The TI -80 allows for undefined values on a graph.
¦
The increment in
FOR(
is
0
or has the wrong sign.
You are attempting to reference a variable or use a function in a place where it is not valid. For example,
Y n
cannot reference
Y
,
XMIN
,
@ X
, or
TBLMIN
.
¦
The dimension of the argument is not appropriate for the operation.
¦
List element dimensions must be integers between 1 and
99; for example,
L1(100)
will cause an error.
The label in the
GOTO
instruction is not defined with a
LBL
instruction in the program.
¦
There is insufficient memory in which to perform the desired command. You must delete item(s) from memory
(Chapter 12) before executing this command.
¦
Using an
IF
/
THEN
or
FOR(
with a
GOTO
that branches out of the loop can also cause this error because the
END
statement that terminates the loop is never reached.
You are attempting a
ú
SIMP
in
AUTOSIMP
mode.
This error occurs when any nested combination of function evaluation,
NDERIV(
or
SEQ(
exceeds 5 levels.
You are attempting to enter, or you have calculated, a number that is beyond the range of the calculator. This error does not occur during graphing. The TI
-80 allows for undefined values on a graph.
B-12 Service and Warranty Information
STAT
STAT PLOT
¦
You are attempting a linear regression with a vertical line.
¦
Statistical analyses must have at least two data points;
QUADREG
must have at least three data points.
¦
The list of
s
(frequency) elements must be
≥
0, and at least one
F
value must be
≥
0.
¦
The frequency list, when used for “sorting” statistics
(median,
Q
ã
,
Q
å
, or boxplot), must be an integer
≥
0 and
99.
¦
(XMAX
.
XMIN)
à
XSCL
must be 31 for a histogram.
You are trying to display a graph when there is a statistical plot turned on that uses an undefined list.
SYNTAX
The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. See Appendix
A and the appropriate chapter.
UNDEFINED
You are attempting to reference a variable that is not currently defined. For example, a statistical variable , which has no current value because a list has been edited, has been referenced.
WINDOW RANGE
There is a problem with the Window variables.
¦
You may have defined
XMAX
XMIN
,
YMAX
YMIN
,
TSTEP=0
, or
TMAX
TMIN
and
TSTEP>0
(or vice versa).
¦
The Window variables are too small or too large to graph correctly. This can occur if you attempt to zoom in or out so far that you are not within the numerical range of the calculator.
ZOOM
A point or a line, rather than a box, is defined in
ZBOX
; or a math error has resulted from a Zoom operation.
Service and Warranty Information B-13
Support and Service Information
Product Support
Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands
For general questions, contact Texas Instruments Customer Support: phone: e-mail:
1
.
800
.
TI
.
CARES (1
.
800
.
842
.
2737) [email protected]
For technical questions, call the Programming Assistance Group of Customer
Support: phone:
1
.
972
.
917
.
8324
Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands
Contact TI by e-mail or visit the TI
calculator
home page on the World Wide Web.
e-mail:
Internet:
education.ti.com
Product Service
Customers in the U.S. and Canada Only
Always contact Texas Instruments Customer Support before returning a product for service.
Customers outside the U.S. and Canada
Refer to the leaflet enclosed with this product or contact your local Texas
Instruments retailer/distributor.
Other TI Products and Services
Visit the TI
calculator
home page on the World Wide Web.
education.ti.com
Refer to the leaflet enclosed with this product or contact your local Texas
Instruments retailer/distributor.
B–14 Service and Warranty Information
99APXB2.DOC TI-80, Service & Waranty Bob Fedorisko Revised: 02/15/01 11:34 AM Printed: 02/15/01
11:36 AM Page 14 of 3
Warranty Information
Customers in the U.S. and Canada Only
One-Year Limited Warranty for Electronic Product
This Texas Instruments (“TI”) electronic product warranty extends only to the original purchaser and user of the product.
Warranty Duration.
This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date.
Warranty Coverage.
This TI electronic product is warranted against defective materials and construction.
THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN
DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER
SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS
OR CONSTRUCTION.
Warranty Disclaimers.
ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE,
INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED
IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL
NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL
OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE
CONSUMER OR ANY OTHER USER.
Some states/provinces do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you.
Legal Remedies.
This warranty gives you specific legal rights, and you may also have other rights that vary from state to state or province to province.
Warranty Performance.
During the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality (at TI’s option) when the product is returned, postage prepaid, to Texas
Instruments Service Facility. The warranty of the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer.
Other than the postage requirement, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value prior to mailing.
Software.
Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is
provided “AS IS.”
Copyright.
The software and any documentation supplied with this product are protected by copyright.
Service and Warranty Information B-15
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed:
02/27/01 12:25 PM Page 12 of 13
Australia & New Zealand Customers only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product.
Warranty Duration.
This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date.
Warranty Coverage.
This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or construction.
Warranty Disclaimers. Any implied warranties arising out of this sale, including but not limited to the implied warranties of merchantability and fitness for a particular purpose, are limited in duration to the above one-year period. Texas Instruments shall not be liable for loss of use of the product or other incidental or consequential costs, expenses, or damages incurred by the consumer or any other user.
Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from jurisdiction to jurisdiction.
Warranty Performance.
During the above one (1) year warranty period, your defective product will be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TI’s option) when the product is returned to the original point of purchase. The repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to return the product, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value if you mail it.
Software.
Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements.
All software is provided “AS IS.”
Copyright.
The software and any documentation supplied with this product are protected by copyright.
All Customers Outside the U.S. and Canada
For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas
Instruments retailer/distributor.
B-16 Service and Warranty Information
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed:
02/27/01 12:25 PM Page 13 of 13
Index
A
a
a
À
b
º
c MODE
8 a
À
b
º
c
ABS
ALPHA
,
ALPHA-LOCK
Angle entry indicators (
¡,
r
ANGLE
Angle
MODE
ANS
Applications
Building height and city size,
Graphing the inverse of a function,
Graphing a piecewise function,
Graphing a polar equation,
Newton’s numerical solve routine,
Numerical integration,
Probability experiments: coins, dice,
Unit circle and trig curves, 11
Windows variables store and recall,
Arcsine, arccosine, arctangent. See
SIN
-1
,
COS
-1
,
TAN
-1
A
(Cont.)
ARGUMENT
AUTOSIMP MODE
B
b
b
º
c MODE
8 b
º
c
BOX
(
VARS
BOX
BREAK
C
c
CHECK RAM
CLRDRAW
CLRHOME
CLRLIST
Coefficients (regression equation),
CONNECTED MODE
Index I-1
C
(Cont.)
Conversions
Correlation coefficient
r
COS
,
COS–1
CTL
(
PRGM
Cube:
3
D
(Cont.)
Display (Cont.)
Division:
DOMAIN
DOT MODE
DRAW
DRAWF
Drawing
D
DATA TYPE
8
DEC
DEGREE MODE
Degree notation
Deleting
@
TBL
@ X
,
@ Y
Derivative. See Numerical derivative
DIM
DIM MISMATCH
DISP
DISPGRAPH
E
e^
e
Y=
Element
ELSE
END
Entering
EQ
(
VARS
I-2 Index
E
(Cont.)
Exponent:
E
EXPREG
F
F
Factorial:
!
FIX MODE
FLOAT MODE
FNOFF
,
FNON
FOR(
FPART
FRACTION
Fractions
8
FRAC
FUNC MODE
G
Getting Started. See Applications
GOTO
Graph
Greater than or equal:
GRIDOFF
,
GRIDON
H
HISTOGRAM
HORIZONTAL
I
IF
INCREMENT
INPUT
I/O
INT
INT
÷
INVALID
INVALID DIM
Inverse:
–1
IPART
Index I-3
K
L
L n
LABEL
LBL
Less than or equal:
LINE(
LINREG
LIST MATH
LIST OPS
LN
LNREG
LOG
M
MANSIMP MODE
MARK
(
STAT
MATH
MAX(
I-4 Index
M
(Cont.)
MAXX
,
MAXY
MEAN(
MED
MEDIAN(
MEMORY
MEMORY
MEMORY
ANGLE
BOX
(
VARS
DRAW
EQ
(
VARS
I/O
(
PRGM
LIST MATH
LIST OPS
MATH MATH
MEMORY
NUM
(
MATH
POINTS
(
DRAW
PRB
(
MATH
PRGM EXEC
PRGM EDIT
PRGM NEW
G (
VARS
STAT CALC
STAT EDIT
STAT MARK
STAT PLOTS
STAT TYPE
TEST
VARS
X/Y
(
VARS
Y-VARS
ZOOM
MIN(
MINX
,
MINY
MODE
Multiplication:
×
N
n
nCr
NDERIV(
Negation:
-
NEST LEVEL
NORMAL MODE
Not equal:
nPr
NUM
(MATH)
P
(Cont.)
PRGM EXEC
PRGM EDIT
PRGM I/O
PRGM NEW
PROD
P 8 Rx(
,
P 8 Ry(
PT-CHANGE(
,
PT-OFF(
,
PT-ON(
PWRREG
O
OFF
,
ON
1-VAR STATS
OVERFLOW
P
PARAM MODE
PAUSE
Pi:
PLOT
n
(
PLOTSOFF
,
PLOTSON
POINTS
(
DRAW
Power of ten:
10^
Powers:
^
PRB
(
MATH
PRGM_
PRGM CTL
Q
Q
1
,
Q
3
Quadratic fit/regression, 9 -16
QUADREG
R
ô (radian notation), 2-14, A-14
r
r
RADIAN
RAND
RANDINT(
REGEQ
(regression equation),
REMANINDER(
Index I-5
R
(Cont.)
RETURN
root
ROUND(
R
8
Pr(
,
R
8
P q
(
S
SCATTER
SCI MODE
2nd
SEQ(
Sequence
SEQUENTIAL
SHADE(
SHADE_Y>(
SHADE_Y<(
s X
,
s Y
G ( VARS
G
X
,
G
Y
,
G
X
G
G
XY
ú
SIMP
SIMUL
SIN
,
SIN–1
SORTA(
,
SORTD(
Square root:
STAT
STAT CALC
I-6 Index
S
(Cont.)
STAT EDIT
STAT
STAT MARK
STAT PLOT
STAT PLOTS
STAT TYPE
STOP
Store:
SUM
SX
,
SY
SYNTAX
T
T
TABLE SETUP
TAN
,
TAN–1
TBLMIN
TEST
THEN
TMAX
,
TMIN
TRACE
TSTEP
T
(Cont.)
Turning functions on and off, 1
2-VAR STATS
U
UNDEFINED
Y
(Cont.)
Y-VARS
Y
n
Y1
,
Y2
,
Y3
Y
n
T
Y=
Y=
functions. See
Y
n
,
X
n
T
, functions
YFACT
YL
YMAX
,
YMIN
,
YSCL
V
VARS
VERTICAL
Viewing rectangle, viewing window. See
Window
W
WINDOW RANGE
Z
ZBOX
ZDECIMAL
ZOOM
ZOOM
ZOOM FACTORS
ZOOM IN
ZOOM
ZOOM OUT
ZSQUARE
ZSTANDARD
ZTRIG
X
X
,
T
X
-5, 4-11 to 4-13, 6-3, A-26, B-11
X
n
T
XFACT
XL
XMAX
,
XMIN
,
XSCL
X/Y
(
VARS
XYLINE
@ TBL
@
X
,
@
Y
s
X
,
s
Y
G (
VARS
G
X
,
G
Y
,
G
X
2
,
G
Y
2
,
G
XY
Y
Y
Index I-7
TI-80
STAT PLOT
x x x x
E
X,T
FRAC
{ } b c
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