ti-83 guidebook - Sears Parts Direct

ti-83 guidebook - Sears Parts Direct
TEXAS
|NSTIRUMENTS
TI-83
GRAPHING
CALCULATOR
GUIDEBOOK
TI-GRAPH
Constant
LINK, Calculator-Based
Memory,
Instruments
Windows
Laboratory,
CBL, CBL 2, Calculator-Based
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ilnplied,
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inerchantability
makes
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to any
for a particular
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or
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availaMe
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US FCC
Information
Concerning
Radio Frequency
Interference
This equiplnent has been tested and found to cornply with the
limits for a Class B digital device, pumuant to Pm't 15 of the F(C
rules. These limits are designed to provide reasonable protection
against harmflfl interference
in a residential installation. This
equiprnent generates, uses, and can radiate radio frequency enet}4y
and, if not installed and used in accordance
with the instructions,
inay cause hannflll inte_ferenee with radio colnmunications.
However, there is no guarantee that inte_ferenee will not occur in
a particular instailation.
If this equiplnent does cause harrnful interference
to radio or
telexdsion reception, which can be determined
by turning the
equipment off and on, you can try to correct the inte_ference by
one or inore of the following measures:
•
Reorient
or relocate
the receiving
•
Increase
the separation
•
Connect the equipment into an outlet on a circuit
fl_m that to which the receiver is connected.
•
Consult the dealer or an experienced
technician for help.
between
antenna.
the equiplnent
and receiver.
different
radio/television
Caution:
Any changes or modifications
to this equiprnent not
expressly approved by Texas Instrulnents
may void your authority
to operate the equiplnent.
Table of Contents
This
nlanual
describes
how
to use the TI-83
Graphing
Calculator,
Getting
Started is an overview
of TI-83 features.
Chapter
1 describes
how the TI-83
operates.
Other chapters
describe
various
interactive
features.
Chapter
17
shows
how to combine
these features
to solve problems,
Getting Started:
Do This First!
TI-83 Keyboard
..........................................
TI-83 Menus .............................................
2
4
First Steps ...............................................
Entering a Calculation:
The Quadratic
Formula ..........
Converting
to a Fraction:
The Quadratic
Formula
........
I)isplaJ_ng ('omplex
Results: The Quadratic
Formula
....
Defining a Function:
Box with Lid .......................
Defining a Table of Values: Box with Lid ...............
Zooming In on the Table: Box with Lid .................
Setting tile Viewing Window-: Box with Lid .............
I)isplaJ_ng and Tracing the Graph: Box with Lid .......
Zooming In on tile Graph: Box with Lid ................
F)
Finding the Calculated
Maximum:
Box with Lid ........
Other TI-83 Features .....................................
Chapter 1 :
Operating the
TI-83
Turning On and Turning Off the TI-83 ....................
Setting the Display Contrast
.............................
The Display ..............................................
Entering Expressions
and Instructions
...................
TI-83 Edit Keys ..........................................
6
7
8
9
10
11
12
13
15
16
17
1-2
1-3
1-4
1-6
1-8
Setting Modes
...........................................
Using TI-83 Variable Names
.............................
Storing Variable Values ..................................
Recalling Variable Values ................................
ENTRY (Last Entry) Storage A_'ea ........................
Ans (Last Pmswer) Storage Pa'ea .........................
TI-83 Menus .............................................
VARS and VARS Y-VARS Menus .........................
1-9
1-13
1-14
1-15
1-16
1-18
1-19
1-21
Equation Operating
System (EOS TM) .....................
Error Conditions
.........................................
1-22
1-24
Introduction
iii
Chapter 2:
Math, Angle, and
Test Operations
Getting Started: Coin Flip ................................
Keyboard Math Operations
..............................
MATH Operations
........................................
Using tile Equation
Solver ...............................
MATH NUM (Numbe 0 Operations
........................
Entering and Using Complex Nmnbers ...................
MATH CPX (Complex)
OperatMns
.......................
MATH PRB (Probability)
Operations
.....................
ANGLE Operations
.......................................
TEST (Relational)
Operations
............................
TEST LOGIC (Boolean)
Operations
......................
Chapter 3:
Function
Getting Started: Graphing a Circle .......................
Defining Graphs
.........................................
Setting the Graph Modes .................................
Defining Funetions
......................................
Graphing
Graphing
Chapter 5:
Polar Graphing
iv
Introduction
3-2
3-3
3-4
3-5
Seleeting and Deseleeting
Punetions
.....................
Setting Graph Styles for Flmetions
.......................
Setting the Viewing Window \Tariahles ...................
Setting the Graph Format ................................
3-7
3-9
3-11
3-13
Displaying
Exploring
Exploring
Exploring
3-15
3-17
3-18
3-20
Graphs
.......................................
Graphs with the Free-Moving
Cursor ..........
Graphs with TRACE ...........................
Graphs with the ZOOM Instructions
...........
Using ZOOM MEMORY ..................................
Using the CALC (Calculate)
Operations
..................
Chapter 4:
Parametric
2-2
2-3
2-5
2-8
2-13
2-16
2-18
2-20
2-23
2-25
2-26
3-23
3-25
Getting Started: Path of a Ball ...........................
Defining and Displaying
Parametric
Graphs ..............
Exploring Parametrie
Graphs ............................
4-2
4-4
4-7
Getting Started: Polar Rose ..............................
Defining and Displaying
Polar Graphs
...................
ExNodng
Polar Graphs ..................................
5-2
5-3
5-6
Chapter
6:
Getting Started: Forest and Trees ........................
Defining and Displaying
Sequence
Graphs ...............
Selecting Axes Combinations
............................
Exploring
Sequence Graphs ..............................
Graphing Web Plots ......................................
Using Web Plots to Illustrate
Convergence
...............
Graphing Phase Plots ....................................
Comparing
TI-83 and TI-82 Sequence Variables ..........
Keystroke
Differences
Between
TI-83 and TI-82 .........
Chapter
Tables
7:
Getting Started: Roots of a Function
.....................
Setting Up the Table .....................................
Defining the Dependent
Variables ........................
I)isplaying
the Table .....................................
7-2
7-3
7-4
7-5
Chapter
DRAW
8:
Getting
8-2
Sequence
Graphing
Operations
Started:
Drawing
a Tangent
Line .................
Using the DRAW Menu ...................................
Clearing Drawings
.......................................
Drawing Line Segments
..................................
8-3
8-4
8-5
Drawing Horizontal
and Vertical Lines ...................
Drawing Tangent Lines ..................................
Drawing Functions
and Inverses
.........................
Shading Areas on a Graph
...............................
Drawing Circles ..........................................
Placing Text on a Graph .................................
UsHlg Pen to Draw on a Graph ...........................
Drawing PoHlts on a Graph ..............................
Drawing Pixels
..........................................
StorH N Graph Pictures (Pic) .............................
Recalling Graph Pictures
(Pic) ...........................
StorHlg Graph Databases
(GDB) .........................
Recalling Graph Dadabases
(GDB) .......................
Chapter 9:
Split Screen
(;-2
6-3
6-8
(;-9
6-11
6-12
6-13
6-15
6-16
Getting Started: Exploring
the Unit Circle ................
Using Split Screen
.......................................
Horiz (Horizontal)
Split Screen ...........................
G-T (Graph-Table)
Split Screen ..........................
TI-83 Pixels in Horiz aim G-T Modes .....................
Introduction
8-6
8-8
8-9
8-10
8-11
8-12
8-13
8-14
8-16
8-17
8-18
8-19
8-20
9-2
9-3
9-4
9-5
9-6
v
Chapter 10:
Matrices
Getting Started: Systems of Linear Equations
............
Defining a Matrix ........................................
Viewing and Editing Matrix Elements
....................
Using Matrices with Expressions
........................
I)isplaying
and Copying Matrices
........................
Using Math Functions
with Matrices
.....................
Using the MATRX MATH Operations
.....................
10-2
10-3
10-4
10-7
10-8
10-9
10-12
Chapter 11:
Lists
Getting Started: Generating
a Sequence
..................
Naming Lists .............................................
Storing and Displaying
Lists .............................
Entering List Names .....................................
Attaching
Formulas
to List Names .......................
Using Lists in Expressions
...............................
LIST OPS Menu ..........................................
LIST MATH Menu ........................................
11-2
11-3
11-4
11-6
11-7
11-9
11-10
11-17
Chapter 12:
Statistics
Getting Started: Pendulum
Lengihs and Periods
Setting up Statistical Palalyses ...........................
Chapter 13:
Inferential
Statistics and
Distributions
vi
Introduction
.........
12-2
12-10
Using the Stat List Editor ................................
Attaching
Formulas
to List Names .......................
I)etaehi_lg Fornmlas
from List Names ....................
Switching
Stat List Editor Contexts
......................
Stat List Editor Contexts .................................
STAT EDIT Menu ........................................
12-11
12-14
12-16
12-17
12-18
12-20
Regression
Model Features
..............................
STAT CALC Menu ........................................
Statistical Variables ......................................
12-22
12-24
12-29
Statistical
Statistical
Statistical
12-30
12-31
12-37
Analysis
Plotting
Plotting
in a Program
.........................
.......................................
in a Program
.........................
Getting Started: Mean Height of a Population
hfferential
Star Editors ...................................
8TAT TESTS Menu ......................................
............
13-2
13-6
13-9
Inferential
Statistics
Input Descriptions
..................
Test and Interval Output Variables .......................
Distribution
Functions
...................................
13-26
13-28
13-29
Distribution
13-35
Shading
.....................................
Chapter 14:
Financial
Functions
Getting Started: Finzmeing a Car. ........................
Getting Started: (;omputing
Compound
Interest ..........
Using tile TVM Solver ....................................
Using tile Financial
Functions
...........................
Calculating
Time Value of Money (TVM) .................
Calculating
(;ash Flows ..................................
Calculating
Amortization
................................
Calculating
Interest Conversion
..........................
Finding I)ays between [)ates_)ef'nm N Payment Method .....
Using tile TVM Variables .................................
14-2
14-3
14-4
14-5
14-6
14-8
14-9
14-12
l '4-13
14-14
Chapter 15:
CATALOG,
Strings,
Hyperbolic
Functions
Browsing tile TI-83 CATALOG ...........................
Entering and Using Strings ...............................
Storing Strings to String Variables .......................
String Functions and Instructions in the CATALOG ......
Hyperbolic Functions in the CATALOG ..................
17)-2
15-g
1:)-4
1.5-6
15-10
Chapter 16:
Programming
Getting Started: Volume of a Cylinder ....................
Creating and Deleting Progrmns
.........................
Entering Command
Lines and Executing
Programs
Editing Programs
........................................
Copying and Renmning
Programs
........................
PRGM CTL (Control)
Instructions
.......................
PRGM I/O (Input/Output)
Instructions
...................
('ailing Other Programs
as Subroutines
..................
Chapter 17:
Applications
16-2
16-4
......
16-5
16-6
16-7
16-8
16-16
16-22
Comparing Test Results Using Box Plots ................
Graphing Pieeewise Punetions ...........................
Graphing Inequalities ....................................
Solving a System of Nonlinear Equations ................
Using a Program to ( reate the Sierpinski Triangle .......
Graphing Cobweb Attractors ............................
Using a Program to Guess the Coefficients ...............
Graphing the Unit Circle and Trigonometric (;m_es ......
Finding the Area between Curves ........................
Using Parametric Equations: Ferris Wheel Problem ......
Demonstrating the Fundamental Theorem of Calculus...
Computing Areas of Regular N-Sided Polygons ..........
Computing and Graphing Mortgage Payments ...........
17-2
17-4
17-5
17-6
17-7
17-8
17-9
17-10
17-11
17-12
17-14
17-16
17-18
Introduction
vii
Chapter 18:
Memory
Management
{'heeLing Awailable MemolTy".............................
Deleting Items from MemoKy" ............................
Clearing Entries and List Elements ......................
Resetting the TI-8:3 ......................................
18-2
18-3
18-4
18-5
Chapter 19:
Communication
Link
Getting Started: Sending Variables
.......................
TI-83 LINK ...............................................
19-2
19-3
Selecting Items to Send ..................................
Receiving Items ..........................................
Transmitting
Items .......................................
Transmitting
Lists to a TI-82 .............................
Transmitting
from a TI-82 to a TI-83 .....................
Backing Up MemoKy" .....................................
19-4
19-5
19-6
19-8
19-9
1%10
Appendix A:
Tables and
Reference
Information
TabD
Menu Map ...............................................
Vm'iables
................................................
Statistical Formulas
.....................................
Financial Fommlas
......................................
A-39
A-49
A-50
A-.M
Appendix B:
General
Information
BatteKy" Information
......................................
In Case of Difficulty
.....................................
En'or Conditions
.........................................
B-2
B-4
B-5
of Functions
Accuracy hfformation
Support and Service
Win'rarity Information
Index
viii
Introduction
and Instructions
.....................
....................................
Infommtion
.........................
....................................
A-2
B-10
B-12
B-13
GettingStarted:
Do This First!
Contents
TI-83 Keyboard
..........................................
TI-S3 Menus .............................................
First Steps
...............................................
Entering a Calculation:
The Quadratie
Fonuula
..........
('onverting
to a Fraction:
The Quadratie Formula
........
Displaying Complex Results: The Quadratic
Formula
....
Defining a Function:
Box with Lid .......................
Defining a Table of Values: Box with Lid ...............
Zooming In on the Table: Box with Lid .................
Setting tile Viewing Window-: Box with Lid .............
Displaying and Traeing the Graph: Box with Lid .......
Zooming In on tile Graph: Box with Lid ................
Finding the ('aleulated
Maximum:
Box with Lid ........
Other TI-83 Features .....................................
TEXAS
\
X=:I..5:B;!:=I_fiB
13
15
16
17
T1=83
INSTRUMENTS
/
2
4
5
6
7
8
9
10
11
12
\.
_Y=_;i:.90_;i:_lfi
=
J
STATPLOT
TBLSET
FORMAT
CALC
TABLE
Getting
Started
1
TI-83 Keyboard
Generally,
keys,
the keybom'd
advanced
Keyboard
is dwided
function
Zones
keys,
Graphing
Editing
Graphing
Editing
allow
calculator
scientific
Keys
Scientific
Calculator Keys
Started
keys
Scientific
standard
Keys
these
access
function
functions.
FuncffonKeys
Getting
keys
Advanced
advanced
Advanced
2
into
and scientific
zones:
graphing
calculator
keys,
the interactive
graphing
you to edit expressions
keys
display
keys access
calculator.
editing
keys.
menus
features.
and values.
that
access
the capabilities
the
of a
Using the
Color-Coded
Keyboard
The
keys
locate
on the TI-83
are color-coded
to help you easily
the key you need.
The gray keys are the number keys. The blue keys along the
right side of the keyboard
are the conunon
math functions.
The blue keys across the top set up and display graphs.
The primaKF function
of each key is printed
in white on the
key. For example,
when you press FMA_], the MATH menu is
displayed.
Using the K_
and @
Keys
The secondary
function
of each key- is pnnted
in yellow
above the key-. When you press the yellow [_
key, the
character,
abbreviation,
or word printed
in yellow above
the other keys becomes
active for the next keystroke.
For
example,
when you press [_ and then [M#Y_, the TEST
menu is displayed.
This guidebook
describes
this keystroke
combination
as [_
[TEST],
The alpha function
the key. When you
of each key is printed
press the green @
in green above
key, the alpha
character
printed
in green above the other keys becomes
active for the next keystroke.
For example,
when you press
@
and then [MATH],the letter A is entered.
This
guidebook
describes
this keystroke
combination
as @
[A].
The_key
accesses
the second function
printed in yeltow above
each key
--'_
[email protected]
accessesthe
alpha
function printedin
green above each key
Getting
Started
3
TI-83 Menus
Displaying
a Menu
While using your TI-83, you often
to access items from its menus,
will need
[5+9|
When you press a key- that displays
a menu,
that menu temporarily
replaces
the screen
where you are working.
For example,
when
you press _,
the MATH menu is displayed
as a full screen.
_
After you select an item fronl
screen where you m'e working
displayed
again.
5+9_
Moving
Solne
from
keys
One
access
Menu
nlore
a menu,
usually
the
is
or letter
item is highlighted.
beyond
the screen,
replaces
the colon
than
one
lnenu.
CPX
PRB[
CPX
PRB
4:_(
5:_
6:¢Min(
74€Max(
When
next to the current
round(
5:int(
_sl_[
6:Min(
74.max(
menu
If the menu continues
a down arrow ( _ )
( : ) in the last displayed
item. If you scroll beyond the last displayed
item, an up arrow ( t ) replaces
the colon in
the first item displayed.You
can select all item
in either of two ways.
• Press [] or [] to
number
or letter
• Press the key or
number
or letter
Leaving
lnove the cursor
to the
of the item; press [g_.
key combination
fia" the
next to the item.
a Menu without
Making
You can leave a lnenu without
selection
in ally of three ways.
4
PRB
an Item from a Menu
The number
• Press
where
• Press
screen.
• Press
CPX
to Another
you press such a key, the names of all
accessible
menus
are displayed
on the top
line. When you highlight
a menu name, the
items in that menu are displayed.
Press [] and
[] to highlight
each menu nalne.
Selecting
NUM
Pao
:*Dec
[
Getting
Started
lnenu
4:?Part(
5:int(
5:Min(
74Max(
3tiPar.t(
4:?Part(
5:int(
6:Min(
7:max(
MRTH _
8:fOR(
i_lEIgcd(
a Selection
lnaking
a
@
to return to the screen
you were.
[2_] [QUIT] to t_tum
to the home
a key for another
round(
3:iPart(
or screen.
15+9_
I
First Steps
Before starting the sample pr()blems in this chapter, follow the steps on this
page to reset the TI-83 to its factotT settings and cleat" all nlenlot_y-. This
ensures that the keystrokes in this chapter will produce the illustrated results.
To reset the TI-83, follow these steps.
FOR]
to
1,
Press
turn
on the calculator.
2,
Press and release [_,
[MEM] (above []).
and then press
When you press [2_], you access the
operation printed in yellow above the next
key that you press. [MEM]is the
operation of the [] key.
RRM...
3:Clear Entries
4:ClrRllLists
5:Reset...
The MEMORY menu is displayed.
3.
Press 5 to select 5:Reset.
The RESET menu is displayed.
4,
_MeMoru..,
a. DeCaults...
Press 1 to select 1:All Memory,
The RESET MEMORY menu is displayed.
Resettin9
memoru
erases all data
and PrograMs.
5,
Press
2 to select
2:Reset.
M1 nlenlot_y- is cleared, and the calculator
is reset to the factor T default settings.
When you reset the TI-83, the display
contrast is reset.
|
MeM
oleared
If the screen is vetT light or blank, press
and t_lease D_], and then press and
hold [] to darken the screen.
If the screen is very dark, press and
release [2_, and then press and hold []
to lighten the screen.
Getting
Started
5
Entering
a Calculation:
Use the quadratic
fornmla
to solve
the quadratic
with the
equation
and 2X 2 - X + 3 = 0, Begin
3 _
@
the coefficient
The Quadratic
[n] (above 1_])
of the X 2 tenn.
Press
store
2,
Press @
[ : ] (above [_). The colon
allows you to enter more than one
instruction
on a line,
3,
Press 6 _
@
[B] (above _)
to
store the coefficient of the X term. Press
@
[ : ] to enter a new instruction on
the same line. Press 2 _
@
[c]
(above _)
to store the constant.
4,
Press [NY_ to store the values to the
variables A, B, and C.
to
[]
@
[B] []
[A]_
_
[<] @
[B]
[c] []17113[] 2
@
[A] [] to enter the expression
one of the solutions
for the quadratic
formula,
for
- b+
2a
Press _
equation
to find one solution
3X 2 + 5X + 2 = 0.
for the
The answer is shown on the right side of
the display. The cursor nloves to the next
line, ready for you to enter the next
expression.
6
Getting
Started
3X 2 + 5X + 2 = 0
3÷R: 5÷B: 2÷C|
The last wdue you stored is shown on the
right side of the display. The cursor moves
to the next line, ready for your next entt3z,
D [] 4_
equations
3X 2 + 5X + 2 = 0,
1,
Press[]
Formula
÷R: 5÷B: 2÷C
2
Converting
to a Fraction:
You can show the solution
1. Press [_
The Quadratic
Formula
as a fl'action.
to display the MATH lnenu.
Pao
NUN
eo
CPX
PRB
3:_
4:_#(
5: *#
6:¢Min(
7¢€Ma× (
Press 1 to select 1:)Frac froln the MATH
(-B+#(BZ-4RC))/(
2R)
%6666666667
lnenu,
When you press 1, AnsJ,Frac is displayed
the home screen. Arts is a variable that
contains the last calculated answer.
Press 1_
fl'action.
to convert
on
the result to a
Rns*Fr, ac|
(-B+4-(BZ-4RC)
2R)
To save keystrokes, you can recall the last expression
edit it for a new calculation.
Press [2_ [ENTRY](above [gNT_) to recall
the fraction conversion entry, and then
press Fffffd][ENTRY]again to recall the
quadratic-fornmla
expression,
2a
5,
you entered,
)/(
and then
I-B+E(BZ-4RC))/(
R)
-.6666666667
Rns*Fpac
-2/3
(-B+E(BZ-4RC))/(
2R)|
Press [] to nlove the cursor
onto the + sign
in the fornmla,
Press [] to edit the
quadratic-fornmla
expression
to become:
2R)
-.6666666667
Rns_Frac
(-B-.r(BZ-4RC))/(
-2/31
2a
6,
Press 1_
the quadratic
to find the other solution
for
equation
3X 2 + 5X + 2 = 0.
-1
_R)
Getting
Started
7
Displaying
Now
solve
mode,
Complex
the equation
the TI-83
Results:
The Quadratic
2X 2 - X + 3 = 0. When
displays
complex
Formula
you set a+bi complex
number
results.
Press 1_
[] [] [] [] [] [] (6 times),
and
then press [] to position
the cursor
over
a+bi. Press @
to select a+bi coinplexnumber
mode.
2,
Press [_ [QU*T]
the home screen,
cleat" it.
Press 2 _
@
_E])
to return to
and then press @
to
(above
[A] @
[: ] []
z G-T
1
[c] F_q.
The coefficient
of the X 2 term, the
coefficient
of the X term, and the constant
for the new equation
are stored to A, B,
and C, respectively.
Press [_
[ENTRY] to recM1 the store
instruction,
and then press [_
[ENTRY]
again to recall the quadratic-fornmla
expression,
eR:-leB:3aC
2+R: -1+B:3+C
3
3
2o
Press @
to find one solution
equation
2X 2 - X + 3 = 0.
for the
12+R:-I+B:3+C
i25-I.
Press [2_ [ENTRY]repeatedly
quadratic-fornmla
expression
until this
is displayed:
2a
Press @
the quadratic
to find the other solution
for
equation:
2X 2 - X + 3 = 0.
198957881t
(-B-g(BZ-4RC))/_
2R)
.25-1.198957881t
(-B+E(BZ-4RC))/(
2R)
i25+1.198957881t
Note: An alternative for solving equations for real numbers is to use the built-in Equation
Solver (Chapter 2).
8
Getting
Started
Defining
Take
a Function:
a 20 enl. x 25 enl. sheet
Box with Lid
of paper
and cut X × X squm'es
fronl
two
comers,
Cut X × 12,5 cm. rectangles
from the other two corners
as shown in the
diagram
below,
Fold the paper into a box with a lid. What value of X would
give your box the nlaxinmln
volume
V? [ _se the table and graphs to determine
the solution,
Begin by defining
a function
volunle
of the box.
From
the diagram:
Substituting:
that
describes
the
2X + A = 20
2X + 2B = 25
V=ABX
V = (21) - 2X) (25/2
- X) X
1. Press [] to display the Y= editor, which is
where you define functions for tables and
graphing.
Press[]
volume
20[] 2 _
[] [] 25[]
2[]
[] _
[_
to define the
function
as Y1 in terms of X.
lets you enter X quickly, without
having to press @.
The highlighted
sign indicates
that Y1 is selected.
_
x
PloL:L
Plot;'
B
PICL3
","?t =I
\y._=
xY_=
"_y_=
,..y_=
,,y_=
xY?=
\'14tB<20-2X)
-X)X
_Yz=l
<25/2
,..y_=
=
xYfi=
Getting
Started
9
Defining
a Table of Values:
Box with Lid
The table feature of the TI-83 displays numeric
You can use a table of values fl'om the function
an answer to the problem,
1, Press [2_ [TBLSET] (a|)ove
_)
display the TABLE SETUP menu,
to
Tb IStart=O
aTbl=l
Indent:
2,
Press [gNT_ to accept TblStart=0.
3.
Press 1 [ggY_ to define the table increment
ATbI=I. Leave Indpnt: Auto and
Depend: Auto so that the table will be
generated automatically,
4.
Press [2_ [TABLE](above _)
the table,
Notice
that
the nlaxilnuln
(box's volunm) occurs
between
3 and 5.
TABLE
SETUP
Depend:
X
to display
I
value
when
inforlnation about a function.
defined on page 9 to estimate
for Y1
X is about
91
o
1
Z
207
3_6
_99
hOB
6
3t_
4,
X=O
5,
Press and hold [] to scroll the table until a
negative result for Y1 is displayed.
Notice that the nmxinmm length of X for
this problem occurs where the sign of Y1
(box's volume) changes from positive to
negative, between 10 and 11,
6,
Press[2_
Getting
V1
_t2
F
B
231
lhh
10
0
X=12
[TBLSET].
Notice that TblStart h_s changed to 6 to
reflect the first line of the table as it was
last displayed, (In step 5, the first value of
X displayed in the table is 6.)
10
X
E
Started
TblStart=6
_Tbl=l
IndPn÷: P._
TRBLE SETUP
Depend:
_.
Rsk
Zooming
In on the Table: Box with Lid
You can adjust the way a table is displayed to get lnore inforlnation
about a
defined function. With smaller values for aTbl, you can zoom in on the table.
Press 3 _
to set TblStart. Press [] 1
[gNT_ to set ATbl.
This adjusts the table setup to get a nlore
accurate estimate of X for lnaxilnuln
volunle
Y1.
2, Press[2_
3.
[TABLE],
X
Notice that tile nlaxinluln value for Y1 is
410.26, which occurs at X=3.7. Therefore,
nlaxinmln
TABLE
SETUP
Depend:
Press [] and [] to scroll the table.
the
TblStart=3
_Tbl=. 1
IndPnt: r=Rg_t_
occurs
where
3.6<X<3.8,
r=_r;J_
91
_.6
4±0.11
:<;'
KB
_.0.z6
hOg,gtl
_
't0a
u06.x9
h0h.3B
2,.9
h09.19
X=4.2
Press [2_ [TBLSET].
Press 3 [] 6 _
to
set TblStart. Press [] 01 [gNT_ to set ATbl.
Press [2_ [TABLE], and then press [] and []
to scroll the table.
Four equivalent nlaxinluln values are
shown, 410.60 at X=3.67, 3.68, 3.69, and
3.70.
TRBLE SETUP
TblStart=3.6
_Tbl=.Ol
IndPnt: _
Rsk
Depend:
Rsk
g
_
YI
K67
3,68
K69
3.?
hi0&6
h10,?.6
h10.;':6
h:t0._:6
h:t0.23
X=3, 72
Press [] and [] to inove the cursor to 3.67.
Press [] to lnove the cursor into tile Y1
colulnn,
Tile value of Y1 at X=3.67 is displayed
the bottoln line in full precision as
410.261226.
Press
[] to display
tile other
on
nlaxinlunls.
The value of Y1 at X=3.68 in full precision
is
410.264064, at X=3.69 is 410.262318, and at
X=3.7 is 410.266.
The lnaxilnuln volulne of the box would
occur at 3.68 if you could lneasure and cut
the paper at .01-eln. increments.
X
Y_
-_:.6B
hlO.Z6
3.69
3.?
3.71
_.72
h10,_':6
hlO,Z6
h10.25
h10.2_
V, =410,
X
261226
V_
3.66
3.6}'
h10.2_
K6B
K69
h10,?.6
3.7
3.71
2;.72
h10,;':6
h10._:5
ht0.23
V, =410,
264064
Getting
Started
11
Setting
You also
the Viewing
can use the
graphing
Window:
features
Box with Lid
of the TI-83
to find the nlaxinlunl
value
of a previously
defined
function.
When the graph is activated,
the viewing
window
defines
the displayed
portion
of the coordinate
plane. The values
the window
variables
determine
tile size of tile xqewing window.
WINDOW
XMin=-lO
XMax=lO
Press _
to display tile window
editor, where you can view and edit the
values of the window
variables.
The standard
window
variables
define
XscI=I
VMin=-lO
VMax=lO
Vscl=l
Xres=l
the
viewing window
_ shown. Xmin, Xmax,
Ymin, and Ymax define the boundm'ies
of
:_Ymax
Xscl
j Xmm
the display.
Xscl and Yscl define the
distance
between
tick nmrks on the X and
Y taxes. Xres controls
resolution.
2.
Press 0 _
3.
Press 20 [] 2 to define Xmax using an
expression.
to define Xmin.
Xma×
iZ
Ysd
Ymin \
WINDOW
Xmin=O
4.
Press [g_gO. The expression is evaluated,
and 10 is stored in Xmax. Press [gffT_] to
accept Xscl as 1.
5.
Press 0 [ggggm 500 [ggggm 100 [g_gN 1 [ggggm
to define the remaining window variables.
12
Getting
Started
of
XMax=20/2I
Xscl=l
VMin=-lO
YMax=IO
Yscl=l
Xres=l
WINDOW
XMin=O
Xmax=lO
XS61=I
VMin=O
VMax=500
Yscl=100
Xres=l
/
Displaying
Now
that
and Tracing
you have
defined
the Graph:
the function
which to graph it, you can displayfunction
using the TRACE feature.
1.
to be graphed
and explore
The graph of Y1--(20 - 2X)(25/2 - X)X is
displayed.
Press
functionill
the _viewing to window.
graph the selected
Press
[] to activate
the free-moving
Box with Lid
and the window
the graph.
I_i/f
in
You call trace
.-_.-_-,
Nj
Getting
Started
along
a
graph
cursor,
The X and Y coordinate
position
of the graph
on the bottom
line.
3.
values
cursor
for the
are displayed
Press _], [], [], and [] to move the freemoving cm\sor to the apparent
nlaxinmln
of the function.
As you move
coordinate
the cursor,
values
the X and Y
are updated
continually.
13
4.
Press _.
The trace cursor
on the Y1 function.
is displayed
The function
that you are tracing
displayed
in the top-left corner.
is
Press [] and [] to trace along Y1, one X dot
at a time, evaluating
Y1 at each X.
You also can enter your
nlaxinmln
value of ×.
6.
estimate
?t: G:'_)
- ::"}D_.::'_
/ ::"- }{)}:
for the
t/
[?t:{20-2g:l{2gc'2:-{,l)g
Press a [] 8. When you press a number key
while in TRACE, the X= prompt is displayed
in the bottom-left corner.
'¢l=€.RO-l_g)(2g/l_-l{)g
7. Press [gNT_.
The trace cursor jumps to tile point on the
Y1 function evaluated at X=a.8.
Press [] and [] until
nlaxinlunl
Y wdue.
you
are on the
This is the nlaxinlunl of YI(X) for the X
pixel values. The actual, precise nl_kxinlunl
may lie between pixel values.
14
Getting
Started
?t:G_O-_:8)(2:gd_-R):_
',..
Zooming
In on the Graph:
To help identify
nlaxinlulns,
nlininlulns,
you can magnify
instructions.
the viewing
window
1. Press _
Box with Lid
roots,
to display- the ZOOM lnenu.
This menu is a typical TI-83 menu. To
select an item, you can either press the
number or letter next to the item, or you
can press [] until the item number or letter
is highlighted, and then press [_.
2.
and intersections
at a specific
location
using
of functions,
tile ZOOM
MEMORY
In
3:Zoom Out
4:ZOeoiMal
5:ZS_uare
6:ZStandard
?4ZTPig
Press 2 to select 2:Zoom In.
The graph is displayed
again. The cursor
has changed
to indicate
that you m'e using
a ZOOM instruction.
X=.3.7;_.3LI0_
.Y=_:tl.=90.3;: .
With the cm_sor near the nlaxinlunl vMue
of the function (as in step 8 on page 14),
press [_.
The new viewing window is displayed.
Both Xmax-Xmin and Ymax-Ymin have
been adjusted by factors of 4, the default
values for the zoom factors.
Press _
settings.
to display the new window
WINDOW
Xmin=2.4734042_.
XMax=4.9734042...
Xsol=l
YMin=348.79032...
YMaX=473.79032...
Yscl=100
Xres=l
Getting
Started
15
Finding the Calculated
You can use
function.
a CALCULATE
menu
Maximum:
operation
Box with Lid
to calculate
a local
maxinmm
Press [2_ [CALC] (above
_)
to display
the CALCULATE menu. Press 4 to select
4:maximum.
The graph is displayed
Left Bound? prompt,
again
with
a
Press [] to trace along the curve to a point
to tile left of the nlaxinluln,
and then press
[N!N.
A _ at the top of the screen indicates
selected bound.
A Right Bound? prompt
3.
the
is displayed.
Press [] to trace along the curve to a point
to the right of the nlaxinluln,
and then
press [g_gm.
A _ at the top of the screen indicates
selected bound.
the
A Guess? prompt is displayed.
4.
Press [] to trace to a point neat" the
inaxiinuin, and then press [ggT_q.
Or, press 3 [] 8, and then press [ggT_q to
enter a guess for the nmxinmm.
When you press a number key in TRACE,
the X= prompt is displayed in the bottomleft corner.
Notice how the values for the calculated
nlaxinlunl
compare
with the nlaxinlunls
found with the free-moving cursor, the
trace cursor, and the table.
Note: In steps 2 and 3 above, you can entervalues
directlyfor Left Bound andRight Bound,in the same
way as describedin step 4.
16
Getting
Started
Gu¢_=?
X=_.O69i_g9
Y=_06.9_216
of a
Other TI-83 Features
Getting Started has introduced
describes in detail the features
other features and capabilities
you to basic TI-83 operation. This guidebook
you used in Getting Started. It also covers the
of the TI-83.
Graphing
You can store, graph, and analyze up to 10 functions
(Chapter 3), up to six parametric functions (Chapter 4), up
to six polar functions (Chapter 5), and up to three
sequences (Chapter 6). You can use DRAW operations to
annotate graphs (Chapter 8).
Sequences
You can generate sequences and graph thenl over time. Or,
you can graph them as web plots or as phase plots
(Chapter 6).
Tables
You can create function
functions sinmltaneously
Split Screen
You can split the screen horizontally to display- both a
graph and a related editor (such msthe Y= editor), the
table, the stat list editor, or the home screen, Ms(), you can
split the screen verticMly to display a graph and its table
sinmltaneously
(Chapter 9),
Matrices
You can enter and save up to 10 matrices and perform
standard matrix operations on them (Chapter 10).
Lists
You can enter and save as nlany lists as lllelllOl_y-allows for
use in statistical analyses. You can attach fornmlas to lists
for automatic computation.
You can use lists to evaluate
expressions at nmltiple values sinmltaneously
and to graph
a family of curves (Chapter 11).
Statistics
You can perform
one- and two-variable,
list-based
statistical
analyses,
including
logistic and sine regression
analysis.
You can plot the data as a histogram,
xyLine,
scatter
plot, modified
or regulm" box-and-whisker
plot, or
normal
probability
plot. You can define and store up to
three stat plot definitions
(Chapter
12).
evaluation
(Chapter
tables to analyze nlany
7).
Getting
Started
17
Inferential
Statistics
You can perform 16 hypothesis tests and confidence
inte_'als and 15 distribution functions. You can display
hypothesis test results graphically or numerically
(Chapter 13).
Financial
Functions
You can use tilne-value-of-lnoney
(TVM) functions to
analyze financial instruments
such as annuities, loans,
mortgages, leases, and sa_lngs. You can analyze the value
of money over equal time periods using cash flow
functions. You can amortize loans with the amortization
functions (Chapter 14).
CATALOG
The CATALOG is a convenient, alphal_etieal list of all
functions and instructions
on the TI-83. You can paste any
function or instruction from the CATALOG to the current
cursor location (Chapter 15).
Programming
You can enter and store programs that include
control and input!output
instructions
(Chapter
Communication
Link
The TI-83 has a port to connect and conlnlunieate
with
another TI-83, a TI-82, the Calculator-Based
Laborato_sJ u
(CBL 2
CBL
System, a Calculator-Based
Ranger
(CBWM), or a personal computer. The unit-to-unit link
cable is included with the TI-83 (Chapter 19).
TM,
18
Getting
Started
TM)
extensive
16).
TM
1
Contents
Operating
the TI-83
Turning On and Turning Off tile TI-83 ....................
Setting the Display Contrast
.............................
Tile Display" ..............................................
Entering Expressions
and Instructions
...................
TI-83 Edit Keys ..........................................
Setting Modes
...........................................
Using TI-83 Variable Names
.............................
Storing Variable Values ..................................
Recalling Variable Values ................................
1-2
1-3
1-4
1-6
1-8
1-9
1-13
1-14
1-15
ENTRY (Last Entry) Storage Area ........................
Ans (Last Answer) Storage Area .........................
TI-8:_ Menus .............................................
VARS and VARS Y-VARS Menus .........................
1-16
1-18
1-19
1-21
Equation Operating
System (EOS TM) .....................
En'or Conditions
.........................................
1-22
1-24
TEXAS
TI-83
INSTRUMENTS
Sol Eng
123456789
Degree
Pol Se_
Dot
Si_ul
Horiz
G-T
J
STAT
PLOT
TBLSET
FORMAT
CALC
TABLE
Operating
tile
TI-83
1-1
Turning
On and Turning
Turning On the
Calculator
To turn
Off the TI-83
on the TI-83,
press
ION].
•
If you previously
had turned
pressing
K_] [OFF], the TI-83
as it was when you last used
off the calculator
by
displays
the home screen
it and clears any error.
•
If Automatic
Power Down m (APD TM) hal p_eviously
turned
off the calculator,
the TI-83 will return exactly
you left it, including
the display, cursor, and any em)r.
To prolong the life of the batteries,
APD turns
automatically
after about five minutes
without
Turning Off the
Calculator
To turn
Operating
the
manually,
All settings
and memory
Constant
Memo_y TM.
•
Any er_)r
TI-83
replaceable
To replace
in memory,
1-2
TI-83
•
The
Batteries
offthe
TI-83
condition
uses
press
contents
[_
as
off the TI-83
any actixqty.
[OFF].
are retained
by
is cleared.
four AAA alkaline
batteries
and has a user-
backup
lithium batte_Ty- (CR1616 or CR1620).
batteries
without
losing any information
stored
follow the steps in Appendix
B.
Setting
the Display
Adjusting the
Display Contrast
Contrast
You can adjust
the display
contrast
to suit your
angle and lighting conditions.
As you change the
setting, a number
from 0 (lightest)
to 9 (darkest)
top-right
corner indicates
the current level. You
able to see the number
if contrast
is too light or
viewing
contrast
in the
may not be
too dark.
Note: The T1-83 has 40 contrast settings, so each number 0 through 9
represents four settings.
The TI-83 retains
turned
off.
tile
To adjust
the
contrast,
1. Press
and release
contrast
follow
setting
these
in nlenlol_y- when
it is
steps.
the D_] key.
2. Press and hold [] or [], which are below and above
contra_t
sjnnbol
(yellow,
half-shaded
circle).
•
[] lightens
the
•
[] darkens
the screen.
the
screen.
Note: If you adjust the contrast setting to 0, the display may become
completely blank. To restore the screen, press and release _, and
then press and hold [] until the display reappears.
When to Replace
Batteries
When the batteries are low, a low-battelT message
displayed when you turn on the calculator.
Your
is
battePies
ape lou.
Recommend
change
of
batteries,
To replace the batteries without losing any- information
memory, follow tile steps in Appendix B.
in
Generally-, the calculator
will continue
to operate
for one
or two weeks
after the low-batte<F
message
is fil_t
displayed.
After this period, the TI-83 will turn off
automatically
and the unit will not operate.
Batteries
nmst
be replaced.
All nmmow
is retained.
Note: The operating period following the first low-battery message
could be longer than two weeks if you use the calculator infrequently.
Operating
the
TI-83
1-3
The Display
Types of
Displays
The
TI-83
displays
both
text
and graphs.
Chapter
3
Home
The home screen
is the prima_T screen
of the TI-83. On
this screen,
enter instructions
to execute
and expressions
to evaluate.
The answers
are displayed
on the same screen.
describes
graphs.
Chapter
9 describes
how the TI-83 can
display- a horizontally
or vertically
split screen to show
graphs and text simultaneously.
Screen
Displaying
Entries and
Answers
When text is displayed,
the TI-83 screen can display a
nlaxinmm
of eight lines with a nmxinmm
of 16 characters
per line. If all lines of the display
are full, text scrolls
off
the top of the display.
If an expression
on the home screen,
the Y= editor (Chapter
3), or the program
editor
(Chapter
16) is longer than one line, it wraps to the
beginning
of the next line. In numeric
editors
such as the
window
screen (Chapter
3), a long expression
scrolls to
the right and left.
VC]mn an enhT is executed
on the home screen,
is displayed
on the right side of the next line.
Entry
Answer
io9(2)
• 3010299957
The mode
expressions
the answer
settings
control
and displays
the way the TI-83 interprets
answers
(page 1-9).
If an answer,
such as a list or matrix,
is too long to display
entirely
on one line, an ellipsis
(...) is displayed
to the right
or left. Press [] and [] to scroll the answer.
ILl
1{25.12
874.2
36_
Returning to the
Home Screen
To return
Busy Indicator
When the TI-83 is calculating or graphing, a vertical
moving line is displayed as a busy indicator in the top-right
corner of the screen. When you pause a graph or a
program, the busy indicator becomes a vertical moving
dotted line.
1-4
Operating
[_
the
to the honle
screen
Entry
Answer
fronl
any- other
screen,
press
[QUIT].
TI-83
Display Cursors
In most
cases,
will happen
menu item
the appearance
of the cursor
when you press the next
to be pasted
as a character.
indicates
key- or select
what
the next
Cursor
Appearance
Effect of Next Keystroke
EntKF
Solid
•
A character
is entered
at the
cursor;
any existing
character
ove_wvritten
rectangle
Insert
Underline
A character
Second
Reverse
[]
a_TOW A 2nd character
(yellow on the
keyboard)
is entered
or a 2nd
operation
is executed
Alpha
Reverse
[]
A
Full
Checkerboard
rectangle
iiiiiii
An alpha
keyboard)
executed
is inserted
in front
is
of
character
(green on the
is entered
or SOLVE is
No ently; the lnaxilnuln
are entered at a prompt
is full
ehara('te_
or lnelnory
If you press @
during an insertion,
the cursor becomes
an underlined
A (A) ff you p_ss
[_
during an insertion,
the
underline
cursor
becomes
Graphs and editors
which are described
an underlined
sometimes
in other
display
chapters.
Operating
I' (I').
additional
the
cursors,
TI-83
1-5
Entering
Expressions
What Is an
Expression?
and Instructions
An expression is a group of numbers, variables, functions
and their arguments, or a combination
of these elements.
An expression evaluates to a single answer. On the TI-83,
you enter an expression in the same order _.s you would
write it on paper. For exalnple, xR 2 is an expression.
You can use an expression on tile home screen to calculate
an answer. In most places where a value is required, you
can use an expression to enter a value.
(i/3) •
z 111111111
Entering an
Expression
I
WINDOW
Xmin=-10
Xmax=2x
[
I
To create an expression,
you enter numbers,
variables,
and
functions
from the keyboard
and menus.
AI_ expression
is
coinpleted
when you press [gNY_, regardless
of the cursor
location.
The entire expression
is evaluated
according
to
Equation
Operating
System (EOS TM) rules (page 1-22), and
the answer
is displayed.
Most TI-83 functions
and operations
are s3qnbols
comprising
several
characters.
You nmst enter the symbol
from the keyboard
or a menu; do not spell it out. For
example,
to calculate
the log of 45, you nmst press [UfN 45.
Do not enter the letters
t., O, and 6. If you enter LOG, the
TI-83 inteqorets
the enttT as implied
nmltiplication
of the
variables
L, O, and G
Calculate 3.76 + (-7.9 + _5) + 2 Iog 45.
a[E][email protected]@
[d 5DD
@21 q 45D
2. 642575252
Multiple Entries
on a Line
To enter two or more expressions
or instructions
on a line,
separate them with colons (@
[:]). All instructions
are
stored together in last enttT (ENTRY; page 1-16).
15+R:2+B:R/B
1-6
Operating
the
TI-83
2.51
Entering a
Number in
Scientific
Notation
To enter
a number
in scientific
notation,
ff)llow
these
steps.
1. Enter the part of the number
that precedes
exponent.
This value can be an expression.
2. Press
[_
[EE]. E is pasted
to the cursor
the
location.
3. If the exponent
is negative,
press D, and then
exponent,
which can be one or two digits.
l(19/2)
When
£-2
you enter
enter
the
.0951
a number
in scientific
notation,
the TI-83
does not automatically
display
answers
in scientific
or
engineering
notation.
The mode settings
(page 1-9) and the
size of the number
determine
the display- format.
Functions
A function
returns
a value. For example,
+, -, +, _(, and log(
are tlle functions
in the example
on page 1-6. In general,
the
first letter of each function
is lowercase
on the TI-83. Most
functions
take at least one a_gument,
parenthesis
( ( ) following
the name.
_qui_s
one argument,
sin(value).
as indicated
For exalnple,
by _m open
sin(
Instructions
An instruction
initiates
an action. For example,
ClrDraw is
an instruction
that clears any- drawn
elements
from a
graph. Instructions
cannot be used in expressions.
In
general,
the first letter of each instruction
name is
uppercase.
Some instructions
take more than one
argument,
as indicated
by an ()pen parenthesis
( ( ) at the
end of the name. For example,
Circle( requires
three
arguments,
Circle(X,Y, radius).
Interrupting a
Calculation
To intetTupt
a eMeulation
or graph in progress,
would be indicated
by the busy indicator,
press
When
you interrupt
a calculation,
•
To return
•
To go to the location
When
to the home
you interrupt
screen,
the menu
select
a graph,
To return to the home
nongraphing
key.
•
To restart
graphing,
graphing
instruction.
a partial
screen,
press
is displayed.
1:Quit.
of the interruption,
•
which
[_].
select
graph
press
a graphing
Operating
2:Goto,
is displayed.
@
or any
key or select
the
TI-83
a
1-7
TI-83 Edit Keys
Keystrokes
Result
[] or []
[] or []
Moves the cursor
within an expression;
these keys repeat.
Moves the cursor from line to line within an expression
occupies more than one line; these key-s repeat.
that
On the top line of an expression on the honle screen, [] nloves
the cursor to the beginning of the expression.
On the bottom line of an expression on the home screen,
nloves the cursor to the end of the expression.
Moves the cursor
to the beginning
Moves the cursor
to the end of an expression.
Evaluates
an expression
of an expression.
or executes
an instruction.
On a line with text on the home screen,
On a blank line on the honle screen,
home screen.
In an editor, clears the expression
located; it does not store a zero.
Deletes
[_
tINS]
a character
clears the current
clears everything
or value where
line.
on the
the cursor is
at the cursor; this key repeats.
Changes the cursor to __ ; inserts
underline cursor; to end insertion,
[], or [].
[]
chm'acters in front of the
press [2_] [,NS] or press [], [],
[_
Changes the cursor to n; the next keystroke performs a 2nd
operation (an operation in yellow above a key- and to the left); to
cancel 2nd, press [2_] again.
@
Changes the cursor to i51;the next keystroke pastes an alpha
character (a character in green above a key and to the right) or
executes SOLVE (Chapters 10 and 11); to cancel @,
press
@
or press _, [], [], or [].
[_
[A-LOCK]
Changes the cursor to r/l;sets alpha-lock; subsequent keystrokes
(on an alpha key) paste alpha characters; to cancel alpha-lock,
press @;
name prompts set alpha-lock automatically.
Pastes an X in Func Inode, a T in Par Inode, a O in Pol Inode, or an
n in Seq mode with one keystroke.
1-8
Operating
the
TI-83
Setting
Modes
Checking Mode
Settings
Mode
settings
control
how the TI-83
displays
and
interprets
numbers
and graphs.
Mode settings
are retained
by the Constant
Meln(aTy- feature
when the TI-83 is turned
off. All numbet_,
including
elements
of matrices
and lists,
are displayed
according
to the current
mode settings.
To display- the mode settings,
press [Mff_]. The current
settings
are highlighted.
Defaults
are highlighted
below.
The following
pages describe
the mode settings
in detail.
Normal
Sci
Eng
Float
0123456789
Radian
Degree
Func Par Pol Seq
Connected
Dot
Sequential
Simul
Real
a+b i re^0 i
Ful 1 H0ri z G T
Changing Mode
Settings
To change
Numeric
notation
Nulnber
of deeilnal
places
Unit of angle men,sure
Type of graphing
Whether
to connect
graph points
Whether
to plot sinmltaneously
Real, rectangular
cplx, or polar eplx
Full screen,
two split-screen
modes
nlode settings,
follow these steps.
1. Press [] or [] to lnove the cm\sor to the line of the
setting that you want to change.
2. Press [] or [] to nlove the cursor
want.
3. Press
Setting a Mode
from a Program
to the setting you
[ggY_,
You call set a mode fronl a program by entering the name
of the mode as all instruction; for example, Func or Float.
Fronl a blank eonlnland line, select the nlode setting fronl
the mode screen; the instruction is pasted to the cursor
location.
PROGRRM: TEST
: FuncI
I
Operating
the
TI-83
1-9
Normal,
Sci, Eng
Notation
modes
only
'affect the way
an answer
is displayed
on the home screen.
Numeric
answers
can be displayed
with up to 10 digits and a two-digit
exponent.
You can
enter a number
in any- format.
Normal notation
numbers,
with
in 12345.67.
mode is the usual way we express
digits to the left and right of the decimal,
as
Sci (scientific)
notation
mode expresses
number,s
in two
pm'ts. The significant
digits display- with one digit to the left
of the decimal.
The app_)priate
power
of 10 displays
to the
right of E, t_sin 1.234567E4.
Eng (engineering)
notation
mode is similm" to scientific
notation.
However,
the number
can have one, two, or three
digits before the decimal;
and the power-of-10
exponent
is
a nmltiple
of three, as in 12.34567E3.
Note: If you select Normal notation, but the answer cannot display in
10 digits (or the absolute value is tess than .00I ), the TF83 expresses
the answer in scientific notation.
Float,
0123456789
Float (floating)
the sign
decimal
mode
displays
up to 10 digits,
plus
and decimal.
0123456789
(fixed)
decimal
mode specifies
the number
of
digits (0 through
9) to display to the right of the decimal.
Place the cursor
on the desired
and then press [ENYE_.
The decimal
setting
notation
modes.
applies
The decimM setting applies
•
•
•
•
•
1-10
Operating
the
number
to Normal,
of decimal
digits,
Sci, and Eng
to these numbers:
An answer displayed on the home screen
Coordinates on a graph (Chapters 3, 4, 5, and 6)
The Tangent( DRAW instruction equation of the line, x,
and dy/dx values (Chapter 8)
Results of CALCULATE operations (Chapters 3, 4, 5,
and 6)
The regression equation stored after the execution of a
regression lnodel (Chapter 12)
TI-83
Radian,
Degree
Angle modes control how the TI-83 inteq)rets angle values
in trigonometric
functions and polar/rectangular
conversions.
Func, Par, Pol,
Seq
Radian mode intelprets
display- in radians.
angle values as radians. Answers
Degree mode interprets
display- in degrees.
angle vMues as degrees. Answers
Graphing modes define the graphing paralneters.
3, 4, 5, and 6 describe these nlodes in detail.
Chapters
Func (function) graphing mode plots functions,
a function of X (Chapter 3).
where Y is
Par (parametric)
graphing mode plots relations,
and Y are functions of T (Chapter 4).
where X
Pol (polar) graphing mode plots functions,
function of 0 (Chapter 5).
Seq (sequence)
Connected, Dot
where
graphing mode plots sequences
r is a
(Chapter
6).
Connected plotting mode draws a line connecting
point eMeulated for the selected functions.
each
Dot plotting mode plots only the e;flculated
selected functions.
of the
Operating
points
the
TI-83
1-11
Sequential, Simul
Sequential graphing-order
mode evaluates
and plots one
function
completely
before the next function
is evaluated
and plotted.
Simul (sinmltaneous)
graphing-order
mode evaluates
and
plots all selected
functions
for a single wdue of X and then
evMuates
and plots them for the next value of X.
Note: Regardless of which graphing mode is selected, the TI-83 wil!
sequentially graph all stat plots before it graphs any functions.
Real, a+bi,
re^Of
Real mode does not display
complex
results
complex
numbers
are entered
as input.
Two
Full, Horiz, G-T
display-
a+bi (rectangulm"
complex
numbers
in the form a+bi.
•
re^0i (polar
in the fornl
complex
re^Oi.
Full screen mode
or edit screen.
uses
Each split-screen
sinmltaneously.
nlode
•
Operating
modes
•
•
1-12
complex
the
complex
mode)
results.
displays
mode)
displays
the entire
screen
displays
complex
complex
to display-
numbers
a graph
two screens
Horiz (horizontal)
mode displays the
the top half of the screen; it displays
an editor on the bottom h'alf (Chapter
G-T (graph-table) mode displays the
the left half of the screen; it displays
the right half (Chapter 9).
TI-83
unless
current graph on
the home screen or
9),
current graph on
the table screen on
Using TI-83 Variable
Variables
and
Defined Items
Names
On the TI-83 you can enter and use several types of data,
including real and complex numbe_\s, matrices, lists,
functions, stat plots, graph databases, graph pictures, and
strings.
The TI-83 uses ansigned names for variables and other
items saved in nlenlol_yL For lists, you 'also can create your
own five-character
names.
Variable
Real
Type
Complex
numbers
A, B,...,
Z, 0
A, B,...,
Z, 0
Matrices
[A], [B], [C], . . . , [J]
Lists
Cl, L2, L3, L4, LS, L6, and userdefined haines
Functions
Y1, Y2,...,
Parametric
Polar
equations
Yg, Yo
XIT and YIT, ...
functions
Sequence
, X6T and Y6T
rl, r2, r3, r4, r5, r6
functions
u, v, w
Stat plots
Plot1, Plot2, Plot3
Graph
GDB1, GDB2,...,
databases
GDB9, GDB0
Graph pictures
Picl, Pic2,...,
Pic9, Pic0
Strings
Strl,
Str9, Str0
System
Notes about
Variables
Names
numbers
variables
Str2,...,
Xmin, Xmax, and others
•
You can create
(Chapter
11).
•
Progranls
have user-defined
with variables
(Chapter
16).
•
FI_)lll
the
honle
as many
screen
to matrices
(Chapter
(Chapter
15), system
1), TblStatt (Chapter
3, 4, 5, and
list names
nanles
and
will Mlow
share
nlenlory
or fronl
a progranl,
you can store
10), lists (Chapter
11), strings
variables
such me Xmax (Chapter
7), and all Y= functions
(Chapters
6),
•
FI_Olll an editor, you can store
Y= functions
(Chapter
3).
•
FI_Olll
the
store
a value
•
as nlenlo_y-
honle
to matrices,
lists,
and
sereen_ a progranl,
or all editor, you
to a lnatrix
element
or a list element.
You can use DRAW STO menu
graph datab_kses and pictures
items to store
(Chapter
8).
Operating
the
can
and reeM1
TI-83
1-13
Storing
Variable
Storing Values in
a Variable
Values
Values are stored to and recalled fronl nlenlol_- using
variable names. When an expression containing the name
of a variable is evMuated, the vMue of the variable at that
time is used.
To store a value to a vm'iable fronl the home screen or a
program using the _
key, begin on a blank line and
follow these steps.
1. Enter the value you want to store. The value can be an
expression.
2. Press _.
-> is copied to the cursor
location.
3. Press @
and then the letter of the variable
you want to store the value.
to which
4. Press [gg_O. If you entered an expression, it is
evaluated. The value is stored to the variable.
[5+8_'3÷Q
Displaying a
Variable Value
To display- the value of a vm'iable, enter the name on a
blank line on the home screen, and then press IgOr.
I°
1-14
Operating
517[
the
5171
TI-83
Recalling
Using Recall
(RCL)
Variable
Values
To recall
and copy
location,
follow
variable
these
contents
steps.
to the current
To leave
1. Press [2_] ERCL]. Rcl and the edit
the bottom
line of the screen.
Enter
the name
of the variable
are displayed
on
in any of five ways.
Press
•
Press [g_ [LIST], and then
or press [g_ [Ln].
•
Press
•
Press [V_g] to display
the VARS menu or _
[] to
display the VARS Y-VARS menu; then select the type
and then the name of the variable
or function.
•
Press NRgM] [_, and then
program
(in the program
_,
variable
bottom
and then
cursor
cursor
@.
•
The
@
RCk, press
the letter
and then select
name
the name
the name
select
editor
you selected
line and the cursor
of the variable.
select
of the matrix.
the name
only).
is displayed
of the list,
of the
on the
disappeat\s.
100+
Rol 0
Press IENTEEI.The variable
contents
are inserted
the cursor
w_s located
befot_ you began these
1100+517I
where
steps.
I
Note: You can edit the characters pasted to the expression without
affecting the value in memory.
Operating
the
TI-83
1-15
ENTRY
(Last Entry)
Using ENTRY
(Last Entry)
Storage
Area
When you press [g_
on the holne screen to evaluate an
expression or execute an instruction, the expression or
instruction is placed in a storage area called ENTRY (last
ent_T). When you tu_ off the TI-83, ENTRY is retained in
lllelllOl_y',
To recall ENTRY, press 12_ [ENTRY].The last entry is
pasted to the cur_nt cursor location, where you can edit
and execute it. On the home screen or in an editor, the
current line is clea_d and the last entry is pasted to the
line.
Because
the TI-83 updates
ENTRY only when you press
[g_,
you can recall the previous
entry even if you have
begun to enter the next expression.
5 [] 7
F_a] [ENTRY]
Accessing a
Previous Entry
5+7
5 +711
12
The TI-83 retains
as many previous
entries
as possible
in
ENTRY, up to a capacity
of 128 bytes. To scroll those
entries,
press [_
[ENTRY] repeatedly.
If a single ent_T is
more than 128 bytes, it is retained
for ENTRY, but it cannot
be placed
in the ENTRY storage
area.
2_B
I_
I_A
[_
[ENTRY]
2+B
1÷1::1
2+BI
12
If you press [[email protected]] [ENTRY] after displaying
the oldest stored
enttT, the newest
stored entry is displayed
again, then the
next-newest
entry, and so on,
[ENTRY]
1-16
Operating
the
TI-83
2eB
1+RII
Reexecuting the
Previous Entry
After
you
have pasted
the last
entt'y to the home
and edited it (if you chose to edit it), you can
entry-. To execute
the last ent_T, press [_T_].
screen
execute
the
To reexecute
the displayed
entry, press _
again. Each
reexecution
displays
an answer
on the right side of the
next line; the entry- itself is not redisplayed.
F_°
_
@
@N[][email protected]
Multiple Entry
Values on a Line
N
O+N
N+I÷N:NZ
0
To store to ENTRY two or more expressions
or
instructions,
separate
each expression
or instruction
with
a colon, then press [_T_.
All expressions
and instructions
separated
by colons
are stored in ENTRY.
When you press K_ [ENTRY], all the
instructions
separated
by colons
are
cursor locatkm.
You can edit any of
execute
all of them when you press
expressions
and
p_sted
to the current
the entries,
and then
[_R].
For the equation A=_r 2, use trial and error to find the radius of a
circle that covers 200 square centimeters. Use 8 as your first
guess.
[:][_
[_-]@
R [_7 [_E_
F_ [E.TR¥]
[]
F_t_q
7 [_
[INS] []
95
8÷R:_RZ
201.0619298
8÷R:=RZI
8+R:_Rz
201.0619298
7.95+R:_Rz
198.5565097
Continue until the answer is as accurate as you want.
Clearing ENTRY
Clear Entries (Chapter 18) cleats all data that the TI-83 is
holding in the ENTRY storage area.
Operating
the
TI-83
1-17
I
Ans (Last Answer)
Using Ans in an
Expression
When
Storage
an expression
Area
is evaluated
successfully-
home screen (Jr from a program,
answer to a storage
at_a called
be a real or complex
number,
a
When you turn off the TI-83, the
fronl
the
the TI-83 stores the
Ans (last answer).
Ans nlay
list, a lnatrix,
or a string.
value in Ans is t_tained
in
nlenlol_y.
You can use the variable Ans to represent
the last answer in
most places. Press [2_] tANS] to copy the vm'iable name Ans
to the cm'sor location.
When the expression
is evaluated,
the
TI-83 uses the value of Ans in the calculation.
Calculate the area of a garden plot 1.7 meters by 4.2 meters.
Then calculate the yield per square meter if the plot produces a
total of 147 tomatoes.
1[]TN4C32
147 []
Continuing an
Expression
Storing Answers
_
[ANS]
1.7.4.2
147/Rn_
14[
7
5882s5291
You can use Ans as the first enhTy in the next expression
without entering the value again or pressing [_ tANS]. On
a blank line on the home screen, enter the function. The
TI-83 pastes the vm'iable name Ans to the screen, then the
function.
s[]2
5/2
_gDg[N_ffl
Rns*9.9
To store an answer, store Ans to a variable
evMuate another expression.
2.5
24.75
before you
Calculate the area of a circle of radius 5 meters. Next, calculate
the volume of a cylinder of radius 5 meters and height 3.3 meters,
and then store the result in the variable V.
1-18
Operating
I_ [_]s []
xSZ
N3D3
78.53981634
Rns*3.o
I
__v
Rns+U 259.1813939
259.1813939
the
TI-83
TI-83 Menus
Using a TI-83
Menu
You can access lnost TI-83 operations using lnenus. When
you press a key or key- combination
to display a menu, one
or more menu names appear on the top line of the screen.
•
•
•
•
The menu name on the left side of the top line is
highlighted. Up to seven items in that menu are
displayed, beginning with item 1, which 'also is
highlighted.
A number or letter identifies each menu item's place in
the menu. The order is 1 through 9, then 0, then A, B, C,
and so on. The LISTNAMES, PRGM EXEC, and PRGM
EDIT menus only label items 1 through 9 and 0.
When the menu continues beyond the displayed items, a
down arrow ( $ ) replaces the colon next to the last
displayed item.
When a menu item ends in an ellipsis, the item displays
a secondat7 menu or editor when you select it.
To display any
or [] until that
location within
displayed with
other menu listed on the top line, press []
menu name is highlighted. The cursor
the initial menu is irrelewmt. The menu is
the cursor on the first item.
Note: The Menu Map in Appendix A shows each menu, each
operation under each menu, and the key or key combination
you press
to display each menu.
Scrolling a Menu
To scroll down the menu items, press []. To scroll up the
menu items, press [].
To page down six menu items at a time, press @
[]. To
page up six menu items at a time, press @
[]. The
green arrows on the calculator, between [] and [], are the
page-down and page-up symbols.
To wrap to the last menu item directly fronl the first menu
item, press []. To wrap to the first menu item directly fi'om
the last menu item, press [].
Operating
the
TI-83
1-19
Selecting an Item
from a Menu
You can
select
an item
from
a menu
in either
of two ways,
•
Press the number
or letter of the item you want to
select. The cursor
can be anywvhere on the menu, and
the item you select need not be displayed
on the screen,
•
Press [] or [] to move
and then press [E6T_.
the cursor
After you select an item from
displays
the previous
screen,
to the item
a menu,
the TI-83
you want,
typically
Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT
menus, only items 1 through 9 and 0 are labeled in such a way that
you can select them by pressing the appropriate number key. To move
the cursor to the first item beginning with any alpha character or 6,
press the key combination for that alpha character or e. If no items
begin with that character, then the cursor moves beyond it to the next
item.
Calculate
Leaving a Menu
without
Making a
Selection
1-20
Operating
:_27.
You can leave
four ways.
a menu
without
making
a selection
•
Press
[_]
[QUIT] to return
•
Press
@
to return
•
Press a key or key- combination
such as [M_
or [_
[LIST].
for a different
menu,
•
Press a key or key combination
such as [] or _
[TABLE],
for a different
screen,
the
TI-83
to the home
in any- of
to the prexdous
screen.
screen.
VARS and VARS Y-VARS
VARS Menu
You can
enter
Menus
the
in an expression
haines
of functions
or store
to them
and systeln
varial>les
directly.
To display the VARS inenu, press _.
All VARS inenu
items display
secondm:y- menus, which show the names of
the system
variables.
1:Window, 2:Zoom, and 5:Statistics
each
access
lnore
VARS Y VARS
i: Window...
2 : Zoom.,.
3: GDB...
one
secondaYy
lnenu,
X/Y, T/O, and U/VNV variables
ZX/ZY, ZT/ZO, and ZU wuiables
Graph database
vmiables
Picture variables
4:Picture.,.
5:Statistics.,.
6: Table...
XY, Z, EQ, TEST, and
TABLE vmiables
7: String..,
Selecting a
Variable from the
VARS Menu or
VARS Y-VARS
Menu
than
PTS vmiables
String variables
To display the VARS Y-VARS menu, press _
[].
1:Function, 2:Parametric, and 3:Polar display seconda[3_
menus of the Y= function vmiables.
VARS Y VARS
i:
Yn functions
Function...
2: Parametric...
3:Polar...
X_?,T,Y'rtT functions
rn functions
4:On/Off...
Lets you select/deselect
functions
Note: The sequence variables (u, v, w) are located on the keyboard
as the second functions olin, 1%1,
and El.
To select a variable
follow these steps.
1. Display
fronl
the VARS or VARS Y-VARS menu,
the VARS or VARS Y-VARS menu.
•
Press
[_
to display
•
Press
_
[] to display
the VARS menu.
the VARS Y-VARS lnenu.
2. Select the type of variable,
such as 2:Zoom from the
VARS menu or 3:Polar froln the VARS Y-VARS menu.
secondm:y-
menu
A
is displayed.
3. If you selected
1:Window, 2:Zoom, or 5:Statistics
from
the VARS menu, you can press [] or [] to display ()the["
secondal_y- lnenus,
4.
Select
CUrSOr
a variable
location.
name
from
the menu.
Operating
It is pasted
the
TI-83
to the
1-21
Equation
Order of
Evaluation
Operating
System
(EOS
TM)
The Equation Operating System (EOS
defines the order
in which functions in expressions
are entered and
evaluated on the TI-83. EOS lets you enter numbers and
functions in a simple, straightfot_vard sequence.
TM)
EOS evaluates
the functions
in an expression
in this order:
1
Single-argument
argument,
such
2
Functions
that are entered
after the argument,
such _ks2, -1, 1, o, r, and conversions
3
Powers
4
Pernmtations
5
Multiplication,
division
6
Addition
7
Relational
8
Logic operator
9
Logic operators
Within a priority
right.
functions
that precede
as ¢(, sin(, or log(
and roots,
(nPr)
such
as 2^5 or 5x¢32
and combinations
implied
the
nmltiplication,
(nOr)
and
and subtraction
functions,
such
_
> or <
and
or and xor
level, EOS evaluates
functions
fronl left to
Calculations within parentheses
are ewduated first.
Multiargument
functions, such as nDeriv(A2,A,6), are
evaluated as they are encountered.
1-22
Operating
the
TI-83
Implied
Multiplication
The
TI-83
recognizes
implied
nmltiplication,
so you need
not press [] to express
nmltiplication
in all cases. For
example,
the TI-83 intel_rets
2_, 4sin(46), 5(1+2), and (2"5)7
as implied
nmltiplication.
Note: TI-83 implied multiplication
rules differ from those of the TI-82.
For example, the TI-83 evaluates 1/2X as (1/2)*X,
while the TI-82
evaluates 1/2X as 1/(2"X)
(Chapter 2).
Parentheses
All calculations
inside a pair of pm'entheses
first. For example,
in the expression
4(1+2),
evaluates
the portion
inside the pm'entheses,
nmltiplies
the answer,
3, by 4.
4(1+2)
4.1+2
are completed
EOS first
1+2, and then
I_
You can omit tile ('lose parenthesis
( ) ) at tile end of an
expression.
All ()pen parenthetical
elements
are closed
automatic_dly
at the end of an expression.
This is Mso true
for open parenthetical
elements
that precede
the store or
display-conversion
instructions.
Note: An open parenthesis following a list name, matrix name, or Y=
function name does not indicate implied multiplication. It specifies
elements in the list (Chapter I1) or matrix (Chapter 10) and specifies a
value for which to solve the Y= function.
Negation
To enter a negative
number,
use the negation
key. Press []
and then enter the number.
On the TI-83, negation
is in the
third level in the EOS hierm'chy.
Functions
in the fil\st
level,
such
as squaring,
For example,
[ _se parentheses
-2z
(-2) z
ale ewduated
-X 2, evaluates
to square
_
_
before
to a negative
a negative
negation.
number
(or 0).
number.
12->R
-AZ
42
( -A ) z
-4
Note:Use the[] key forsubtraction
and the[] keyfornegation.
If
you press [] to enter a negative number, as in 9 [] [] 7, or if you
press [] to indicate subtraction, as in !) [] 7, an error occurs. If you
press @
A [] @
B, it is interpreted as implied multiplication
(A*-B).
Operating
the
TI-83
1-23
Error Conditions
Diagnosing
Error
an
The TI-83 detects
•
•
•
•
errot\s while performing
these tasks.
Ewduating an expression
Executing an instruction
Plotting a graph
Storing a value
VClmnthe TI-83 detects
message as a menu title,
ERR:DOMAIN. Appendix
possible reasons for tile
an error, it returns an etTor
such _ts ERR:SYNTAX or
B describes each error type and
etTor.
ERR: S_,"NTRX
_a[IQuit
2: Goto
I
•
•
I
If you select 1:OuR (or press [_ [QUIT]or @),
then
tile home screen is displayed.
If you select 2:Goto, then the prexqous screen is
displayed with the cut\sot at or neat" the error location.
Note: If a syntax erroroccurs in the contentsof a Y= functionduring
program execution, thenthe Goto option returnsto the Y= editor, not
to the program.
Correcting
Error
an
To eotTect an error, follow these steps.
1. Note the error type (ERR:e_9"or type).
2. Select 2:Goto, if it is available. The previous screen is
displayed with the cursor at or neat" the error location.
3. Determine the error. If you cannot recognize
refer to Appendix B.
4. Correct
1-24
Operating
the
TI-83
the expression.
the error,
Math,Angle,
Operations and Test
Contents
Getting Started: Coin Flip ................................
Keyboard Math Operations
..............................
MATH Operations
........................................
Using the Equation
Solver ...............................
MATH NUM (Number)
Operations
........................
Entering and Using Complex Nmnbers ...................
MATH CPX (Complex)
Operations
.......................
MATH PRB (Probability)
Operations
.....................
ANGLE Operations
.......................................
TEST (Relational)
Operations
............................
TEST LOGIC (Boolean)
Operations
......................
'_
TEXAS
2-2
2-3
2-5
2-8
2-13
2-16
2-18
2-20
2-23
2-24
2-26
T1=83
iNSTRUMENTS
Q^3+PZ-125=O
-Q=4.6415888336...
P=5
bound={-50,50}
-le_t-rt=O
J
STAT
PLOT
TBLSET
FORMAT
Math,
CALC
Angle,
TABLE
and
Test
Operations
2-1
Getting
Getting
Started:
Started
Coin Flip
is a fast-paced
introduction.
Read the chapter
for details.
Suppose you want to model flipping a fair coin 10 times. You want to track
how many of those 10 coin flips result in heads. You want to perform this
sinmlation 40 times. With a fair coin, the probability of a coin flip resulting in
heads is 0.5 and the probability of a coin flip resulting in tails is I).5.
1. Begin on tile home screen. Press [_
[] to
display the MATH PRB menu. Press 7 to
select 7:randBin( (random Binomial).
randBin( is pasted to the home screen. Press
10 to enter the number of coin flips. Press
[]. Press [] 5 to enter the probability of
heads. Press []. Press 40 to enter the
number of sinmlations.
Press D2.
3.
Press _
to evaluate the expression. A
list of 40 elements is displayed. The list
contains the count of heads resulting from
each set of 10 coin flips. The list has 40
elements because this sinmlation was
performed 40 times. In this example, the
coin came up heads five times in the first
set of 10 coin flips, five times in the second
set of 10 coin flips, and so on.
_andBin(10,.5,40
{5574663_.
Press [_
[_ [L1][gNTgmto store the data
to the list name L1.You then can use the
data for another activity, such as plotting a
histogram (Chapter 12).
Rgs_L_
4.
Press [] or [] to view the additional counts
in the list. Ellipses (...) indicate that the list
continues beyond the screen.
Note: Since randBin( generates random
numbers, your list elements may differ from those
in the example.
2-2
10,. 5,40
_andBin(
Math,
Angle,
and Test
Operations
4 6 6 3 ...
andBin( 10,. 5, 40
5 5 7 4 6 6 3 ,..
..£._._L_6 5 7 5 ...
Keyboard
Math Operations
Using Lists with
Math Operations
Math operations that are valid ff)r lists return a list
calculated element by element. If you use two lists in the
same expression, they nmst be the same length.
{1,2}+{3,
+ (Addition),
- (Subtraction),
* (Multiplication),
/ (Division)
4}+5
{9 113
You can use + (addition, E]), - (subtraction, E]), *
(nmltiplieation,
[_), and / (division, []) with real and
complex numbers, expressions,
lists, and lnatrices. You
cannot use / with matrices.
valueA+valueB
valueA*valueB
Trigonometric
Functions
valueA
valueA
- valueB
/ valueB
You can use the trigonometric
(trig) functions
(sine, [gN];
cosine, [Ugg]; and tangent,
_)
with real number\%
expressions,
and lists. The current
angle mode setting
'affects
tetut]ls
interpretation.
-.9880316241;
sin(value)
For example,
sin(a0) in Radian mode
in Degree mode it returns
.5.
cos(value)
tan(value)
You can use the inverse
trig functions
arccosine,
[g_] [c05-t];
and arctangent,
real nmnbers,
expressions,
and lists.
mode setting affects interpretation.
sin -1(value)
(aresine,
[g_] [StN-1];
[g_] [TAN-t])with
The current
angle
cos -1(value)
tan -1(value)
Note: The trig functions do not operate on complex numbers.
^ (Power),
2 (Square),
,[( (Square Root)
You can use ^ (power, [_), 2 (square, [77]), and _/( (square
root, [g_] [4]) with teal and complex numbers, expressions,
lists, and nmtrices. You cannot use _( with matrices.
value^power
-1
(inverse)
value 2
_[(value)
You can use -1 (inverse, []
) with real and complex
numbers, expressions,
lists, and matrices. The
nmltiplieative
inverse is equivalent to the reciprocal,
l/x.
value-1
15'
.21
Math,
Angle,
and
Test
Operations
2-3
You can use log( (logarithln,
FO_), 10^( (power
of 10, [_
[10x]), and In( (natural
log, @) with real or eolnplex
log(,
10^(,
In(
nulnbers,
expressions,
log(value)
e^( (Exponential)
and lists,
lO^{power)
In(value)
e^( (exponential,
[2_ [ex]) returns
the constant
a power.
You can use e^( with real or complex
expressions,
and lists.
e raised
numbers,
to
eA(t)owe_ ,')
le^(5)148.41315911
e (constant, [g_] [el) is stored as a constant on the TI-83.
Press Kfid][el to copy e to the cursor location. In
calculations, the TI-83 uses 2.718281828459 for e.
e (Constant)
e
2.718281828
- (negation, D) returns the negative of value. You can use with real or complex numbers, expressions,
lists, and
matrices.
- (Negation)
-value
EOS rules (Chapter 1) determine when negation is
evaluated. For example, -A2 t_turns a negative nulnber,
because squaring is evaluated before negation. Use
parentheses
to square a negated number, as in (-A)2,
2+R:
2z, ( {-RZ,
-2)z} ( -R>a, {-4 4 -4 4}
Note: On the TI-83, the negation symbol (-) is shorter and higher than
the subtraction sign (-), which is displayed when you press D.
(Pi)
(Pi, [g_ [_]) is stored
calculations,
the TI-83
Ix
2-4
Math,
Angle,
and
3.1415926541
Test
Operations
as a constant
in the
uses 3.1415926535898
TI-83, In
for _.
MATH Operations
MATH Menu
To display the MATH menu, press [MKTgl.
MATH NUMCPX PRB
1 : _Fra c
Displays
2:_Dec
3:3
4:3_(
5: x#
6: fMin(
7: fMax(
8:nDeriv(
9: fnlnt(
O: Solver.,.
_Frac,
_Dec
the answer
as a fraction.
Displays
the answer
as a decimal.
Calculates
the cube.
Calculates
the cube root.
Calculates
the x t;_root.
Finds
Finds
the nlininmln
the nlaxinlunl
of a function.
of a function.
(3olnputes
the numerical
derivative.
(Tonlputes
tile function
integral.
Displays
the equation
solver.
_Frac (display at a fraction) displays an answer _L_its
rational equivalent. You can use _Frac with real or complex
numbers, expressions,
lists, and matrices. If the answer
cannot be simplified or the resulting denominator
is more
than three digits, the decimal equivalent is returned. You
can only use _Frac following value.
value _Frac
_Dec (display as a decimal)
displays
an answer
in decimal
form. You can use *Dec with real or complex
numbet_,
expressions,
lists,
following
value.
value
and matrices.
You
can only use _Dec
_Dec
I/2+I/3_Frac o/61
Ans_Deo
.8333333333
Math,
Angle,
and
Test
Operations
2-5
3(Cube),
3_r( (Cube
3 (cube)
Root)
returns
or complex
nmtrices.
the cube
numbers,
of value.
expressions,
You can use 3 with
lists,
real
and square
value 3
3_( (cube root) returns
the cube root of value.
3_( with
real or complex
numbers,
expressions,
You can use
and lists.
3_(value)
{2,3,4,5}3
{8 27
64 125}
3 4 5}
_J'(Rns){2
x_ (Root)
x_ (xth root) returns the x th root of value. You can use x_
with real or complex numbers, expressions,
and lists.
xthrootX-_ value
5 N'32
fMin(,
fMax(
2
fMin( (function
retun_ the value
and fMax( (function
the local ndninmm
nlininlunl)
at which
nlaxinlunl)
or local
nmxinmnl
value of expression
with respect
to variable
occurs, between/ower
and upper values for variable,
fMin(
and fMax( are not valid in expression.
The accuracy" is
controlled
iE-5),
by tolerance
(if not specified,
the default
is
fMin(expression,variable,lower,upper[,toleranoe])
fMax(expression,variable,lower,
upper[,toleranoe])
Note: In this guidebook, optional arguments and the commas that
accompany them are enclosed in brackets ([ ]).
f'Min(_in(R),
R,
-_
-I. 570797171
r_x(sir,(A), R,-:_
•
2-6
Math,
Angle,
and
1.570797171
Test
Operations
nDeriv(
nDeriv(
(numerical
derivative)
returns
an approximate
derivative
of expression
with respect
to variable,
given the
value at which to calculate
the derivative
and e (if not
specified,
the default
is 1E-3). nDeriv( is valid only for real
numbers,
nDeriv(expression,variable,value[,a])
nDeriv( uses the s:nnmetrie
difference
quotient
which approximates
the numerical
derivative
slope of the secant
line through
these points.
f(x+e)-f(x-e)
f'(x) =
2e
As e becomes
nlore accurate.
nDer
method,
value as the
iv(RA3,
smaller,
the approxinmtion
usually- becomes
R, 5,.
01 )
75,0001
nDeriv(R^3o
R, 5,.
0001
)
75
You can use nOeriv( once
method
used to calculate
false derivative
fnlnt(
value
in expression.
Because
of the
nDeriv(, the TI-83 can return a
at a nondifferentiable
point.
fnlnt( (function
integral)
returns
the numerical
integral
(Gauss-Kronrod
method)
of expression
with respect
to
variable,
given/ower
limit, upper limit, and a tolerance
(if
not specified,
the default
is 1E-5). fnlnt( is valid only- for real
nunlbers.
fnlnt(expression,variable,lower,
upper[,tolerance])
?nlnt(A_,R,O&l)
•3333330333
Tip: To speed the drawing of integration graphs (when fnlnt( is used
in a Y= equation), increase the value of the Xres window variable
before you press _.
Math,
Angle,
and
Test
Operations
2-7
Using the Equation
Solver
Solver
Solver displays
the equation
solver, in which you can solve
for any variable in an equation,
The equation
is assunled
to
be equal to zero. Solver is valid only for real numbers.
Vcl_en you select
Entering an
Expression in the
Equation Solver
Solver,
one of two screens
•
The equation
editor (see step 1 picture
below)
is
displayed
when the equation
wu'iable
eqn is empty,
•
The interactive
2-9) is displayed
solver editor
(see step 3 picture
on page
when an equation
is stored
in eqn.
To enter an expression
in the equation
solver, assunling
that the variable
eqn is empty, follow these steps.
1, Select 0:Solver from
equation
editor.
EQUATION
e_n: 0=|
2, Enter
the MATH menu
the expression
in any of three
•
Enter the expression
solver,
directly
•
Paste
lnenu
•
Press [_
[act_], p_kste a Y= variable
VANS Y-VANS lnenu,
and press [_,
expression
is pasted
to the equation
a Y= vmiable
name from
to the equation
solver,
is stored
EQURTION
SOLVER
e_n: O=Q"3+P
z-125
|
Math,
Angle,
to display-
and Test
the
SOLVER
The expression
enter it.
2-8
is displayed.
Operations
ways,
into
the equation
the VANS Y-VANS
to the variable
name from
The
solver.
eqn as you
the
3, Press _
displayed.
or [_. The interactive
solver editor is
1%35 -1 5=8
P=8
bound={
•
•
•
•
-1 E99, 1...
The equation stored in eqn is set equal to zero and
displayed on the top line.
Variables in the equation are listed in tile order in
which they appear in the equation. Any values stored
to the listed variables also are displayed.
The default lower and upper bounds appeal" in the
last line of the editor (bound={-1E99,1E99}).
A 4 is displayed in the first colunul of the bottonl line
if tile editor continues beyond the screen.
Tip: To use the solverto solve an equationsuch as K=.SMV2, enter
eqn:0=K-.SMV 2 inthe equationeditor.
Entering and
Editing Variable
Values
When you enter or edit a value for a variable in the
interactive solver editor, the new value is stored in
nlenlol_yto that varialfle.
You can enter an expression for a variable value. It is
ewduated when you move to the next varialfle.
Expressions
nmst resolve to real numbers at each step
during the iteration.
You can store equations to any VAR8 Y-VARS variables,
such as Y1 or r6, and then reference the w_riables in tile
equation. The interactive solver editor displays all
varialfles of all Y= functions referenced in the equation.
EQURTION
e_n:
8=V., +7SSL_)ER
I
Y_+7=Obound=C=BR=SX=8
{ -i E99, I.,.
Math,
Angle,
and
Test
Operations
2-9
Solving for a
Variable in the
Equation Solver
To solve
for a variable
equation
has been
using
stored
the equation
to eqn, follow
solver
these
after
an
steps.
1. Select 0:Solver from the MATH menu to display the
interactive
solver editor, if not already
displayed.
I% ;P -125=°P=o
L.
bound={-1E99,
2. Enter
Ol" edit tile value
of each
known
variable.
variables,
except the unknown
variable,
nmst
value. To move the cm\sor to the next wuiable,
All
contain
press
INto or _.
QQ3;PZ-125=0p=5I 1...
bound={
3. Enter
-1 E99,
an initial
guess
for tile variable
for which
you are
solving. This is optional,
but it may help find the
solution
more quickly-. Also, for equations
with nmltiple
roots, the TI-83 will attempt
to display the solution
that
is closest
to your
guess,
IQ"3+Pp=sQ=4I
z- 125=0
bound={
-I E99,
1...
(upper+
The
2-10
Math,
Angle,
and
default
Test
guess
is calculated
Operations
as
lower)
2
a
4. Editbound={lower,upper},
lower and
bounds
between
which
the TI-83
upper are the
searches
for a solution.
This is optional,
but it may help find the solution
quickly. The default is bound={- 1E99,1E99}.
more
5. Move the cursor to the variable for which you want to
solve and press @
[SOLVE](above the [gNTgNkey-).
Q_'3+PZ-125=0
I,Q=4.6415888336...
P=5
bound={-50,50}
leCt-rt=O
The solution
is displayed
next to tile variable
for
which you solved. A solid square
in the fil_t colunm
marks the variable
for which you solved and
indicates
that the equation
is balanced.
An ellipsis
shows that tile value continues
beyond
the screen.
Note: When a number continues beyond the screen, be sure to
press [] to scroll to the end of the number to see whether it
ends with a negative or positive exponent. A very small number
may appear to be a large number until you scroll right to see
the exponent.
The values of the variables are updated in nlenlot'y.
left-rt=diffis
displayed in the last line of the editor.
diffis tile difference between the left and right sides
of the equation. A solid square in the first colunm
next to left-rt= indicates that the equation has been
evaluated at the new value of tile variable for which
you solved.
Math_
Angle_
and
Test
Operations
2-11
Editing an
Equation Stored
to eqn
To edit or replace an equation stored to eqn when the
interactive equation solver is displayed, press [] until the
equation editor is displayed. Then edit the equation.
Equations with
Multiple Roots
Sonle equations
have nlore than one solution.
You can
enter a new initial guess (page 2-10) or new bounds
(page 2-11) to look for additional
solutions.
Further Solutions
After you solve for a varialfle,
solutions
from the interactive
you can continue
to explore
solver editor.
Edit the values
of one or more varialfles.
When you edit any variable
value,
the solid squares
next to the previous
solution
and
left-rt=diff
disappear.
Move the cursor
to the varialfle
for
which you now want to solve and press @
[SOLVE].
Controlling
the
Solution for
Solver
or solve(
The TI-83 solves equations
through
an iterative
process.
To
control that process,
enter bounds
that are relatively
close
to the solution
and enter an initial guess within those
bounds.
This will help to find a solution
more quickly. Also,
it will define which solution
you want for equations
with
nmltiple
Using solve( on
the Home Screen
or from a
Program
solutions.
The function
solve( is available
only fronl CATALOG or
from within a program.
It returns
a solution
(root) of
expression
for variable,
given an initial guess, and lower
and upper bounds
within which the solution
is sought.
The
default for lower" is -1E99. The default
for upper is 1E99.
solve( is vMid only for real numbers.
soNe(expression,variable,guess[
,{lower, upper'} ])
expression
is assumed
equal to zero. The value of variable
will not be updated
in nlenlory,
guess nlay be a value or a
list of two values. Values must be sto[_d
for eve_Ty"variable
in expression,
except
variable,
before expression
is
evaluated./ower
and upper
nmst be entered
in list format.
4. 641588834
2-12
Math,
Angle,
and
Test
Operations
MATH NUM (Number)
MATH NUM Menu
To display
Operations
the
MATH NUM menu,
MATH NUM CPX PRB
i : ab s (
2: round(
Al_solute
Round
3 : i Part (
Integer
4:
5:
6:
7:
Fractional
part
Greatest
integer
Mininmln
value
Maxinlunl
value
f Pa r t (
i nt(
mi n (
max (
8 : ] cm(
9 :gcd (
abs(
press
[Z],
_
value
part
Legist eonlnlon
nmltiple
Greatest
eonnnon
divisor
abs( (absolute
value)
returns
complex
(modulus)
numbers,
matrices.
the absolute
expressions,
value of real
lists, and
or
abs(value)
abs ( -256 )
2561,
abs( {I.25, -5.67}
I
{1.25
5.67}
Note: abs( is also available on the MATH CPX menu.
round(
round( returns a nunlber,
expression, list, or nlatrix
rounded to #decimals (_<9). If #decimals is omitted, value
is rounded to the digits that are displayed, up to 10 digits.
rou nd(value [,#decimals
])
123456789012÷C
I
1.23456789E111
round
(x, 4) 3. 1416
C-round(C)
!21
123456789012-Iz3
456789000
Math,
Angle,
and Test
Operations
12
2-13
iPart( (integer
iPart(,
fPart(
or complex
part)
numbers,
returns
the integer
expressions,
lists,
part
or parts
of ++al
and matrices.
iPart(value)
fPart( (fra('tional
real or complex
paxt) returns
the fractional
part or p_u'ts of
numbe_,
expressions,
lists, and lnatrices.
fPart(value)
int(
iPart
(-23.45)
-23
f Part
( -23.45)._ 45
int( (greatest
integer)
returns
the largest integer
_<real
complex
numbers,
expressions,
lists, and nmtrices.
or
int(value)
lint(-23.45)
_241
Note:Fora givenvalue,
theresult
ofint(isthesame as theresult
of
iPart( for nonnegative numbers and negative integers, but one integer
less than the result of iPart( for negative noninteger numbers.
2-14
Math,
Angle,
and
Test
Operations
min(,
max(
min( (ndnimum
value)
valueB
or the smallest
returns
element
the smaller
of valueA
and
in list, If listA and listB are
compared,
min( returns
a list of the smaller
of each pair
elements,
If list and value are compared,
min( compares
each element
in list with value,
of
max(
(n]axin]on]
value) returns
the larger of valueA
and
valueB
or the largest element
in list. If listA and listB are
con]pared,
max( retm'ns
a list of the larger of each pair of
elements.
If list and value are compared,
max( compares
each element
in list with value,
min(valueA,valueB)
min(list)
min(listA,listB)
min(list,value)
max(valueA,valueB)
max(list)
max(listA,listB)
max(list,value)
r,,in
(3,2+2)=
3[
r,,in( {3, 4, _,}, 4)
{3 4 4}
r,Jax( {4, 5, 6})
I
6
Note: rain( and max( also are available on the LIST MATH menu.
Icm(,
gcd(
Icm( t_tums
the least eonlnlon
nmltiple
of valueA
and
valueB,
both of which must be nonnegative
integers,
When
listA and listB are specified,
Icm( retm'ns
a list of the lcm
of each pair of elements.
If list and value are specified,
Icm( finds
the leln of each
element
in list and value,
gcd( returns
the greatest
conlnlon
divisor
of valueA
and
valueB,
both of which must be nonnegative
integers,
When
listA and listB are specified,
gcd( t'etun_s
a list of the ged
of each pair of elements.
If list and value are specified,
gcd( finds the ged of each element
in list and value,
Icm(valueA,valueB)
Icm(listA,listB)
Icm(list,value)
gcd(valueA,valueB)
gcd(listA,listB)
gcd(list,value)
10M(2,5)
10
god( {48, 66}, {64,
122} )
{16
Math,
2}
Angle,
and
Test
Operations
2-15
Entering
and Using Complex
Complex-Number
Modes
Numbers
The TI-83 displays complex numbers in rectangular form
and polar forln. To select a complex-nulnber
lnode, press
[MffffE],
and then select either of the two modes.
•
•
a+bi (rectangular-complex
lnode)
re^0/(polar-colnplex
mode)
Sci
Eng
Dot
Horiz
G-T
On the TI-83, complex numbet\s can be stored to variables.
Also, complex numbers are valid list elements.
In Real mode, COlnplex-nulnber results return an error,
unless you entered a complex number as input. For
example, in Real mode In(-1) returns an error; in a+bi nlode
In(-1) returns an answer.
Real
a+bi lnode
mode
lin<-i;,m
l
I
Iln( -l>m
4,
ERR-'NONRERL
ilBQuit
2: Goto
RNS
i
i
Entering
Complex
Numbers
Complex numbers are stored in rectangular form, but you
can enter a complex number in rectangulm' form or polar
form, regm'dless of the mode setting. The components
of
complex numbers can be real numbers or expressions that
evMuate to reM numbers; expressions
m'e evMuated when
the connnand is executed.
Note about
Radian versus
Degree Mode
Radian mode is reconnnended
for conlplex number
calculations. Internally-, the TI-83 converts all entered
values to radians, but it does not convert values for
exponential, logarithmic, or hyperbolic functions.
trig
In degree mode, complex identities such as
e ^ (i0) = cos(0) + i sin(0) are not generally true because
the values for cos and sin are converted to radians, while
those for e ^ () are not. For example,
e^(i45) = cos(45) + i sin(45) is treated internally as
e ^ (i45) = cos(_/4) + i sin(x/4). Complex identities are
always tree in radian mode.
2-16
Math,
Angle,
and
Test
Operations
Interpreting
Complex
Results
Complex numbers in results, including list elements, are
displayed in either rectangular or polar form, as specified
by the mode setting or by a display conversion instruction
(page 2-19). In the example below, re^0/and Radian modes
are set.
_2+t)-(le'-(x/4t)
1.325654296e^( ....
RectangularComplex
Mode
Rectangular-complex
mode recognizes and displays a
complex number in the fore1 a+bi, where a is the ten
component, b is the imagimuy component, and i is a constant
equM to @'1.
-1)
lln< 3.141592654tI
To enter a complex nulnber in rectangular
form, enter the
value of a (real component),
press [] or [], enter the value
of b (imaginary
component),
and press [_ [i] (constant).
Polar-Complex
Mode
real component(÷
or -)imaginary
14+2t
4+2t
cornponenti
I
Polar-complex mode recognizes and displays a complex
number in the form re ^ 0/, where r is the nmgnitude, e is the
b_e of the natm'al log, 0 is the angle, and i is a constant equM
in(-I)
3.141592654e^
( I...
To enter a complex number
of r (magnitude),
press [_
enter the value of 0 (angle),
then press D.
in polar ff)nn, enter the value
[ex] (exponential
function),
press [_ [i] (constant),
and
ma_dtudeea(anglei)
10e._(n/3t)
10e"(I.04719755...
Math,
Angle,
and
Test
Operations
2-17
MATH CPX (Complex)
MATH CPX Menu
To display
Operations
the
MATH CPX menu,
press
[_
[] [],
MATH NUM CPX PRB
Returns
Returns
Returns
Returns
Returns
Displays
Displays
1:conj(
2:real(
3:imag(
4:angle(
5:abs(
6:_Rect
7:_Polar
con j(
the
the
the
the
the
the
the
complex conjugate,
real part.
imaginary part,
polar angle.
magnitude (modulus),
result in rectangular
form,
result in polar form,
conj((conjugate) returns the complex conjugate
complex number or list of complex numbers,
of a
conj(a+bi) returns a-bi in a+bi nlode,
conj(re^(0i)) returns re^C0/) in re^ei mode,
toni (3+4t)
3-4t1
c°nJ (3e^(4t
>>
3e"(2.
28318530?._
real( (real part) returns the real part of a complex
or list of complex nmnbers,
real(
number
real(a+bi) returns a,
real(f'e^(0i)) returns _"*cos(O).
r.eal(3+4t)
imag(
3[
real (3e_'(4t
>>
-I.968938863
imag( (imaginary
part) returns
the imagining(nonreal)
of a complex
number
or list of complex
numbers.
imag(a+bi) t_tunls
b.
imag(re^(Oi)) returns
_'_sin(O),
Iimag(3+4t )
2-18
Math, Angle,
and Test
Operations
41
imag(3e^(4t
>-2.
270407486
>
part
angle(
angle( returns
the polar angle of a complex
number
or list
of complex
numbers,
calculated
as tan -1 (b/a), where b is
the imaginatT
part and a is the real part. The calculation
adjusted
by +x in the second
quadrant
or -x in the third
quadrant.
angle(a+bi)
returns
tan-l(b/a).
angle(re^(Oi)) returns
0, where
-x<O<x.
an91 e ( 3+4t )
• 927295218
abs(
abs( (absolute
_(real2+imag2)
nulnl)ers,
value)
is
an91 e (38^ ( 4i.) )
-2. 283185387
returns
the lnagnitude
, of a complex
nulnber
(lnodulus),
or list of eonlplex
abs(a+bi) returns _
.
abs(re^(Oi)) returns r (nmgnitude),
labs(3+4t )
_Rect
51
[abs(3e^(4t
))
31
)Rect (display as reetanguhu') displays a complex t_sult in
rectangular
form. It is valid only at the end of an
expression, It is not valid if the result is real,
complex
result_Rect
returns
a +bi.
_Rec.t
1#(-2_.414213562t1
)Polar
)Polar (display as polar) displays a coInplex result in polar
form, It is valid only at the end of an expression. It is not
valid if the result is real.
corr_plexresult_Polarreturnsre
^
(_).
#(-2)_PolaP
1.4142135628^(I...
Math,
Angle,
and
Test
Operations
2-19
MATH PRB (Probability)
MATH PRB Menu
To display
the
Operations
MATH PRB menu,
press
_
E},
MATH NUM CPX PRB
i:
rand
Randonl-nunlber
generator
Number
of pernmtations
Number
of combinations
Factorial
2: nPr
3:nCr
4:!
5: randlnt(
Random-integer
Random
# from
Random
# from
6: randNorm(
7: randBin(
rand
generator
Normal
distribution
Binomial
distribution
rand (random
number)
generates
and returns
one or more
random
numbers
> 0 and < 1. To generate
a list of randomnumbers,
specify- an integer
> 1 for numt'rials
(number
of
trials). The default
for numt'rials
is 1.
rand [(num
trials)]
Tip: To generate random numbers beyond the range of Oto I, you
can include rand in an expression. For example, rand*5 generates a
random number > 0 and < 5.
With each rand execution, the TI-83 generates the salne
randonl-number
sequence for a given seed value. The TI-83
factoFf-set seed value for rand is 0. To generate a different
randonl-number
sequence, store any nonzero seed value to
rand. To restore the factoFy--set seed vMue, store 0 to rand
or reset the defaults (Chapter 18).
Note: The seedvalue also affectsrandlnt(, randNorm(, and
randBin( instructions(page2-22).
r'and
• 1272157551
1÷rand 2646513087
rand(3)
{. 7455607728
2-20
Math,
Angle,
and
Test
Operations
nPr,
nCr
nPr (number of permutations)
returns the number of
pernmtations
of items taken number at a time. items and
number must be nonnegative integers, Both items and
number can be lists.
items
nPr number
nCr (number of combinations)
returns the number of
combinations of items taken number at a time. items and
number nmst be nonnegative integers. Both items and
number can be lists.
itemsnCrnumb_"
5
5 nCe
nPe 2
2
(2_2_i;
{2,3> nPP
_ 6}
! (Factorial)
! (factorial)
returns
the factorial
of either an integer
or a
nmltiple
of .5. For a list, it returns
factorials
for each
integer
or nmltiple
of .5. value nmst be _>-.5 and _<69.
value!
£120 24 720}
Note: The factorial is computed recursiveiy using the relationship
(n+t)! = n.n!, until n is reduced to either 0 or -1/2. At that point, the
definition 0!=I or the definition (-1/2)!=_- is used to complete the
calculation. Hence:
n!=n*(n-I )*(n-2)* ... *2* I, if n is an integer >0
n!= n*(n-1 )*(n-2)* ....1/2.-_;,
if n+1/2 is an integer >O
n! is an error, if neither n nor n+I/2 is an integer >0.
(The variable
n equals value
Math,
in the syntax
Angle,
and
description
Test
above.)
Operations
2-21
randlnt( (random
randlnt(
integer)
generates
and displays
a random
integer
within a range specified
by lower and upper integer
bounds.
To generate
a list of random
numbers,
specify
an
integer
> 1 for numt,Fials
(number
of trials); if not
specified,
the default
is 1.
randlnt(lower,upper[,numtrials])
rand Int ( 1,6)+ra
dlnt(1,6)
1,{26, 3)i5}
randInt(
randNorm(
G
randNorm( (random
Normal)
generates
and displays
a
random
real number
fi'onl a specified
Normal
distribution.
Each generated
value could be any real number,
but most
will be within the intercal
[p-3(_),
p+3(o)].
To generate
a
list of random
numbers,
specify- an integer
> 1 for
numtrials
(number
of trials); if not specified,
the default
is 1.
randNorm(p,ol,numtrials])
randNorm(O,
1)
.0_7207G175
_ndNo:r,(35,2,10
_34.02r01938
37_.
randBin(
randBin( (randon]
Binomial)
generates
and displays
a
random
integer
from a specified
Binomial
distribution.
numtrials
(nmnber
of trials)
lnust be _>1, prob (probability
of success)
must be _>0 and _<1. To generate
a list of
randonl
nunlbers,
specify an integer
> 1 for
numsimulations
(nmnber
of sinmlations);
if not specified,
the default
is 1.
randBin(numtrials,prob[,numsimulations])
randBirKS,,2)
randBin(7,.
3
4, 10)
{3 3 2 5 1 2 2 ...
Note: The seed value stored to rand also affects randlnt(,
randNorm(, and randBin( instructions (page 2-20).
2-22
Math,
Angle,
and
Test
Operations
ANGLE
Operations
ANGLE Menu
To display
the ANGLE menu,
menu displays
Radian/Degree
interpretation
press [_
[ANGLE]. The ANGLE
angle indicatot\_
and instruetions.
mode setting
affects the TI-S3's
of ANGLE menu entries.
The
ANGLE
1: °
3: r
Degree
notation
DMS minute notation
Radian notation
4: ,DMS
Displays
as degree/lninute/seeond
5: R,Pr(
Returns
Returns
Returns
Returns
r, given X and Y
0, given X and Y
x, given R and 0
y, given R and 0
2:'
6:
R_PO(
7: P_Rx(
8: PmRy(
DMS Entry
Notation
DMS (degrees/minutes/seconds)
entlT notation
comprises
the degree sjonbol
(°), the minute
sjonbol ('), and the
second
symbol ("). degrees nmst be a real number;
minutes
and seconds
nlust be real numbers
_>0.
degrees°minutes'seconds
For exalnple,
enter
''
for 30 degrees,
1 minute,
the angle nlode is not set to Degree,
the TI-83 call interpret
the atgulnent
and seconds.
23 seconds.
If
you nmst use ° so that
as degrees,
minutes,
Radian mode
Degree mode
I
sin(30° 1'23")
I
sin(30° 1'23")
-. 98421299951
sin(30 °l 23 o)
.5003484441
° (Degree)
•5003484441
° (degree)
designates
an angle or list of angles as degrees,
regardless
of the current
angle mode setting.
In Radian
nlode, you Call use ° to convert
degrees
to radians.
value °
{value1
,value2,value3,value_
,...,value
n} °
° also designates
degrees (D) in DMS format.
' (minutes)
designates
minutes
(M) in DMS format.
" (seconds)
designates
seconds
(S) in DMS format..
Note: " is not on the ANGLE menu. To enter ", press @
Math,
Angle,
and
Test
Operations
[-].
2-23
r (radians)
r (Radians)
designates
an angle
regardless
of the cmTent angle
mode, you can use r to convert
or list of angles
as radians,
mode setting.
In Degree
radians
to degrees.
value r
Degree mode
sin
(<_/4.')
r )
• 7071067812
sin(
{0,
,/2}
_)
%w.J
1}
(x/4> r
45
_DMS
_DMS (degree/minute/second)
displays
answer
in DMS
format (page 2-23). The nlode setting lnust be Degree for
answer
to be interpreted
as degrees,
minutes,
and seconds.
_DMS is valid only at the end of a line.
answe_'_DMS
54°32'30"*2
I
109.08333331
Rns*DMS
10905 0
RI_Pr(converts rectangular
coordinates
to polar
coordinates
and returns r, R_PO( converts rectangular
coordinates to polar coordinates
and returns O.x and y can
be lists.
R_Pr (,
R_,Pe (,
P_-Rx(,
P*Ry(
R*Pr(x,y),
R*PO(x,y)
I
R*Pr(-1,O)
e,eo( }
,05
! I
Note: Radian mode is set
14i5926541
PI_Rx( converts
polar coordinates
to rectangular
coordinates
and returns
x. PI*Ry( converts
polar
coordinates
to reetangulm"
coordinates
and returns
0 can be lists.
y. r and
P*Rx(r,_,P*Ry(v,_
P*Rx(I,x)
-10
P*R_(I,x)
2-24
Math,
Angle,
and
Test
Operations
Note: Radian mode is set.
TEST (Relational)
TEST Menu
>_ ->,
<,_<
Operations
To display
the TEST menu,
[_
This operator...
TEST LOGIC
Returns
1: =
2: _
3: >
Equal
Not equal to
Greater
than
4: >
5: <
Greater
than
Less than
6: <
Less than
[TEST].
1 (true)
if,..
or equal
or equal
to
to
Relational
operators
compare
valueA
and valueB
and
return
1 if the test is true or 0 if the test is false, valueA
valueB
can be real numbet_,
expressions,
and _ only, valueA
and valueB
also can
complex
numbers.
If valueA
and valueB
nmst have the same dimensions.
Relational
program
operators
are often
flow and in graphing
function
over
valueA
valueA
valueA
specific
=valueB
>value B
<valueB
and
or lists. For =
be matrices
or
are matrices,
both
used in programs
to eont_x)l
to control
the graph of a
values.
valueA
valueA
valueA
_valueB
>valueB
<valueB
el
25=26
{i'2'3}<3{i
Using Tests
press
1 0}
Relational operatot_ are evMuated after lnathelnatieal
functions according to EOS rules (Chapter 1).
•
The expression
2+2=2+3 returns
0. The TI-83 performs
the addition
first because
of EOS rules, and then it
compares
4 to 5.
•
The expression
2+(2=2)+3 returns
6. The TI-83 performs
the relational
test first because
it is in parentheses,
and
then it adds 2, 1, and 3.
Math, Angle,
and Test
Operations
2-25
TEST LOGIC
(Boolean)
TEST LOGIC
Menu
To display
Operations
the TEST LOGIC menu, press [_
[TEST]
[_.
This operator...
TEST LOGIC
Returns
1:
2:
3:
4:
Both values are nonzero
(true).
At least one value is nonzero
(tree),
Only one value is zero (false),
The value is zero (false).
an d
0c
x0c
n0t (
a 1 (true} if...
Boolean
Operators
Boolean operators are often used in programs to control
program flow and in graphing to control the graph of the
function over specific values. Values are interpreted
_ts
zero (false) or nonzero (ttlle).
and,
and, or, and xor (exclusive or) return a value of 1 if an
expression is true or 0 if an expression is false, according
to the table below, valueA and valueB can be real
numbers, expressions,
or lists.
or_
xor
and valueB
or valueB
xor valueB
valueA
valueA
valueA
not(
valueA
valueB
and
or
xor
€0
€0
returns
1
1
0
€0
0
returns
0
1
1
0
€0
returns
0
1
1
0
0
returns
0
0
0
not( returns
1 if value
(which
can be an expression)
is O,
not(value)
Using Boolean
Operations
Boolean logic is often used with relational tests. In the
following program, the instructions
store 4 into C,
:If" R=2 and B=3
:Then: 4eC
PROGRAM::
2+R: 3+BBOOLEAN
:Else:
5eC
:End
2-26
Math_
Angle_
and
Test
Operations
I
Contents
Getting Started: Graphing a Circle .......................
Defining Graphs
.........................................
Setting tile Graph Modes .................................
Defining Funetions
......................................
Selecting and Deseleeting
Ftmetions
.....................
Setting Graph Styles for Ptmetions
.......................
Setting the Viewing Window \Tariables ...................
3-2
3-3
3-4
3-5
3-7
3-9
3-11
Setting the Graph Format ................................
DisNaying
Graphs
.......................................
Exploring
Graphs with the Free-Mo_ng
Cursor
..........
3-13
3-15
3-17
Exploring
Graphs with TRACK ...........................
Exploring
Graphs with the ZOOM Instructions
...........
Using ZOOM MEMORY ..................................
Using the CALC (Calculate)
Operations
..................
3-18
_-20
G-23
3-25
_
TEXAS
T|=83
INSTRUMENTS
J
STAT
PLOT
TIBLSET
FORMAT
CALC
TABLE
Fllnction
Graphing
3-1
Getting
Getting
Started:
Started
Graphing
is a fast-paced
a Circle
introduction.
Read the chapter
for details.
Graph a circle of radius 10, centered on the origin in the standard viewing
window. To graph this circle, you nmst enter separate formul_ts for the upper
and lower portions of the circle. Then use ZSquare (zoom square) to adjust the
display- and make tile functions appear as a circle.
In Func mode, press [] to display tile
Y= editor. Press _
[_] 100 [] _
[] []
to enter the expression Y=f(100-X2),
which defines the top half of the circle.
The expression Y=-f(100-X
2) defines the
bottom half of the circle. On the TI-83, you
can define one function in terms of another.
To define Y2=-Y1, press [] to enter the
negation sign. Press FqAgg][] to display- the
VARS Y-VARS menu. Then press _
to
select 1:Function. The FUNCTION seeondatT
menu is displayed. Press 1 to select 1:Y1.
Press _
6 to select 6:ZStandard. This is a
quick way- to reset the window wu'iables to
the standard values. It also graphs the
functions; you do not need to press [ggAPH].
Notice that the functions appear as an
ellipse in the standard xqewing window.
To adjust the display- so that each pixel
represents an equal width and height, press
6 to select 8:ZSquare. The functions
are replotted and now appear as a circle on
the display.
To see the ZSquare window variables, press
and notice the new values for Xmin,
Xmax, Ymin, and Ymax.
3-2
Function
Graphing
_INOOW
Xmin=-15.16129...
Xmax=15.161290...
XsGI=I
Vnin=-lO
9max=lO
Vscl=l
Xres=l
Defining
Graphs
TI-83--Graphing
Mode Similarities
Defining a Graph
Chapter
3 specifically
describes
function
graphing,
but
the
steps shown
here are similar for each TI-83 graphing
mode. Chapters
4, 5, and 6 describe
aspects
that are unique
to paralnetric
graphing,
polar graphing,
and sequence
graphing.
To define a graph
steps. Some steps
1. Press
(page
in any graphing
are not always
[ff0_] and set the
3-4).
mode, follow
necessmT.
appropriate
graph
these
mode
2. Press [] and enter, edit, or select one or more
in the Y= editor (page 3-5 and 3-7).
3. Deselect
4.
stat
plots,
ifnecessmT
Set the graph
style
ff)r each
and define
(page
function
5. Press
(page
_
3-11).
6. Press
(page
_
[FORMAT] and select
3-13).
3-7).
(page
the viewing
functions
3-9).
window
the graph
variables
format
settings
Displaying and
Exploring a
Graph
After you have defined a graph, press [ffg_] to display- it.
Explore the behavior of the function or functions using the
TI-83 tools described in this chapter.
Saving a Graph
for Later Use
You can store the elements
that define the current
graph to
any- of 10 graph database
variables
(GDB1 through
GDBg,
and GDB0; Chapter
8). To recreate
the current
graph later,
simply recall the graph database
to which you stored
the
original graph.
These
types
of information
•
Y= functions
•
Graph
•
Window
•
Format
style
m'e stored
in a GDB
settings
settings
settings
You can store a picture
of the current
graph display to any
of 10 graph picture
variables
(Picl through
Picg, and Pie0;
Chapter
8). Then you can superimpose
one or more stored
pictures
onto
the current
graph.
Function
Graphing
3-3
Setting
the Graph
Checking and
Changing the
Graphing Mode
Modes
To display- the mode screen, press [_.
settings are highlighted below. To graph
nmst select Func mode before you enter
window vm'iables and before you enter
Sci
The default
functions, you
values for the
the functions.
Eng
Dot
Horiz
The
TI-83
G-T
has four
•
Func (function
•
Par (parametric
•
Pol (polar
•
Seq (sequence
graphing
modes.
graphing)
graphing;
graphing;
Chapter
Chapter
graphing;
4)
5)
Chapter
6)
Other mode settings
affect graphing
describes
each mode setting.
•
Float or 0123456789
(fixed)
displayed
graph coordinates.
•
Radian
some
Setting Modes
from a Program
or Degree
functions.
angle
decinlal
mode
Connected
or Dot plotting
selected
functions.
mode
•
Sequential
or Simul graphing-order
function
plotting
when nlore than
selected.
1
affects
interpretation
'affects
plotting
of
of
mode affects
one function
is
To set the graphing
mode and other nlodes fronl a
program,
begin on a blank line in the program
editor
follow these steps.
[MO_] to display-
the
lnode
2. Press [], [], [_, and [] to place
that you want to select.
3. Press _
location.
The
Function
Chapter
nlode
affects
•
1. Press
3-4
results.
Graphing
nlode
to paste
is changed
the Inode
when
and
settings.
the cursor
name
the program
to the
on the mode
cursor
is executed.
Defining
Functions
Displaying
Functions in the
Y= Editor
To display the Y= editor, press @. You can store up to 10
functions to tile function variables Y1 through Y9, and YO.
You can graph one or more defined functions at once. In
this example, functions Y1 and Y2 are defined and selected.
PI,'.,LI
PloLg
Pl,:,t_:
-,y1B4"(100-ga:)
.,YaB -YI
\Y_=
..Y_=
,,y_=
,,y_=
-,y_=
Defining or
Editing a
Function
To define or edit a function,
follow these steps.
1. Press [] to display the Y= editor.
2, Press [] to nlove the cursor to the function you want to
define or edit, To erase a function, press @,
3. Enter or edit the expression
to define the function.
•
You lnay use functions and variables (including
matrices and lists) in the expression. When the
expression ewduates to a nonreal number, the value
is not plotted; no error is returned.
• The independent
variable in the function is X. Func
lnode defines _
as X. To enter X, press
or press @
[x].
• When you enter the first character, the = is
highlighted, indicating that the function is selected.
As you enter the expression, it is stored to the variable
Yn as a use>defined function in the Y= editor.
4. Press [gNY_ or [] to l:love the cursor to the next
function.
Function
Graphing
3-5
Defining a
Function from
the Home Screen
or a Program
To define
begin
a function
on a blank
fronl
the home
line and follow
1. Press
@
@
[,], enter
[-1 again.
2. Press
_.
Select
cursor
5. Press
or a prograln,
steps.
the expression,
3. Press _
[] 1 to select
VARS Y-VARS menu,
4.
screen
these
1:Function
and then
press
fl'om the
the function
name, which p_stes the name to the
location
on the home screen or program
editor.
_
to complete
"expression
the instruction.
" _ Yn
I"X z''÷Vt
Donel
"J',JtI_IX
2PI':'tt P10t;: Plot,
I
When the instruction
is executed,
the TI-83 stores the
expression
to the designated
variable
Yn, selects the
function,
and displays
the message
Done.
Evaluating Y=
Functions in
Expressions
You can
calculate
specified
value
Yn(value)
Yn({valuel
the value
,value2,value3,
Pl*tlB. Pl*{2
P10t)
\V1
2Xs-2X+6
,,..z=
xV_-=
3-6
Function
Graphing
of a Y= function
of X. A list of values
. . .,value
I
I
returns
Yn at a
a list.
n})
Y1 (0)
6
'_1
._6({0,
4.2 1,2,3,4}
3.6 5.4 ) ...
Selecting
and Deselecting
Selecting and
Deselecting a
Function
You can
functkm
Functions
select and deselect
(turn on and turn off) a
in the Y= editor. A function
is selected
when
the =
sign is highlighted.
The TI-83 graphs only the selected
functions.
You can select any or all functions
Y1 through
Yg, and Y0.
To select or deselect
these steps.
1. Press
[]
a function
to display
2. Move the cursor
deselect.
in the Y= editor,
follow
the Y= editor.
to the function
3, Press [] to place the cursor
you want
to select
on the functkm's
4. Press [gg_g] to change the selection
or
= sign.
status.
When you enter or edit a function, it is selected
automatically.
When you clem' a function, it is deselected.
Turning On or
Turning Off a Stat
Plot in the Y=
Editor
To view and change the OlVOff status of a stat plot in the
Y= editor, use Plot1 Plot2 Plot3 (the top line of the
Y= editor).
When a plot is on, its name is highlighted
on this
line.
To change the OlgOff status of a stat plot fronl the
Y= editor, press [] and [] to place the cursor
on Plot1,
Plot2, or Plot& and then press [g_N.
_lotz
Plet_
_
",YI =. 2X 3-2X+6
\Vz= -Yt
J
-'1---,_
I
,_.y_=2X+XZ
j
\Y_=
",us =
",'¢_=
J
-W=
I
Plott
isturnedon.
Plot2 and Plot3 are turned off
/
Function
Graphing
3-7
Selecting and
Deselecting
Functions from
To select or deselect a function fronl the home screen or a
program, begin on a blank line and follow these steps.
the Home Screen
1. Press _
or a Program
2. Select 4:On/Off to display the ON/OFF secondary
[] to display- the VANS Y-VANS menu.
menu.
3. Select l:FnOn to turn on one or more functions or
2:FnOff to turn off one or more functions. The
instruction you select is copied to the cursor location.
4. Enter the number (1 through 9, or 0; not the variable
Yn) of each function you want to turn on or turn off.
•
If you enter two or more numbers,
with eonunas.
separate
•
To turn on or turn off all functions,
number after FnOn or FnOff,
do not enter a
FnOn [function#function#,.,,
FnOff[function# function#
function
function
....
them
n]
n]
5, Press [ggTig], When the instruction is executed, the
status of each function in the eutTent mode is set and
Done is displayed.
For example, in Func mode, FnOff :FnOn 1,3 turns off all
functions in the Y= editor, and then turns on Y1 and Y3.
FnOff
3-8
Function
Graphing
:FnOn
Dlo3e
I Pl<,tl
Plo_Z
Plot._
",Y1 B. 2X_-2X+6
_,Y;_= -Y1
",YsBXZ
xy_=
xY_=
\Y_=
,,y_=
Setting
Graph Styles for Functions
Graph Style
Icons in the Y=
Editor
This
table
describes
the
graph
graphing.
Use the styles
to be graphed
together,
solid line, Y2 as a dotted
styles
available
for function
to visually
differentiate
functions
For example,
you can set Y1 as a
line, and Y3 as a thick line,
Icon Style
Description
"..
Line
A solid line connects
plotted
points;
the default
in Connected
mode
"i
Thick
A thick
'_.i
Above
Shading
covers
the area
a*bove
ik
Below
Shading
covet\_
the area
below
'1!
Path
A circular
the graph
cursor
traces the
and draws a path
(!
Aidmate
A circular
the graph
cursor
without
".
Dot
A snlall dot represents
each plotted
this is the default
in Dot mode
solid
line connects
plotted
this is
points
the graph
the graph
leading
edge
of
traces
the leading
drawing
a path
edge
of
point;
Note: Some graph styles are not available in all graphing modes.
Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.
Setting the Graph
Style
To set the graph
style
for a function,
the Y= editor.
1. Press
[]
to display
2. Press
[]
and [] to nlove
follow
the cut\sor
these
steps.
to the function.
3. Press [] [] to move the cm'sor left, past the = sign, to
the graph style icon in the first colunm.
The insert
cm'sor is displayed.
(Steps 2 and 3 are interchangeable.)
4. Press _
repeatedly
styles. The seven styles
which
5. Press
they are listed
[],
to rotate through
the graph
rotate in the same order in
in the table
[], or [] when
you have
above.
selected
a style.
PlotJ. F'1ot;_P1ot:_
",Y1B8sin(X)
_YzB8cos(X)
\Y_=
xY_=
\Y_=
xy_=
xy_=
Function
Graphing
3-9
Shading Above
and Below
When
you select
TI-83
rotates
•
Vertical
graph
_mor 1;. for two or more
through
lines
four
shade
shading
the first
the
function
with
a '_.1or b.
style.
•
Horizontal
lines
•
Negatively
sloping
•
Positively
•
The rotation
returns
to vertical
lines for the fifth '_.ior i;.
function,
repeating
the order described
above.
sloping
VClmn shaded
Note:
shade
the second.
diagonal
lines
diagonal
are_Ls intersect,
When _1or h_,is selected
lines
shade
shade
for a Y= function
the third.
the fom'th.
the patterns
curves, such as Yl={1,2,3}X,
the four shading
each member of the family of curves.
Setting a Graph
Style from a
Program
functions,
patterns.
overlap.
that graphs
patterns
a family
of
rotate for
To set the graph style fl'onl a program,
select H:GraphStyle(
from the PRGM CTL menu. To display this menu, press
[V_
while in the program
editor.function#
is the nmnber
of the Y= function
name in the current
graphing
mode.
graphstyle#
is an integer from 1 to 7 that corresponds
to
the graph
style,
1 = ". (line)
4 = 1'.-.(below)
(animate)
as shown
below.
2 = '_i(thick)
8 = ':) (path)
7 = ". (dot)
3 = ,m(above)
6 = (!
GraphStyle(fanction#,graphstyle#)
For example,
when this program
is executed
GraphStyle(1,3) sets Y1 to '_](above),
: OisPGr'aPh
3-10
Function
Graphing
in Func mode,
Setting
the Viewing
The TI-83 Viewing
Window
Window
Variables
The viewing window is the portion of the coordinate plane
defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale)
defines the distance between tick marks on the x-axis. Yscl
(Y scale) defines the distance between tick marks on the
y-axis. To turn off tick marks, set Xscl=0 and Yscl=0.
WINDOW
Xmin=-lO
XMax=lO
Xscl=l
Ymin=-lO
Ymax=lO
Yscl=l
XPes=l
_Ymax
Xsc_
Xmax /
_--Yscl
Ymir_ N
Displaying the
Window
Variables
To display the current window variable values, press
_.
The window editor above and to the right shows
the default values in Func graphing mode and Radian angle
nlode. The window variables differ fronl one graphing
mode to another.
Xres sets pixel resolution
only. The default is 1.
•
•
(1 through
At Xres=l, functions are evaluated
pixel on the x-axis.
At Xres=8, functions are evaluated
eighth pixel along the x-axis.
8) for function
graphs
and graphed
at each
and graphed
at every
Tip: SmalIXres valuesimprovegraph resolutionbut may causethe
TI-83 to draw graphs more slowly.
Changing a
Window Variable
Value
To change a window variable
editor, follow these steps.
value fronl the window
1. Press [] or [] to move the cut\sor to the window
variable you want to change.
2. Edit the value, which can be an expression.
•
•
Enter a new wdue, which clears the original value.
Move the cursor to a specific digit, and then edit it.
3. Press [g_gff], [], or []. If you entered an expression,
TI-83 ewduates it. The new value is stored.
the
Note: Xmin<Xmax andYmin<Ymax must be true in orderto graph.
Function
Graphing
3-11
Storing to a
Window
Variable
from the Home
To store
a value,
variable,
begin
Screen
1, Enter
the value
2, Press
_.
3, Press
_
or a
Program
4,
can be an expression,
line and follow
you want
to display-
to a window
these
to store,
the Func window
•
Press [] to display the Par and Pol window
(T/0 secondm_y- menu).
•
Press [] [] to display the Seq window
(UN/W secondary
menu).
variables
variables
variables
the window
variable
to which you want to store
The name of the variable
is pasted
to the current
CUrSOr
6, Press
steps,
the VARS menu.
Select 1 :Window to display
(X/Y secondmT
menu).
5, Select
value,
AX and AY
which
on a blank
location.
_
to complete
the instruction.
When the instruction
value to the window
is executed,
the TI-83 stores the
variable
and displays
the vMue.
J14+Xv,ax
14J
The variables
AX and AY (items 8 and 9 on the VARS
(1:Window)
X/Y seeondmT
menu) define the distance
from
the center
of one pixel to the center
of any adjacent
pixel
on a graph (graphing
accuracy),
a× and AY are calculated
from Xmin, Xma×, Ymin, and Yma× when you display- a
graph.
AX =
(Xmax - Xmin)
94
AY -
(Ymax - Ymin)
62
You can store values to AX and AY. If you do, Xmax and
Ymax m'e cMculated from AX, Xmin, AY,and Ymin.
3-12
Function
Graphing
a
Setting
the Graph
Displaying the
Format Settings
Format
To display- the format settings,
default settings are highlighted
RectGC
CoordOn
GridOff
AxesOn
LabelOff
PolarGC
CoordOff
GridOn
AxesOff
LabelOn
ExprOn
ExprOff
pl_ss [2_
below.
[FORMAT].
The
Sets
cursor
Sets
Sets
Sets
Sets
Sets
coordinates
display on or off.
grid off or on.
axes on or off.
axes label oft" or on.
expression display on or off.
coordinates.
Format. settings define a graph's appearance
on the display.
Format settings apply to all graphing modes. Seq graphing
mode has an additional mode setting (Chapter 6).
Changing a
Format Setting
To change
a fornlat setting,
follow these steps.
1. Press [_, [}_],[], and [] as necessary- to lnove the cursor
to the setting you want to select.
2. Press [ggYgg]to select the highlighted
RectGC, PolarGC
RectGC (rectangular graphing
cursor location _LSrectangular
coordinates)
coordinates
setting.
displays the
X and Y.
PolarGC (polar graphing coordinates)
displays tile cursor
location as polar coordinates
R and 0.
The RectGC/PolarGC setting determines which wuiables
are updated when you plot tile graph, move the freenloving
cursor, or trace.
•
•
RectGC updates X and Y; if CoordOn format is selected,
X and Y are displayed.
PolarGC updates X, Y, R, and 0; if CoordOn format is
selected, R and 0 are displayed.
Function
Graphing
3-13
CoordOn
CoordOn,
CoordOff
(coordinates
on) displays
CoordOff (coordinates
number
or coordinates,
GridOff,
GridOn
Grid points
correspond
GridOff does
AxesOn,
the cursor
coordinates
at the bottom
of the graph, If ExprOff format is selected,
the function
number
is displayed
in the top-right
corner,
AxesOff
off) does
cover the viewing
to the tick marks
not display
grid points.
AxesOn displays
the
This
overrides
not
the
display-
the function
window
in rows that
(page 3-11) on each axis.
grid points.
GridOn displays
AxesOff does
not
axes.
display-
the axes.
LabelOff/LabelOn
format
setting.
LabelOff,
LabelOn
LabelOff and LabelOn determine
whether
for the axes (X and Y), if AxesOn format
ExprOn, ExprOff
ExprOn and ExprOff determine whether to display- the
Y= expression when the trace cursor is active. This format
setting also applies to stat plots.
When ExprOn is selected, the expression
top-left comer of the graph screen.
to display labels
is also selected.
is displayed
in the
When ExprOff and CoordOn both are selected, the number
in the top-right corner specifies which function is being
traced.
3-14
Function
Graphing
Displaying
Graphs
Displaying a New
Graph
To display
Pausing or
Stopping a Graph
V_l_ile plotting
Smart
Graph
the graph
of the selected
function
or functions,
press _.
TRACE, ZOOM instructions,
and CALC
operations
display- the graph automatically.
As the TI-83
plots the graph, the busy indicator
is on. As the graph is
plotted,
X and Y m'e updated.
a graph,
•
Press
[ggT_
•
Press
[ON]to stop;
you can
to pause;
then
then
press
pause
press
or stop
[ggT_
_
graphing.
to resume.
to redraw.
Snlart Graph is a TI-83 feature that redisplays the last
graph ilnlnediately when you press _,
but only if all
graphing factors that would cause replotting have
remained the same since the graph was last displayed.
If you performed any of these actions since the graph was
last displayed, the TI-83 will replot the graph based on new
values when you press _.
•
Changed
a mode setting that affects graphs
•
•
•
•
•
•
Changed a function in the current picture
Selected or deselected a function or stat plot
Changed the value of a variable in a selected function
Changed a window variable or graph fornlat setting
Cleared drawings by selecting ¢lrDraw
Changed a stat plot definition
Function
Graphing
3-15
Overlaying
Functions on a
Graph
On the TI-83,
Graphing a
Family of Curves
If you
you
can graph
one or more
new functions
without
replotting
existing
functions,
For example,
store
sin(X) to Y1 in the Y= editor
and press [_7.
Then store
cos(X) to Y2 and press _
again. The function
Y2 is
graphed
on top of Y1, the original
function,
enter
a list (Chapter
11) as an element
in an
expression,
the TI-83 plots the function
for each value in
the list, thereby
graphing
a family of curves. In Simul
graphing-order
mode, it graphs 'all functions
sequentiMly
for the fit.st element
in each list, and then for the second,
and so on.
{2,4,6}sin(X)
6 sin(X).
graphs
three
functions:
2 sin(X),
4 sin(X), and
Plot1 PIo_Z Plot_
_.YtB£2, 4, 6}sin(X
xy?=
\y_,=
-.y_=
",y_=
-.y_=
{2,4,6}sin({1,2,3}X)
graphs
2 sin(X), 4 sin(2X),
and 6 sin(3X).
".YI
B(2, 4, 6}sin(
1,2,3}X)
\Yz =
\Y_=
\Y_=
PI_L1
PlOL_:
-.y_=
..y_=
Plot. _
Note: When using
dimensions.
3-16
Function
Graphing
'_
more than one list, the lists must have the same
Exploring
Free-Moving
Cursor
Graphs with the Free-Moving
Cursor
When a graph is displayed, press [], [], [], or [] to nlove
tile cursor around the graph. When you first display- the
graph, no cursor is visible. When you press [], [], [], or [],
the cursor moves from the center of the viewing window.
As you move the cursor around the graph, the coordinate
values of the cursor location m'e displayed at the bottom
the screen if ¢oordOn format is selected. The Float/Fix
decimal mode setting determines tile number of decimal
digits displayed for the coordinate wdues.
of
To display the graph with no cursor and no coordinate
values, press @
or [gg_g]. When you press [], [], [], or
[], the cursor moves froln the same position.
Graphing
Accuracy
The flee-moving cursor nloves fronl pixel to pixel on the
screen. When you move the cursor to a pixel that appears
to be on the function, the cursor nlay be neat', but not
actuMly on, the function. The coordinate value displayed at
the bottom of the screen actuMly lnay not be a point on the
function. To lnove the cursor along a function, use
(page 3-18).
The coordinate values displayed as you move the cursor
approximate
actuM math coordinates,
*accurate to within
the width and height of the pixel. As Xmin, Xmax, Ymin, and
Ymax get closer together (as in a Zoomln) graphing
accuracy
ineretkqes,
and the coordinate values nlore closely
approxinlate
the lnath coordinates.
Free-moving
Function
cursor
'on" the curve
Graphing
3-17
Exploring
Graphs with TRACE
Beginning a
Trace
Use
TRACE to move
the cursor
from
one plotted
point
to
the next along a function•
To begin a trace, press _.
If
the graph is not displayed
already,
press _
to display
it. The trace cursor
is on the first selected
function
in the
Y= editor, at the middle
× value on the screen•
The cursor
coordinates
are displayed
at the bottom
of the screen
if
CoordOn format
is selected.
The Y= expression
is displayed
in the top-left corner
of the screen,
if ExprOn format is
selected.
Moving the Trace
Cursor
To move the TRACE cursor,.,
do this:
• , , to the previous
point,
press [] or [].
or next plotted
•.. five plotted points on a function
(Xres affects this),
press [g_ [] or K_
[].
•.. to any valid X value on a function,
enter a value, and
then press [KNT_.
• fronl one function
to another,
press [] or [].
When the trace cursor nloves along a function, the Y wdue
is calculated from the X value; that is, Y=Yn(X). If the
function is undefined at an X value, the Y value is blank.
'_1='_-_i_*_ J
.....
i
/
_--
--
Trace cursor on the curve
............
g:?,:LB:LLIBgR
f:IL:L:LBLIT09
If you nlove the trace cursor
beyond the top or bottonl
the screen,
the coordinate
values at the bottom
of the
screen
Moving the Trace
Cursor from
Function to
Function
continue
Function
appropriately.
To nlove the trace cursor
fronl function
to function,
press
[] and []. The cursor
follows the order of the selected
functions
in the Y= editor• The trace cursor
moves to each
function
at the same × value• If ExprOn format is selected,
the expression
3-18
to change
of
Graphing
is updated.
Moving the Trace
Cursor to Any
Valid X Value
To move the trace cursor to any valid X value on the
current function, enter the value. When you enter the first
digit, an X= prompt and the number you entered are
displayed in the bottom-left corner of the screen. You can
enter an expression at the X= prompt. The value nmst be
valid for the current viewing window. When you have
coinpleted the enttT, press _
to inove the cursor.
Zt
Note:
This feature
L;t L......
does not apply to stat plots.
Panning to the
Left or Right
If you trace a function beyond the left or right side of the
screen, the viewing window automatically
pans to the left
or right. Xmin and Xmax are updated to correspond to the
new viewing window.
Quick
While tracing, you can press _
to adjust the viewing
window so that the cursor location beconles the center of
the new xqewing window, even if the cursor is above or
below the display. This allows panning up and down. After
Quick Zoom, the cursor remains in TRACE.
Zoom
When you leave and return to TRACE, the trace cursor is
displayed in the same location it was in when you left
TRACE, unless Smart Graph has replotted the graph
(page 3-15).
Leaving and
Returning
to
TRACE
Using TRACE
a Program
in
On a blank line in the prograln editor, press _.
The
instruction Trace is pasted to the cursor location. When the
instruction is encountered
during program execution, the
graph is displayed with the trace cursor on the first
selected function. As you trace, the cursor coordinate
values are updated. When you finish tracing the functions,
press _
to resume program execution.
Function
Graphing
3-19
Exploring
ZOOM Menu
Graphs with the ZOOM
Instructions
To display the ZOOM menu, press _,
You can adjust the
viewing window of the graph quickly- in several ways. All
ZOOM instructions
axe accessible fronl programs.
ZOOM MEMORY
i: ZBox
Draws a box to define the viewing window.
2: Zoom In
Magnifies
the graph around
the cursor.
3: Zoom Out
Views more of a graph atxmnd the cursor.
Zoom
Cursor
ZBox
4: ZDecimal
Sets
aX and aY to O. 1.
5: ZSquare
6: ZStandard
Sets
Sets
equal-size
pixels on the X and Y m,ces.
the standard
window
variables.
7:
8:
9:
0:
Sets the built-in trig window
variables.
Sets integer
values on the X and Y m,ces.
Sets the values for current
stat lists.
Fits YMin and YMax between
XMin and XMax.
ZTrig
Zlnteger
ZoomStat
ZoomFit
When you select 1 :ZBox, 2:Zoom In, or 3:Zoom
cursor on the graph becomes
the zoom cursor
smaller version of the free-mo_dng
cursor
(+).
To define a new viewing window
steps,
Out, the
(+), a
using ZBox, follow these
1, Select l:ZBox from the ZOOM menu. The zoom cursor
displayed at the center of the screen.
is
2. Move the zoonl cursor to any spot you want to define as
a cornet" of the box, and then press [N_N. When you
lnove the cm_or away- from the first defined corner, a
smM1, square dot indicates the spot.
3. Press [_, E], [_, or [_. As you lnove the cursor,
of the box lengthen or shorten proportionately
screen.
Note: To cancel ZBox before you press _,
4.
When you have
the graph.
defined
the box, press
the sides
on the
press @.
[_
to replot
V]\,, ,,/'
X:3,:L9J.tlBBq t:! .B2:.t:LIB3B
To use ZBox to define
repeat
steps 2 through
3-20
Function
Graphing
another
box within the new graph,
4. To cancel ZBox, press @.
Zoom In,
Zoom
Zoom
cursor location.
Zoom Out displays
a greater
portion
of the
graph, centered
on the cut\sor location.
The XFact and
YFact settings
determine
the extent
of the zoom.
Out
In magnifies
To zoom
the part
in on a graph,
of the graph
follow
these
1, Check
XFact and YFact (page
2, Select
2:Zoom
cursor
In from
that
surrounds
the
steps.
3-24);
change
the ZOOM menu.
as needed.
The zoom
is displayed.
3, Move the zoom cut, or to the point
center of the new viewing window,
that
is to be the
4, Press [gNYE_, The TI-83 adjusts
the viewing window
by
XFact and YFact; updates
the window
variables;
and
replots
the selected
functions,
centered
on the cursor
location,
5. Zoonl
in on the graph
in at the same
•
To zoom in at a new point, move
point that you want as the center
window,
and then press [_T_].
To cancel
Zoom
point,
select
In or Zoom
of two
press
3:Zoom
Out, press
ways.
[_T_].
the cm\sor to the
of the new viewing
Out and repeat
@.
ZDecimal replots
the functions
inunediately.
It updates
the
window
variables
to preset values, tks shown
below. These
values set AX and AY equal to 0.1 and set the X and Y value
of each pixel to one decimal
place.
Xmin=-4.7
Xmax=4.7
Xscl=l
ZSquare
in either
To zoom
To zoom out on a graph,
steps 3 through
5.
ZDecimal
again
•
Ymin=-3.1
Ymax=3,1
Yscl=l
ZSquare replots the functions immediately. It redefines the
xqewing window based on the cun'ent values of the
window variables. It adjusts in only one direction so that
AX=AY,which makes the graph of a circle look like a circle.
Xscl and Yscl remain unchanged. The midpoint of the
current graph (not the intersection
of the axes) becomes
the midpoint of the new graph.
Function
Graphing
3-21
ZStandard
ZStandard
replots
window
vm'iables
Xmin=-lO
Xmax=lO
Xscl=l
ZTrig
the functions
immediately,
It updates
to the standm'd
values shown below.
Ymin=-lO
Ymax=lO
Yscl=l
Xres=l
ZTrig replots the functions
immediately.
It updates
the
window
vm'iables
to preset values that are appropriate
ffw
plotting
trig functions.
Those preset values in Radian mode
m'e shown below,
Xmin=-(47/24)_
Xmax=(47/24)_
Xscl=_/2
Zlnteger
Ymin=-4
Ymax=4
Yscl=l
Zlnteger redefines
the viewing window
to the dimensions
shown below,
To use Zlnteger,
move the cursor
to the point
that you want to be the center
of the new window,
and
then press [_T_];
Zlnteger replots the functions,
AX=I
AY=I
Xscl=lO
YscI=IO
ZoornStat
ZoomStat
statistical
modified
ZoomFit
ZoomFit replots
the functions
immediately,
ZoomFit
recalculates
YMin and YMax to include
the nlininmm
nlmNinlunl Y values of the selected
functions
between
current
3-22
the
Function
Graphing
redefines
the viewing window
so that all
data points
m'e displayed.
For regular and
box plots, only Xmin and Xmax m'e adjusted.
and
the
XMin and XMax. XMin and XMax are not changed.
Using ZOOM
ZOOM MEMORY
Menu
MEMORY
To display
the ZOOM MEMORY menu,
ZOOM MEMORY
1:ZPrevious
2:ZoomSto
3:ZoomRcl
4:SetFactors...
p_ss
_
[_.
[ _ses the pre_ious
_iewing
window,
Stores the user-defined
window,
Recalls the user-defined
window.
Changes
Zoom In and Zoom Out factors.
ZPrevious
ZPrevious replots
the graph
the graph that was displayed
ZOOM instruction.
ZoomSto
ZoomSto
inunediately
stores the cmTent viewing window.
The graph is displayed,
and the values of the current
window
variables
are stored in the user-defined
ZOOM
variables
ZXres.
using the window
variables
of
before you executed
the last
ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and
These variables
apply to all graphing
modes.
For example,
changing
the value of ZXmin in Func nlode also changes
it
in Par mode,
ZoomRcl
ZoomRcl graphs
viewing window.
determined
instruction.
user-defined
the selected
functions
in a user-defined
The user-defined
viewing
window
is
by the values stored
with the ZoomSto
The window
variables
are updated
with
values, and the graph is plotted.
Function
Graphing
the
3-23
ZOOM FACTORS
The
zoonl
XFact and YFact, are positive
factors,
numbers
(not necessarily
intege_\_) greater
than or equal to 1, They
define the magnification
or reduction
factor used to Zoom
In or Zoom Out around
a point,
Checking
XFact
and YFact
To display the ZOOM FACTORS screen, where you can
t_iew the current values for XFact and YFact, select
4:SetFactors from the ZOOM MEMORY menu. The values
shown m'e the defaults.
I
XFacL=4
ZOOM
FRCTORS
VFact=4
Changing
XFact
and YFact
Using ZOOM
MEMORY Menu
Items from the
Home Screen
a Program
You can
change
XFact and YFact in either
of two ways.
•
Enter a new
automatically
•
Place the cursor on the digit you want to change,
then enter a value or press [bE[] to delete it,
From
the home
value. The original value is cleared
when you enter the first digit.
screen
or a program,
to any of the user-defined
you can store
and
directly
ZOOM vm'iables.
or
1-5÷ZXr_in:
5÷ZXr_,a5
From a program,
you can select the ZoomSto and ZoomRcl
instructions
fronl the ZOOM MEMORY menu.
3-24
Function
Graphing
Using
the CALC
CALCULATE
Menu
(Calculate)
To display
items
the CALCULATE
on this menu
CALCULATE
i: value
2: zero
3: minimum
4: maximum
nlenu,
to analyze
press I_
tile current
[CALC], Use the
graph
functions,
Calculates a function Y value for a given X,
Finds a zero (x-intercept)
of a function.
Finds a nlininmln of a function,
Finds a nlaxinmln of a function.
Finds an intersection
of two functions,
Finds a numeric derivative of a function.
Finds a numeric integral of a function,
5:intersect
6:dy/dx
7:ff(x)dx
value
Operations
value evaluates one or more currently
for a specified value of X.
selected
functions
Note: Whena value is displayedfor X, press[_
to clear the value.
When no value is displayed, press @
to cancel the value
operation.
To evaluate
a selected
function
at X, ff)llow these steps.
1, Select 1:value froln the CALCULATE menu, The graph is
displayed with X= in tile bottom-left corner.
2, Enter a real value, which can be an expression,
between Xmin and Xmax.
for X
3. Press IE_].
"7i7.J
The cursor is on the first selected function in the Y= editor
at the X value you entered, and the coordinates
are
displayed, even if ¢oordOff fornlat is selected.
To nlove the cm'sor fl'om function to function at the
entered X value, press [] or [], To t_store the free-re(Mug
cursor, press [] or [].
Function
Graphing
3-25
zero
zero finds
a zero
solve(. Functions
value; zero finds
(x-intercept
or root)
can have more
the zero closest
of a function
using
than one x-intercept
to your guess.
The time zero spends
to find the eotTect zero value
depends
on the accuracy
of the values you specify for the
left and right bounds
and the accuracy
of your guess.
To find a zero of a function,
1. Select
graph
2:zero
froln
is displayed
follow
these
the CALCULATE
with
steps.
menu.
The
current
Left Bound? in the bottom-left
corner.
2_
Press [] or [] to move the cm\sor
which you want to find a zero.
onto
the function
%r
3. Press [] or [] (or enter a value) to select the x-value for
the left bound of the interval,
and then press I_T_.
A
indicator
on the graph screen shows the left bound.
Right Bound?
is displayed
in the bottom-left
corner.
Press [] or [] (or enter a value) to select the x-value for
the right bound,
and then press IT_.
A _ indicator
on
the graph
displayed
screen
shows the right bound.
in the bottom-left
corner.
Press [] or [] (or enter
the zero of the function,
press [_T_].
a value)
between
Guess?
is then
to select a point near
the bounds,
and then
ZCYO
The
cursor
is on the solution
and the coordinates
are
displayed,
even if ¢oordOff
format is selected.
To move to
the same x-value for other selected
functions,
press [] or
[]. To restore
the free-moving
cursor,
press [] or [].
3-26
Function
Graphing
minimum,
maximum
minimum and maximum find a ndninmln or nl3xinlunl of a
function within a specified inteP_+al to a tolerance of 1E-5.
To find a nlininlunl
Or
nlaxinlunl,
follow these steps.
1. Select 3:minimum or 4:maximum fronl the CALCULATE
nlenu. The current graph is displayed.
2. Select the function and set left bound, right bound, and
guess _ts described for zero (steps 2 through 4; page 3-26).
The cursor is on the solution, and the coordinates
ate
displayed, even if you have selected CoordOff format;
Minimum or Maximum is displayed in the bottom-left
c()rner.
To nlove to the salne x-value for other selected functions,
press [] or []. To restore the free-moving cursor, press []
or
intersect
[].
intersect finds the coordinates
of a point at which two or
nlore functions intersect using solve(. The intersection
nmst appear on the display to use intersect.
To find an intersection,
follow these steps.
1. Select 5:intersect fi'om the CALCULATE menu. The
current graph is displayed with First curve? in the
bottom-left corner.
c >.J
Fit_t
ll=0
cul_ve?
€
*
Y=.5
2. Press [] or [], if necessatT, to nlove the cursor to the
first function, and then press [gg7_. Second curve? is
displayed in the bottom-left corner.
3. Press [] or [], if necessatT, to nlove the cursor to the
second function, and then press [gg7_.
4. Press [] or [] to nlove the cursor to the point that is
your guess as to location of the intersection,
and then
press [gfff_.
The cursor is on the solution and the coordinates
are
displayed, even if CoordOff format is selected. Intersection
is displayed in the bottom-left corner. To restore the freemoving cursor, press [], [], [], or [].
Function
Graphing
3-27
dy/dx
dy/dx
(numerical
(slope)
derivative)
of a function
finds
at a point,
To find a function's
slope
1, Select 6:dy/dx from
graph is displayed.
the numerical
with
at a point,
the
follow
CALCULATE
2, Press [] or [] to select the function
to find the numerical
derivative.
3, Press [] or [] (or enter a value)
which to calculate
the deriwttive,
The
cursor
is on the solution
derivative
e= 1E-3,
these
menu.
steps,
The current
for which
you want
to select the X value at
and then press [_TE_.
and the numerical
derivative
is displayed.
To move to the same x-value for other selected
functions,
press [] or [], To _store
the free-moving
cursor,
press []
or
ff(x)dx
[].
j'f(x)dx
(numerical
integral)
finds the numerical
integral
of a
function
in a specified
inte[w'al, It uses the fntnt( function,
with a tolerance
of e= 1E-3.
To find the numerical
derivative
of a function,
follow
these
steps.
1, Select 7:jf(x)dx from the CALCULATE menu. The current
graph is displayed
with Lower LimR? in the bottom-left
corner.
2,
Press [] or [] to move the cm\sor to the function
which you want to calculate
the integral.
for
3, Set lower and upper limits as you would set left and
right bounds
for zero (step 3; page 3-26). The integral
value is displayed,
and the integrated
area is shaded.
;'t=X_-3_÷:1. [
J
,,f'I-J,
LeLOeV Limit?
_= - 1 • _II
I,
Sf(x)4x=_._Z?_li7
Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or
any action that invokes Smart Graph to clear the shaded area.
3-28
Function
Graphing
4
Contents
Parametric
Graphing
Getting Started: Path of a Ball ...........................
Defining and Displaying Parametrie Graphs ..............
Exploring Parametric Graphs ............................
_
TEXAS
4-2
4-4
4-7
TF83
INSTRUMENTS
/
J
STAT
PLOT
TBLSET
FORMAT
CALC
TABLE
Parametric
Graphing
4-1
Getting
Getting
Started:
Started
Path of a Ball
is a fast-paced
introduction.
Read the chapter
for details.
Graph the parametric equation that describes the path of a ball hit at an initial
speed of 30 meters per second, at an initial angle of 25 degrees with the
horizontal from ground level. How fat" does the ball travel? When does it hit the
ground? How high does it go? Ignore all forces except gravity.
For initial velocity v0 and angle 0, the position
has horizontal and vertical components.
Horizontal:
Vertical:
The vertical
X1 (t)=tv0cos(0)
Y1 (t)=tv0sin(0)and horizontal
Vertical vector:
Horizontal vector:
Gravity constant:
vectors
of the bali's motion also will be graphed.
X2(t)=0
Y2(t)=Yl(t)
X3(t)=Xl(t)
Y3(t)=0
g=9,8 m/see 2
Press @. Press 30 _
[_
[ANGLE] I (to select °) [] [_
XITin terms of T.
4.
26 [_
to define
_
28 [_ [ANGLE]1 [] []
[] _
to define YIT.
The vertical component
by X2Tand Y2T.
vector
is defined
Press 0 [ggY_ to define X2T.
Press [_
[] to display the VARS Y-VARS
menu, Press 2 to display the PARAMETRIC
secondmT nlenu, Press 2 [gN?_7to define
Y2T,
4-2
Parametric
Graphing
of time
1 ,
g gt 2
Press [_3_. Press [] [] [] [] [_
to
select Par mode. Press [] [] [] [_
to
select 8imul R)r sinmltaneous
graphing of
all three parametric equations in this
example.
Press 30 _
9.8 [] 2 _
of the ball as a function
The horizontal component
defined by X3Tand Y3T,
vector
is
PI,:,I:t
Press [gAg_ [] 2, and then press 1 [gNTgglto
define X3T.Press 0 [gNT_ to define Y3T.
PI,:,L>
PlOI:3
91T B30Tsin (25 ° )
-9.8/2TZ
xXzT Be
VaT B'¢1T
",X_T BX1T
V St 1_10
\X_T
Press [] [] [] _
to change the graph
style to 5 for X3Tand Y3T. Press [] [gNY_
[gNT_ to change the graph style to .41!
for
X2Tand Y2T. Press [] [gNY_ [gNT_ to
change the graph style to "0for XlT and Y1T.
(These keystrokes _tssume that all graph
styles were set to "..originally.)
Press _.
Enter these values for the
window variables.
Tmin=0
Tmax=5
Xmin=-10
Xmax=100
Ymin=-5
Ymax=15
Tstep=,l
Xscl=50
Yscl=10
Press [g_ [FORMAT] [] [] [] [] F_
AxesOff, which turns off the axes.
=
Plo_t
PloLZ
Plot3
_XITB30Tcos(25
°)
YITB30Tsin(25
-9.8/2TZ
_XZT B0
YZT BYI T
°)
_T
_1
T
WINDOW
STsteP=,l
XMin=-lO
gMax=100
Xscl=50
Vmin=-5
Vmax=15
Vsol=lO
PolarGC
CoordO££
GridOn
to set
xPrO_£
10. Press _.
The plotting action
sinmltaneously
shows the ball in flight and
the vertical and horizontal component
vectors of the motion.
/---_,.
Tip: To simulate the ball flying through the air, set
graph style to _)(animate) for XIT and YIT.
1 1. Press _
to obtain numerical results
and answer the questions at the beginning
of this section.
glT=3OTcg¢_;(_
Y1T=30TSin(_:_
Tracing begins at Tmin on the first
pm'ametric equation (X1Tand Y1T), As you
press [] to trace the curve, the cursor
follows the path of the ball over time. The
values for X (distance), Y (height), and T
(time) are displayed at the bottom of the
screen.
Parametric
Graphing
4-3
Defining
and Displaying
Parametric
Graphs
TI-83 Graphing
Mode Similarities
The steps for defining a parametric graph are similar to the
steps for defining a function graph. Chapter 4 assumes that
you are familiar with Chapter 3: Function Graphing.
Chapter 4 details aspects of parametric graphing that differ
from function graphing.
Setting
Parametric
Graphing Mode
To display- the mode screen, press NgffE].To graph
parametric equations, you nmst select Par graphing mode
before you enter window wu'iables and before you enter
tile components
of parametric equations.
Displaying the
Parametric Y=
Editor
After selecting Par graphing
_arametric Y= editor.
mode, press [] to display the
P10L1 Plo_:2 Plot3
_.X1T=11
YtT----
,,X;_T=
'y';_V=
\X_T=
y__T=
In this editor, you can display and enter both the X and Y
conlponents
of up to six equations,
X1T and Y1T through X6T
and YST. Each is defined
in terms of the independent
variable
T. A common
application
of parametric
graphs is
graphing
equations
over time.
Selecting a
Graph Style
4-4
Parametric
The icons to the left of XIT through X6Trepresent the graph
style of each parametric equation (Chapter 3). The default
in Par mode is "..(line), which connects plotted points. Line,
'_i (thick),-(! (path), (!(animate), and ". (dot) styles are
available for parametric graphing.
Graphing
Defining and
Editing
Parametric
Equations
To define
or edit
a parametric
equation,
•
Press
•
[email protected]
the steps
in
_.
[T].
Two components,
X and Y, define a single
equation.
You nmst define both of them.
Selecting and
Deselecting
Parametric
Equations
follow
Chapter
3 for defining
a function
or editing a function.
The
independent
variable
in a paralnetrie
equation
is T. In Par
graphing
mode, you can enter the paralnetric
variable
T in
either of two ways.
parametric
The TI-83 graphs only the selected
parametric
equations.
In the Y= editor, a parametric
equation
is selected
when
= signs of both the X and Y components
are highlighted.
You may select any or all of the equations
XIT and YIT
through
the
X6T and Y6T.
To change the selection
status, move the cursor
onto the =
sign of either the X or Y colnponent
and press [gNYE_. The
status of both the X and Y components
is changed.
Setting Window
Variables
To display" the window variable values, press _.
These vmiables define the viewing window. The values
below are defaults for Par graphing in Radian angle mode.
Tmin=O
Tmax=6.2831853,..
Tstep=.1308996...
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
Smallest T v'Mue to evaluate
Largest T value to evaluate (2x)
T value increment (x/24)
SmMlest X vMue to be displayed
Largest X value to be displayed
Spacing between the X tick nlarks
SmMlest Y vMue to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Note: To ensure that sufficient points are plotted,
change the T window variables.
Parametric
you may want to
Graphing
4-5
Setting the Graph
Format
To display-
the
current
graph
format
Displaying a
Graph
When you press _,
the TI-83 plots the selected
parametric equations, It evaluates the X and Y components
for each value ofT (fronl Tmin to Tmax in intel_'als of
Tstep), and then plots each point defined by X and Y. The
window vm'iables define the viewing window.
As the graph is plotted,
You can
•
•
perform
these
actions
Access functions
by using
component
of the equation
*.5
graphs (Chapter
fronl
the home
3).
screen
or a
Store
•
Select
parametric
Store
1
values
360÷Tnax
Graphing
equations.
"÷Yi TD°neT
"÷Xl
Done
or deselect
FR0t'f"
•
the name of the X or Y
as a vm'iable.
-,
94. r0916375
"cos(T)
"sin(T)
Parametric
[_
program.
NiT
4-6
press
X, Y, and T m'e updated.
Snlart Graph applies to parametric
Window
Variables and
Y-VARS Menus
settings,
[FORMAT], Chapter
3 describes
the format settings
in detail,
The other graphing
modes
share these format settings;
$eq
graphing
mode has an additional
axes format setting,
\XzT="Xl
Bsin(T)yzT=Vin°tIT
T Bcos(T)nOtz
nots
parametric
equations,
Done
Pl0tl =cos(T)
,otz
,,t,
",XlT
YiT=sin(T)
xXzT=
YZT=
directly
to window
360
variables.
I
I
I
Exploring
Free-Moving
Cursor
Parametric
The
Graphs
free-lnoving
cursor
in Par graphing
In RectGC format,
nloving
X and Y; if CoordOn format
displayed.
In PolarGC format,
format is selected,
TRACE
works
the
salne
as
the cursor
updates
the values
is selected,
X and Y are
of
in Func graphing.
X, Y, R, and 0 are updated;
R and 0 m'e displayed.
if CoordOn
To activate TRACE, press _.
When TRACE is active,
you can nlove the trace cursor along the graph of the
equation one Tstep at a time. When you begin a trace, the
trace cursor is on the first selected function at Train. If
ExprOn is selected, then the function is displayed.
In RectGC format, TRACE updates and displays the vMues
of X, Y, and T if CoordOn format is on.
In PolarGC format, X, Y, R, 0 and T are updated; if CoordOn
format is selected, R, 0, and T are displayed. The X and Y
(or R and 0) values are calculated from T.
To nlove five plotted points at a time on a function, press
[] or [2ffd][_. If you nlove the cursor beyond the top or
bottom of the screen, the coordinate values at the bottom
of the screen continue to change appropriately.
Quick Zoom is available
(Chapter 3).
in Par graphing;
Parametric
panning
is not
Graphing
4-7
Moving the Trace
Cursor to Any
Valid T Value
To move
the trace
cursor
to any valid
current
function,
enter the
first digit, a T= prompt
and
displayed
in the bottom-left
enter an expression
at the
valid for the current
_ewing
colnpleted
the ent_% press
T value
on the
number,
When you enter the
the number
you entered
are
corner of the screen.
You can
T= prompt,
The wdue nmst be
window,
When you have
[K_Y_ to lnove the cursor.
PIoI:I PloL2 Plot_
_.X1 T _sir,(T)
YtT_T
XIT=S;n(T)
XIT=_;ifl(T)
T=2
ZOOM
_,Ii
(
_IT=T
T=T
}
T=;_
ZOOM operations
in Par graphing
work the same as in Func
graphing.
Only the X (Xmin, Xmax, and Xscl) and Y (Ymin,
Ymax, and Yscl) window
vm'iables
are affected.
The T window
vm'iables
(Train, Tmax, and Tstep) are only'affected when you select ZStandard. The MARS ZOOM
seeondm_y- menu ZT/Z0 items 1 :ZTmin, 2:ZTmax, and
3:XTstep are the zoom memory
variables
for Par graphing.
CALC
4-8
CALC operations
in Par graphing
work the same as in Func
graphing.
The CALCULATE menu items available
in Par
graphing
are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt.
Parametric
Graphing
Polar
Graphing
Contents
Getting Started: Polar Rose ..............................
Defining and Displaying
Polar Graphs
...................
Exploring Polar Graphs ..................................
TEXAS
5-2
5-3
5-6
T1=83
INSTRUMENTS
J
STAT
PLOT
TBLSET
FORMAT
CALC
TABLE
Polar
Graphing
5-1
Getting
Getting
Started:
Started
Polar Rose
is a fast-paced
introduction.
Read the chapter
for details.
The polar equation R=Asin(B0) graphs a rose. Graph the rose for A=8 and
B=2.5, and then explore the appearance
of the rose for other values of A and B.
Press _
to display the mode screen.
Press [] [] [] [] [] [gfff_] to select Pol
graphing
mode. Select the defaults
(the
options
on tile left) for the other nlode
settings.
Plot:t
Plot2
Plot3
_rl B8sin(2.50)
\r_:=
i_.r_ =
Press [] to display- the polar Y= editor.
Press 8 NTN2.6 _
[] [g_gO to define
%rfi=
rl.
3.
Press _
6 to select 6:ZStandard and
graph the equation in the standard viewing
window. The graph shows only five petals
of the rose, and the rose does not appear
to be synunetrical. This is because the
standard window sets 0max=2= and defines
the window, rather than the pixels, as
square.
4.
Press _
to display the window
variables. Press [] 4 [gfi_ [_] to increase
value of 0max to 4x.
5,
Press _
the graph.
the
5 to select 5:ZSquare and plot
Repeat steps 2 through 5 with new values
for the variables A and B in the polar
equation rl=Asin(B0). Observe how the new
values 'affect the graph.
5-2
Polar
Graphing
WINDOW
Omin=O
OMaX=4X
Ostee=,1308996...
XMin=-lO
Xmax=lO
XSCI=I
_VMin=-lO
Defining
and Displaying
steps
Polar Graphs
TI-83 Graphing
Mode Similarities
The
for defining
a polar
graph
are similar
Setting Polar
Graphing Mode
To display- the mode screen,
press [M6_]. To graph polar
equations,
you nmst select Pol graphing
mode before you
enter values for the window
variables
and before you enter
polar equations.
Displaying the
Polar Y= Editor
After selecting
Pol graphing
_olar Y= editor.
for defining
a function
graph. Chapter
are familiar
with Chapter
3: Function
details aspects
of polar graphing
that
graphing.
PI,:,I:I PloL2
\rl=
\i-- 2---M-_ 3:=
\1,-, tl =
\1.'. _ =
\p6=
mode,
to the steps
5 assumes
that you
Graphing.
Chapter
5
differ from function
press
[]
to display-
the
Plot3
In this editor, you can enter and display up to six polar
equations, rl through r6. Each is defined in terms of the
independent
variable 0 (page 5-4).
Selecting
Styles
Graph
The icons to the left of rl through
r6 represent
the graph
style of each polar equation
(Chapter
3). The default
in Pol
graphing
mode is "..(line), which connects
plotted
points.
Line, "i (thick),
-(! (path), (! (animate),
and ". (dot) styles are
available
for polar graphing.
Polar
Graphing
5-3
Defining and
Editing Polar
Equations
Selecting and
Deselecting Polar
Equations
To define
or edit
a polar
equation,
follow
the steps
•
Press
•
[email protected]
_.
[0].
The TI-83 graphs only the selected polar equations. In the
Y= editor, a polar equation is selected when the = sign is
highlighted. You nlay select any- or M1 of the equations.
To change the selection status, nlove the cursor
= sign, and then press [_.
Setting Window
Variables
Ostep=.1308996...
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
SmMlest 0 value to evMuate
Largest 0 vMue to evaluate (2=)
Increment between @values (=/24)
SmMlest X vMue to be displayed
Largest X value to be displayed
Spacing between the X tick marks
SmMlest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Note: To ensure that sufficient points are plotted,
change the 0 window variables.
Polar
onto the
To display- the window variable values, press _.
These variables define the viewing window. The values
below are defaults for Pol graphing in Radian angle mode.
Omin=O
Omax=6.2831853,..
5-4
in
Chapter
3 for defining
a function
or editing a function.
The
independent
vm'iable in a polar equation
is 0. In Pol
graphing
mode, you can enter the polar variable
0 in either
of two ways.
Graphing
you may want to
Setting the Graph
Format
To display the current graph format settings, press [2_]
[FORMAT].Chapter 3 describes the forlnat settings in detail.
The other graphing lnodes share these format settings.
Displaying a
Graph
When you press _,
the TI-83 plots the selected polar
equations. It evMuates R for each value of 0 (from 0min to
0max in intervals of 0step) and then plots each point. The
window variables define the viewing window.
As the graph is plotted,
Window
Variables and
Y-VARS Menus
X, Y, R, and 0 are updated.
Slnart Graph applies to polm" graphs
(Chapter
You
the
can
perfornl
these
actions
fronl
honle
3).
screen
or
a
program.
•
Access functions
wuiable
by using the name of the equation
rl +r.z
•
8
Store polar equations,
"51_1"÷1"i
•
•
as a
Done
\r?:=\rll_5OPl°tl
P10t_:
Select or deselect
polar equations.
FnOff
Done
1
Plott
xr
I =50PIotZ Plot_
Store values directly to window
IO+Orqih
Plot3
I
I
I
variables.
OI
Polar
Graphing
5-5
Exploring
Polar Graphs
ffee-mo_ing
cursor
in Pol graphing
Free-Moving
Cursor
The
works
the same
as
TRACE
To activate TRACE, press _.
When TRACE is active,
you can nlove the trace cursor along the graph of the
equation one 0step at a time. When you begin a trace, tile
trace cursor is on the first selected function at 0min. If
ExprOn fornlat is selected, then the equation is displayed.
in Func graphing.
In RectGC fonnat,
moving tile cursor
updates
the values of X and Y; if CoordOn format is
selected,
X and Y are displayed.
In PolarGC format,
X, Y, R,
and 0 are updated;
if CoordOn format is selected,
R and 0
m'e displayed.
In RectGC format, TRACE updates the values of X, Y, and 0;
if CoordOn format is selected, X, Y, and 0 are displayed. In
PolarGC format, TRACE updates X, Y, R, and 0; if CoordOn
format is selected, R and 0 m'e displayed.
To nlove five plotted points at a time on a function, press
Kffa][] or Kffa][Z]. If you move tile trace cursor beyond tile
top or bottonl of the selden, the coordinate values at the
bottonl of the screen continue to change appropriately.
Quick Zoom is available
not (Chapter 3).
in Pol graphing
mode; panning
is
Moving the Trace
Cursor to Any
Valid e Value
To nlove the trace cursor to any valid 0 value on the
current function, enter the number. When you enter the
first digit, a 0= prompt and the number you entered are
displayed in tile bottom-left corner of tile screen. You can
enter an expression at the 0= prompt. The value must be
valid for the current viewing window. When you complete
tile enhT, press _
to nlove the cursor.
ZOOM
ZOOM operations
in Pol graphing
work the same as in Func
graphing.
Only the X (Xmin, Xmax, and Xscl) and Y (Ymin,
Ymax, and Yscl) window
variables
are affected.
The 0 window variables
(0rain, 0max, and Ostep) are not
'affected, except when you select ZStandard.
The VARS
ZOOM seeondmTy- menu ZT/ZO items 4:Z0min, 5:Z0max, and
6:Z0step m'e zoom nlemoKy-varialfles
ff_r Pol graphing.
CALC
5-6
CALC operations
in Pol graphing
work the sanle
graphing.
The CALCULATE nlenu items available
graphing
are 1:value, 2:dy/dx, and 3:dr/d0.
Polar
Graphing
as in Func
in Pol
Sequence
Graphing
Contents
Getting Started: Forest and Trees ........................
Defining and Displaying
Sequence
Graphs ...............
Selecting Axes ('ombinations
............................
Exploring
Sequence Graphs ..............................
Graphing Web Plots ......................................
Using Web Plots to Illustrate
Convergence
...............
Graphing Phase Plots ....................................
Comparing
TI-83 and TI-82 Sequence Variables ..........
Keystroke
Differences
Between
TI-83 and TI-82 .........
'_
TEXAS
6-2
6-3
6-8
6-9
6-11
6-12
6-13
6-1.5
6-16
T1=83
iNSTRUMENTS
u= -.Bu(7_-:1.)+3.6
-,_
I=
-%
l
........
>'_=:L5
X=l.F_61172
I'
....
"_
"%_
i'=1._ _:61172
J
STATPLOT
TBLSET
FORMAT
CALC
TABLE
Sequence
Graphing
6-1
Getting
Getting
Started:
Started
Forest and Trees
is a fast-paced
introduction.
Read the chapter
for details.
A small forest of 4,0!)0 trees is under a new forestw plan. Each year 20 percent
of the trees will be hmwested and 1,000 new trees will be planted. Will the
forest eventually- disappear? Will the forest size stabilize? If so, in how many
yeat\_ and with how many trees?
Press IM65E].Press [] [] [] [] [] [] IgffTgR]
to select Seq graphing mode.
Soi Eng
0123456789
Degree
ar Pol
Press [_ [FORMAT] and select Time axes
format and ExprOnformat if neeessatT.
3.
Press @. If the graph-style icon is not ".
(dot), press [] [], press [g_-gRquntil ". is
displayed, and then press [] [].
4.
Press [_
[] a to select iPart( (integer
pro't) because only whole trees are
harvested. After each annual hatw'est, 80
percent (.80) of the trees remain. Press []
8 [_ [u] [] _
[] 1 [] to define the
number of trees after each harvest. Press
[] 1000 [] to define the new trees. Press []
4000 to define the number of trees at the
beginning of the program.
5.
MW
UW
PI_I
PI_tZ
Plot3
_Min=l
'..u(_bBiPart(.Bu(
_-I)+1000)
u(_Min)B4000
".v(_)=
v(_Min)=
".u(_)=
Press [_
0 to set nNin=0. Press [] 60
to set nNax=fi0, nNin and nMax evaluate
forest size over 50 years. Set the other
window variables.
PlotStart=l
Xmin=0
Ymin=0
PlotStep=l
Xmax=50
Xscl=10
Ymax=6000
Yscl=1000
Press _.
Tracing begins at nMin (the
start of the foresttT plan). Press [] to trace
the sequence year by year. The sequence is
displayed at the top of the screen. The
values for n (number of years), X (X=n,
because n is plotted on the x-axis), and Y
(tree count) are displayed at the bottom.
When will the forest stabilize? With how
many trees?
6-2
UM
PolaPGC
CoopdO_
GridOn
RxesO_
LabelOn
Sequence
Graphing
lu=iPart(.Bu(_-l)+lOO0)
I
Defining
and Displaying
Sequence
Graphs
TI-83 Graphing
Mode Similarities
The steps for defining a sequence graph are similar to the
steps for defining a function graph. Chapter 6 assumes that
you are familiar with Chapter 3: Function Graphing.
Chapter 6 details aspects of sequence graphing that differ
froln function graphing.
Setting Sequence
Graphing Mode
To display- the mode screen, press [M6D_.To graph
sequence functions, you nmst select 8eq graphing mode
before you enter window wu'iables and before you enter
sequence functions.
Sequence graphs automatically
plot in Simul mode,
regardless of the current plotting-order
mode setting.
TI-83 Sequence
Functions u, v,
and w
The TI-83 has three sequence functions that you can enter
from the keyboard: u, v, and w. They are above the [7], [],
and [] keys.
You call define sequence
•
•
•
•
functions
in terms off
The independent variable n
The previous term in the sequence function, such as
u(n-1)
The term that precedes tile previous term in tile
sequence function, such as u(n-2)
The previous term or the term that precedes the
previous term in another sequence function, such as
u(n-1) or u(n-2) t_ferenced in the sequence v(n).
Note: Statements in this chapter about u(n) are also true for v(n) and
w(n); statements about u(n-1) are also true for v(n-1) and w(n-1);
statements about u(n-2) are also true for v(n-2) and w(n-2).
Sequence
Graphing
6-3
Displaying the
Sequence Y=
Editor
After selecting
Y= editor.
Seq mode,
press
[]
to display-
the sequence
nMin=l
",.u(n)=
u(nMin)=
"..v(n)=
v(nMin)=
"..u(n)=
u(nMin)=
In this editor, you can display and enter sequences for u(n),
v(n), and w(n), Also, you can edit the value for nMin, which
is the sequence window variable that defines the nlininluln
n value to evaluate.
The sequence Y= editor displays the nMin value because of
its relevance to u(nMin), v(nMin), and w(nMin), which are the
initial values for the sequence equations u(n), v(n), and
w(n), respectively.
nMin in the Y= editor is the same as nMin in the window
editor. If you enter a new value for nMin in one editor, the
new value for nMin is updated in both editors.
Note: Useu(nMin), v(nMin), or w(nMin) only with a recursive
sequence,which requires an initialvalue.
Selecting
Styles
Graph
Selecting and
Deselecting
Sequence
Functions
The icons to the left of u(n), v(n), and w(n)
graph style of each sequence
(Chapter
3).
$eq mode is ". (dot), which shows discrete
"..(line), and "i (thick)
styles m'e available
graphing.
Graph styles m'e ignored
in Web
The TI-83 graphs only the selected sequence functions. In
the Y= editor, a sequence function is selected when the =
signs of both u(n)= and u(nMin)= are highlighted.
To change
move the
then press
sequence
6-4
Sequence
represent
the
The default
in
values. Dot,
for sequence
format.
Graphing
the selection status of a sequence function,
cut\sor onto the = sign of the function name, and
[g_.
The status is changed for both the
function u{n) and its initial value u(nMin).
Defining and
Editing a
Sequence
Function
To define or edit a sequence function, follow the steps in
Chapter 3 for defining a function. The independent
vmiable
in a sequence is n.
In Seq graphing mode, you can enter the sequence
in either of two ways.
•
•
vmiable
Press _.
Press [g67][CATALOG][N].
You can enter the function
name from the keyboard.
•
•
To enter the function
To enter the function
name u, press [gh_][u] (above [_).
name v, press [g6_ [v] (above [_).
•
To enter the function name w, press [g67][w] (above [_).
Generally, sequences are either nonrecursive
or recursive.
Sequences are evaluated only at consecutive integer
values, n is always a series of consecutive integers, starting
at zero or any positive integer.
Nonrecursive
Sequences
In a nonrecursive
sequence, the nth term is a function of
the independent
variable n. Each term is independent
of all
other terms.
For example,
in the nonrecursive
sequence
below, you can
calculate
u(6) directly,
without
fit\_t calculating
u(1) or any
%exdous terlll,
PloL1
PloL2
Plot3
_Hin=l
,.u(_)B2*n
u(_Min)B
"..v(_)=
v(_Min)=
"'.u(_)=
u(_Min)=
The
sequence
2, 4, 6, 8,10,
equation
above
returns
the sequence
. . . for n = 1,2,3,4,5,....
Note: You may leave blank the initial value u(nMin) when calculating
nonrecursive sequences.
Sequence
Graphing
6-5
Recurslve
In a reem\Mve
Sequences
defined in relation
to the previous
term or the term that
precedes
the previous
term, represented
by u(n-1) and
u(n-2). A reem\Mve sequence
may also be defined
in
relation
to n, as in u(n)=u(n- 1)+n.
For example,
u(5) without
sequence,
the nth term
in the sequence
first calculating
plo1:1 PloL2 pl,:a:_:
_Min=l
"..u(_)B2*u(n-1
)
in the sequence
is
below you cannot
calculate
u(1), u(2), u(3), and u(4).
I
I
u(.n[_in)B1
Using an initial value u(nMin) = 1, the sequence
returns
1, 2, 4, 8, 16,...
above
Tip: On the TI-83, you must type each character of the terms. For
example, to enter u(n-1), press _
[u] [] _
[] [] lB.
Recursive
sequences
since they reference
•
require
an initial
undefined
terms.
If each term in the sequence
pre_dous
term, as in u(n-1),
value for the first tenn.
PloLi
plol:._
[-2)
u(r_Min)B{l,O
term
6-6
Sequence
Graphing
value
sequence
is defined in relation
to the
the previous
term, as in u(n-2), you
values for the first two terms. Enter
a list enclosed
in braees
({ }) with
the values.
Plot3
nMin=l
I..u(n)Bu(n-1
The
is defined in relation
to the
you nmst specify an initial
1 )+5
If each term in the
term that precedes
nmst specify- initial
the initial values as
commas
separating
PloI:2
or values,
Plot3
nMin=l
..u (n) B. 8u (n0
u(nMin)B100
Plot't
value
of the first
)+u(n
}
term
is 1 for the sequence
is 0 and the value
u(n).
of the second
Setting Window
Variables
To display- the window variables, press _,
These
variables define the viewing window. The values below are
defaults for Seq graphing in both Radian and Degree angle
nlodes,
nMin=1
nMax:10
PlotStart:1
PlotStepffil
Xmin:-10
Xmax=lO
Xscl=l
Ymin=-lO
Ymax=lO
Yscl=l
Smallest n value to ev'gduate
Largest n value to evaluate
First term number to be plotted
Incremental n value (for graphing only)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
nMin must be an integer k O, nMax, PlotStart, and PlotStep
nmst be integers _>1,
nMin is the smallest n wdue to evaluate, nMin also is
displayed in the sequence Y= editor, nMax is the largest
value to evaluate. Sequences are evaluated at u(nMin),
u(nMin+l), u(nMin+2), ... , u(nMax).
n
PlotStart is the first term to be plotted. PlotStart=l begins
plotting on tile first term in tile sequence. If you want
ph)tting to begin with the fifth term in a sequence, for
exalnple, set PlotStart=& The first four terms are evaluated
but are not plotted on the graph.
PlotStep is the incremental
n wdue for graphing only.
PlotStep does not 'affect sequence evaluation; it only
designates which points are plotted on the graph. If you
specify PlotStep=2, the sequence is ewduated at each
consecutive integer, but it is plotted on the graph only at
evew other integer.
Sequence
Graphing
6-7
Selecting
Axes Combinations
Setting the Graph
Format
To display-
the
current
graph
Time Web uv
vw uw
RectGC
PolarGC
CoordOn
CoordOff
GridOff
GridOn
AxesOn
AxesOff
LabelOff
LabelOn
ExprOn
Setting Axes
Format
format
settings,
press
[_
[FORMAT], Chapter
3 describes
the format settings
in detail,
The other graphing
modes
share these format settings,
The
m,ces setting on the top line of the screen
is available
only
in Seq mode,
ExprOff
Type of sequence plot (m,ces)
Rectangular or polar output
Cursor coordinate
display mdoff
Grid display off or on
Axes display on or off
Axes label display- off or on
Expression display on or off
For sequence graphing, you can select fronl five axes
formats. The table below shows the values that are plotted
on the x-axis and y-m'ds for each axes setting.
Axes Setting
Time
Web
uv
vw
uw
x-axis
y-axis
n
u(n), v(n),w(n)
u(n-1), v(n-1),w(n-1)
u(n), v(n),w(n)
u(n)
v(n)
u(n)
v(n)
w(n)
w(n)
See pages 6-11 and 6-12 for nlore information
on Web
plots. See page 6-13 for more information
on phase plots
(uv, vw, and uw m,ces settings).
Displaying a
Sequence Graph
To plot the selected sequence functions, press _.
graph is plotted, the TI-83 updates X, Y, and n.
Snlart Graph applies to sequence
6-8
Sequence
Graphing
graphs
(Chapter
As a
3).
Exploring
Sequence
Free-Moving
Cursor
The
TRACE
The
Graphs
free-moving
cursor
in Seq graphing
works
the same
as
in Func graphing.
In RectGC fonnat,
nloving tile cursor
updates
the values of X and Y; if CoordOn format is
selected,
X and Y are displayed.
In PolarGC fornlat,
X, Y, R,
and 0 are updated;
if CoordOn format is selected,
R and 0
m'e displayed.
axes
fornlat
setting
affects
TRACE.
When Time, uv, vw, or uw axes format is selected, TRACE
moves the cursor along the sequence one PlotStep
increment at a time. To nlove five plotted points at once,
press [_ [] or [_ [].
•
•
When you begin a trace, the trace cursor is on the first
selected sequence at the term number specified by
PlotStart, even if it is outside the viewing window.
Quick Zoom applies to all directions. To center the
viewing window on the current cursor location after
you have moved the trace cursor, press [_.
The
trace cursor t_tun_s to nMin.
In Web format,
the trail of the cursor helps identify points
with attracting
and repelling
behavior
in the sequence.
When you begin a trace, the cursor
is on the x-axis at the
initial wdue of the first selected
function.
Tip: To move the cursor to a specified n during a trace, enter a value
for n, and press _.
For example, to quickly return the cursor to the
beginning of the sequence, paste nMin to the n= prompt and press
Moving the Trace
Cursor to Any
Valid n Value
To nlove the trace cursor to any valid n vMue on the
current function, enter the number. When you enter the
first digit, an n = prompt and the number you entered are
displayed in the bottom-left corner of the screen. You can
enter an expression at the n = prompt. The value nmst be
valid for the current viewing window. When you have
completed the entKy-,press [gfff_ to move the cursor.
U=U(:O-1)+U(:O-Z)
I
. , . :": "
;o=_:
""
Sequence
Graphing
}1=5"I_
?=3
6-9
ZOOM
ZOOM operations
in Seq graphing
work the same as in
Func graphing,
Only the X (Xmin, Xmax, and Xscl) and Y
(Ymin, Ymax, and Yscl) window
variables
are affected.
PlotStart, PlotStep, nMin, and nMax are only affected
when
you select ZStandard. The VARS Zoom secondary
lnenu ZU
items 1 through 7 are the ZOOM MEMORY variables for Seq
graphing.
CALC
The only CALC operation
Evaluating u, v,
and w
is value.
When Time axes format is selected,
u(n) value) for a specified n value.
•
When Web axes format is selected, value draws the web
and displays Y (the u(n) value) for a specified n value,
•
When uv, vw, or uw axes format is selected, value
displays X and Y according to the axes format setting.
For example, for uv axes format, X represents
u(n) and
Y represents v(n),
value displays Y (the
To enter the sequence names u, v, or w, press [2_] [u], [v], or
[w], You can evaluate these names in any- of three ways,
Calculate the nth value in a sequence.
Calculate a list of values in a sequence.
Generate a sequence with u(nstart,nstop[,nstep]),
is optional; default is 1.
"nz"+u:u(3)
u({1,3,5,7,9})
{i 9 25 49
u(1,9,2)
{1 9 25 49
Sequence
in Seq graphing
•
•
•
•
6-10
available
Graphing
9
81}
81}
nstep
Graphing
Web Plots
Web axes
To select
Valid Functions
for Web Plots
V_l_en Web axes format is selected,
a sequence
graph properly
or will generate
an error.
Displaying the
Graph Screen
format,
press
[FORMAT] []
Graphing a Web
Plot
[_
[E_],
A
web plot graphs
u(n) versus
u(n-1), which you can use to
study long-term
behavior
(convergence,
divergence,
or
oscillation)
of a reeursive
sequence.
You can see how the
sequence
lnay change
behavior
as its initial value changes.
•
It must
(u(n-1)
be recursive
with
but not u(n-2)).
•
It cannot
reference
n directly.
•
It cannot
reference
any defined
only one recursion
In Web format, press _
The TI-83:
•
Draws
•
Plots
the
independent
will not
sequence
level
except
itself.
to display the graph screen.
a y=x reference
line
selected
sequences
variable.
in AxesOn
with
format.
u(n-1)
as the
Note: A potential convergence
point occurs whenever a sequence
intersects the y=x reference line. However, the sequence may or may
not actually converge at that point, depending on the sequence's
initial
value.
Drawing
the Web
To activate
the trace cursor,
press _.
The screen
displays
the sequence
and the emTent
n, X, and Y values (X
represents
u(n-1) and Y represents
u(n)). Press []
repeatedly
to draw the web step by step, starting
at nMin.
In Web format,
the trace cursor
follows
this course.
1. It starts on the x-axis
PlotStart=l).
2. It lnoves
vertically
3. It lnoves
horizontally
4. It repeats
continue
this vertical
to press [].
at the initial
(up or down)
value
u(nMin)
(when
to the sequence.
to the y=x reference
and horizontal
Sequence
line.
movenlent
Graphing
as you
6-11
Using Web Plots to Illustrate
Convergence
Press [] in Seq mode to display the sequence Y= editor.
Make sure the graph style is set to ". (dot), and then
define nMin, u(n) and u(nMin) as shown below.
Example:
Convergence
u(_Min)B{-4}
"-.v(n)=
_Min=lPl_l
PloL_
v(nMin)=
PloL_
)+
".uO?)=
2.
Press
[_
3. Press
[_
nMin=l
nMax=25
PlotStart=l
[FORMAT] _
to set Time axes
and set the variables
Xmin=0
Xmax=25
Xscl=l
ff)rmat,
as shown below.
Ymin=-10
Ymax=l 0
Yscl=l
PlotStep=l
4. Press [g_
5, Press [_
6. Press [_
Xmin=-10
7.
Press [g_
to graph the sequence.
[FORMAT]and select the Web axes setting.
and change the variables
Xmax=10
below.
to graph the sequence.
8. Press _,
and then press [] to draw the web. The
displayed cursor coordinates n, X (u(n-1)), and
Y (u(n)) change accordingly. When you press [], a new n
value is displayed, and the trace cursor is on the
sequence. When you press [] again, the n value remains
the same, and the cursor moves to the y=x reference line.
This pattern repeats as you tra_'e the web.
u=-.au(._._-:t:,*_:.e
N'--_.?_:EII?2
6-12
Sequence
Graphing
t.-*
I?=1,?_:El172
Graphing
Phase Plots
Graphing with uv, The phase-plot m,ces settings uv, vw, and uw show
vw, and uw
relationships
between two sequences. To select a
phase-plot axes setting, press [_ [FORMAT],press [] until
the cursor is on uv, vw, or uw, and then press [_.
Example:
Predator-Prey
Model
Axes Setting
x-axis
y-axis
uv
u(n)
v(n)
vw
v(n)
w(n)
uw
u(n)
w(n)
Use the predator-prey
model to determine the regionM
populations
of a predator and its pt_y that would maintain
population equilibrium for the two species.
This example uses the model to determine the equilibrium
populations
of wolves and rabbits, with initial populations
of 200 rabbits (u(nMin)) and 50 wolves (v(nMin)).
These are the wu'iables
(given values are in pm'entheses):
R
M
K
W
=
=
=
=
number of rabbits
rabbit population growth rate without wolves
rabbit population death rate with wolves
number of wolves
G
D
n
Rn
=
=
=
=
wolf population growth rate with rabbits
wolf population death rate without rabbits
time (in months)
Rn_I(I+M-KWn_I)
W,
= W,_I(I+GRn_I-D
(.05)
(.001)
(.0002)
(.03)
)
1, Press [] in Seq mode to display the sequence Y= editor.
Define the sequences and initial wdues for Rn and Wn as
shown below. Enter the sequence Rn as u(n) and enter
the sequence Wn as v(n).
Plot:l.
Plot::"
F'lot2,
l
nMir,=l
I
".l.l(_) BM(_- 1 )*( 1+1
• 05-. 00 l*v(n-1
) )l
-.u (n) By (_- 1 )*( 1+
• 0002.u (n-1)-.
03
)v(nMin)B{50}
".t0(n)=
u_(r_Min)=
Sequence
Graphing
6-13
2, Press _
[FORMAT] _
3, Press _
nMin=O
nMax=400
PlotStart=l
to select
and set the variables
Xmin=O
Xmax=400
Xscl=100
Time axes format,
as shown below.
Ymin=O
Ymax=300
Yscl=100
PlotStep=l
4, Press
[ghT_]
to graph
the
sequence,
5, Press _
[] to individually trace the number
rabbits (u(n)) and wolves (v(n)) over time (n),
Tip: Press a number,
6,
Press [g_]
format,
7. Press
_
below.
Xmin=84
Xmax=237
Xscl=50
Press _.
the number
[FORMAT]
and then press _
[]
[]
and change
of
to jump to a specific
n
to select uv axes
_
these
variables
as shown
Ymin=25
Ymax=75
Yscl=lO
Trace both the number of rabbits (X) and
of wolves (Y) through 400 generations,
Note: When you press [_,
the
equation for u is displayed in the
top-left corner. Press [] or [] to
see the equation for v.
I g=160.LIB_.=:B y=6;',66;'BLI9
6-14
Sequence
Graphing
Comparing
Sequences and
Window
Variables
TI-83 and TI-82 Sequence
Refer
to the table
shows TI-83
well as their
if you are familim"
sequences
and sequence
TI-82 counterparts.
with
the TI-82.
window
It
vm'iables,
as
TI-82
TI-83
In the
Variables
Y= editor:
u(n)
Un
u(nMin)
U nStart
v(n)
Vn
v(nMin)
VnStart
w(n)
not
available
w(nMin)
not
available
In the window
(window
variable)
(window
vm'iable)
editor:
nMin
nStart
nMax
nMax
PlotStart
nMin
PlotStep
not
available
Sequence
Graphing
6-15
Keystroke
Differences
Between
to the table
TI-83 and TI-82
Sequence
Re%r
Keystroke
Changes
conlpares
TI-83 sequence-name
sy_tax
and variable
sy_tax
with TI-82 sequence-name
syntax
and variable
syntax.
if you are familiar
with
the TI-82.
It
TI183 / TI-82
On TI183, press:
On TI-82,
n/ n
_
_
[,]
u(n) / Un
_
_
[Y-VARS] []
[u]
press:
[]
D_D
v(n)
/ vn
_
w(n)
_
[i
r_ [¥-VARS][] []
[w]
not
available
D_D
D_D
u(n-1)lUn-1
_
[u]
_
[Un-l]
v(n-1)/vn-1
I_
[v]
I_
[vn-_]
w(n-1)
_
[w]
not
available
D_DmD
I]]_E]mD
[]_•mD
6-16
Sequence
Graphing
Tables
Contents
Getting Started: Roots of a Function
.....................
Setting Up the Table .....................................
Defining the Dependent
Variables ........................
Displaying the Table .....................................
'_
TEXAS
T1=83
iNSTRUMENTS
X
0
1
2
Y_
0
"1
h
21
_
11_
h
5
7-2
7-3
7-4
7-5
Y2
0
"_
0
15
hE
10_
X= -1
J
STAT
PLOT
TBLSET
FORMAT
CALC
TABLE
Tables
7-1
Getting
Getting
Started:
Started
Roots of a Function
is a fast-paced
introduction.
Read
Evaluate
the function
Y = X :_- 2X at each integer
many sign changes
occur, and at what X values?
1.
2.
the chapter
between
for details.
-10 and
Press _
[] [] [] FENY_to set Func
graphing mode.
Press @. Press _
Then press [] 2 _
function Y1=X3- 2X.
_
3 to select 3
to enter the
Press [_
[TBLSET] to display- the TABLE
SETUP screen.
Press [] 10 _
to set
TblStart=-10,
Press
1_
to set ATbI=I.
Press _
to select Indpnt: Auto
(automatically
generated independent
values). Press [] [gNT_ to select
Depend: Auto (automatically
generated
dependent values).
Press [_
screen.
[TABLE]to display the table
Plol:l
Press [] until you see the sign changes in
the value of Y1. How many sign changes
occur, and at what X values?
TABLE SETUP
TbIStart= -10
_Tbl=l
Indent: _
Ask
Depend:
X
_
Y_
"9
"B
"?
"6
"7tl
"h96
"329
"_.Oh
"_:
"Jig
"h
"gtl
X
"2
"1
0
1
X=3
Tables
Pl_l:_
P1*{_
-.Y1BX x-2X
,,yz=
b.Y_=
•,.y _ =
\Yg=
".YG=
\YT=
X= -10
7-2
10. How
YI
"h
1
0
"t
h
Ask
Setting
Up the Table
TABLE SETUP
Screen
TodisplaytheTABLESETUPscreen,
TblStart=O
_Tbl=lSETUP
TRBLE
IndPnt:
Depend: i
TblStart, ATbl
press[_[TBLSET].
Rsk
Rsk
TblStart (table start) defines
the initial value for the
independent
variable.
TblStart applies only when the
independent
variable
is generated
automatically
(when
Indpnt: Auto is selected).
ATbl (table
variable.
step)
defines
the increment
for the independent
Note: In Seq mode, both TblStart and ATbl must be integers.
Indpnt: Auto,
Indpnt: Ask,
Depend: Auto,
Depend: Ask
Setting Up the
Table from the
Home Screen or
a Program
Selections
Table Characteristics
Indpnt: Auto
Depend: Auto
Values are displayed
automatically
the independent-variable
colunm
dependent-variable
colunms.
Indpnt: Ask
Depend: Auto
The table is empty; when you enter a value
for the independent
variable,
all
corresponding
dependent-variable
values
are cah:ulated
and displayed
automatically.
Indpnt: Auto
Depend: Ask
Values are displayed
autonmtically
for the
independent
variable;
to generate
a value
for a dependent
variable,
move the cursor
to that cell and press [E_.
Indpnt: Ask
Depend: Ask
The table is empty; enter values for the
independent
variable;
to generate
a value
for a dependent
variable,
move the cm:sor
to that cell and press [EN_,
in both
and in all
To store a value to TblStart, ATbl, or TblInput from the
home screen or a program,
select the variable
name from
the VARB TABLE seconda[w
menu. TblInput
independent-variable
values in the cmTent
is a list of
table.
When you press [2_ [TBLSET] in the program
editor,
can select IndpntAuto, IndpntAsk,
DependAuto, and
DependAsk.
Tables
you
7-3
Defining
the Dependent
Variables
Defining
Dependent
Variables from
the Y= Editor
In the Y= editor, enter the functions that define the
dependent vmiables. Only functions that are selected in the
Y= editor are displayed in the table. The current graphing
mode is used. In Par mode, you nmst define both
components
of each parametric equation (Chapter 4).
Editing
Dependent
Variables from
the Table Editor
To edit a selected
these steps.
Y= function
fronl the table editor, follow
1. Press [_ [TABLE]to display" the table, then press [] or
[] to move the cursor to a dependent-variable
column.
2. Press [] until the cursor is on the function name at the
top of the colunm. The function is displayed on the
bottonl line.
5G
20't
Vt BX_-2X
3, Press [ggT_. The cursor
the function.
X
moves to the bottonl
X
ml
o
I
.-,
o
"t
it
2t
_6
I15
20_
LI
_;
I_
71BII_-2X
line. Edit
m
o
t
o
"1
6
20_
V1BX:-4X
Press [ggT_ or []. The new values are calculated. The
table and the Y= function are updated automatically.
X
"3
Y1
Yt =O
Note:
defines
7-4
Tables
You also can use this feature
a dependent
variable
without
to view the function
having
that
to leave the table.
Displaying
the Table
The Table
To display-
the table,
press
[_q
[TABLE].
Current cell
Independentvariable values
to
X
_ 1 4,
_
in the first
column
lZ
13
-h?.eB -_:Z.BE
-_Z.I_6 -6Z.eE
11
"hh.86
9"_
"_
"_'.gB
1_
1
1h
Yz
-_9.iz
Dependentvariable values in
"_:h.86
"G6.98
"E.q.Z
16
"6h._:B "?h,59
Y1 = -39, 173120459
_.
--
--
the second and
third columns
T
Current cell's full value
Note: The table abbreviates the values, if necessary.
Independent
Dependent
Variables
and
Clearing the
Table from the
Home Screen or
a Program
The current
graphing
lnode determines
which independent
and dependent
varial)les
are displayed
in the table
(Chapter
1). In the tal)le above, for example,
the
independent
variable
X and the dependent
wuiables
Y1 and
Y2 are displayed
because
Func graphing
mode is set.
Graphing Mode
Independent
Variable
Dependent
Variable
Func (function)
X
Y1 through
Y0
Par (parametric)
T
X1T/Y1T through
X6T/Y6T
Pol (polar)
0
rl through
Seq (sequence)
n
u(n), v(n), and w(n)
Yg, and
r6
From the home screen, select the CIrTable instruction
the CATALOG. To clear the table, press [ggY_.
fronl
From a program, select 9:CIrTable from the PRGM I/0 menu
or from the CATALOG. The talfle is cleared upon execution.
If IndpntAsk is selected, 'all independent
and dependent
varialfle values on the table are cleared. If DependAsk is
selected, all dependent variable values on the talfle are
cleared.
Tables
7-5
Scrolling
IndependentVariable Values
If Indpnt:
Auto is selected,
you can press
[] and []
in the
independent-variable
colunm
to display more wdues. As
you scroll the colunm,
the corresponding
dependentvariable
values also are displayed.
All dependent-variable
values may not be displayed
if Depend: Ask is selected.
X
YI
Yz
1
z
"t
4
"_
¢
4
5
6
_6
115
204
4B
105
192
X=O
X
1
.3
YI
"t
4
21
Yz
I "_
io
1_:
18.r.
X= -1
Note: You can scroll back from the value entered for TblStart. As you
scroll, TblStart is updated automatically to the value shown on the top
line of the table. In the example above, TblStart=0 and ATbI=I
generates and displays values of X=0,...,
6; but you can press [] to
scroll back and display the table for X=-I,...,
5.
Displaying
Dependent
Variables
Other
If you have defined more than two dependent
variables,
the first two selected
Y= functions
are displayed
initially-.
Press [] or [] to display dependent
variables
defined
by
other selected
Y= functions.
The independent
wuiable
always remains
in the left colunm,
except
during
a trace
with Par graphing
nlode and G-T split-screen
nlode set.
X
"_
"2
"1
O
1
Z
Yz
Y_
"6
"6
"4
_
G
:L=I
":LB
"10
"LI
O
2
;L
Y_= -28
Tip:
that
and
For
the
7-6
Tables
To simultaneously
display on the table two dependent
variables
are not defined as consecutive
Y= functions,
go to the Y= editor
deselect the Y= functions between the two you want to display.
example, to simultaneously
display Y4 and Y7 on the table, go to
Y= editor and deselect Y5 and Y6.
8
Contents
Dnrs Wuction
s
Getting Started: Drawing a Tangent Line .................
Using the DRAW Menu ...................................
Clearh]g Dra,_lngs
.......................................
Drawing Line Segments
..................................
Drawing Horizontal
and Vertical Lines ...................
Drawing Tangent Lines ..................................
Drawing Functions
and hwerses
.........................
Shading Areas on a Graph
...............................
Drawing ('ircles ..........................................
Plaeing Text on a Graph .................................
Using Pen m Draw on a Graph ...........................
Drawing Points on a Graph ..............................
Drawing Pixels
..........................................
Storing Graph Pictures (Pies) ............................
Recalling Graph Pictures
(Pics) ..........................
Storing Graph Databases
(GDBs) ........................
Recalling Graph Databases (GDBs) ......................
4_ TEXAS INSTnUMENTS
STAT
PLOT
TBLSET
FORMAT
8-2
8-3
8-4
8-5
8-(;
8-8
8-9
8-10
8-11
8-12
8-1:3
8-14
8-16
8-17
8-18
8-19
8-20
T1=83
CALC
T._,B L E
DRAW Instructions
8-1
Getting
Getting
Started:
Started
Drawing
is a fast-paced
a Tangent
introduction.
Suppose you want to find the equation
function Y = sinX.
Read the chapter
of the tangent
Before you begin, select Radian and Func
mode from the mode screen, if necessaw.
1. Press [] to display- the Y= editor. Press
[g_ _
[] to store sin(X) in Y1.
2.
Line
Press _
7 to select 7:ZTrig, which
graphs the equation in the ZOOlll Trig
window.
Press [g_ [DRAW] 6 to select 6:Tangent(.
The tangent instruction is initiated.
line at X = _2
P1,'.,tl
Plot_
/-7--,.
"..>"
[4] 2[]
[] 2.
Pl(,t3
/-7_
/-7\
".,_i_1
?=0
/2"-..
-,_i_1
4=,r(2)/211
8-2
DRAW Instructions
-,,_i__
_
tl=sih((X)
_.--..
Press [ggg_. The tangent line is drawn; the
X value and the tangent-line equation are
displayed on the graph.
".L/
tl==in(:4)
1{=0
Press_
for the
".Y1Bsin(X)
%yz=
",Yx=
-.y_=
-,y_=
,,y_=
xY_'=
/-7_.
4.
for details.
_
[//
",2/
Using the DRAW Menu
DRAW Menu
To display
the
DRAW menu,
press
[DRAW]. The
[_
TI-S3's
interpretation
of these instructions
depends
on whether
you accessed
the menu fronl the honle screen
or the
program
editor or directly- from a graph.
DRAW POINTS STO
1 : C1 rDraw
Clears
2: Line(
3: Horizontal
4: Vertical
5: Tangent(
6: DrawF
elements.
a line segment
between
a horizontal
line.
a vertical
line.
8: Drawlnv
9: Circle(
O: Text(
Draws text on a graph
Activates
the free-form
A: Pen
The DRAW instructions
draw on top
before you use the DRAW instructions,
you want
2 points,
Draws a line segment
tangent to a function.
Draws a function.
Shades an area between
two functions.
Draws the inverse
of a function.
Draws a circle.
7: Shade(
Before Drawing
on a Graph
all drawn
Draws
Draws
Draws
to perform
one or more
•
Change
the mode
•
Change
•
Enter
or edit functions
•
Select
or deselect
•
Change
•
Turn
stat
•
Clear
existing
the fornlat
of graphs.
consider
settings
tool.
Therefore,
whether
of the following
on the mode
actions,
screen,
on the format
screen.
in the Y= editor,
functions
the window
plots
settings
screen.
drawing
variable
in the Y= editor.
values.
on or off.
drawings
with
ClrDraw
(page
8-4).
Note: If you draw on a graph and then pedorm any of the actions
listed above, the graph is reptotted without the drawings when you
display the graph again.
Drawing on a
Graph
You can use any DRAW menu instructions
except Drawlnv
to draw on Func, Par, Pol, and Seq graphs. Drawlnv is valid
only in Func graphing. The coordinates
for all DRAW
instructions
ate the display's x-coordinate
and y-coordinate
values.
You can
instructions
to identify
instructions
use most
DRAW menu
and DRAW POINTS
menu
to draw directly
on a graph, using the cursor
the coordinates.
You also can execute
these
from the home screen or from within a
progranl.
If a graph is not displayed
DRAW menu instruction,
the home
when
screen
you select a
is displayed.
DRAW Instructions
8-3
Clearing
Drawings
Clearing
Drawings When
a Graph Is
Displayed
All points,
Clearing
Drawings from
the Home Screen
or a Program
To clem' drawings on a graph fronl the holne screen or a
program, begin on a blank line on the home screen or in
the program editor. Select 1 :CIrDraw from the DRAW menu.
The instruction is copied to the cursor location. Press
instructkms
lines,
and shading
drawn
on a graph
with
DRAW
are temporm'y.
To elem' drawings
from the currently
displayed
graph,
select 1 :ClrDraw from the DRAW menu, The current
graph
is replotted
and displayed
with no drawn elements,
When CIrDraw is executed, it clears 'all drawings from the
current graph and displays the message Done. When you
display the graph again, all drawn points, lines, circles, and
shaded areas will be gone.
ClrOraw
Done
Note:Beforeyou cleardrawings,you can store them withStorePic
(page 8-17).
8-4
DRAW Instructions
Drawing
Line Segments
Drawing a Line
Segment Directly
on a Graph
To draw
is displayed,
follow
2. Place the cursor
on the point where you want
segment
to begin, and then press [_E_.
the line
these
a line segment
when
a graph
steps.
1. Select
2:Line( from
the DRAW menu.
3. Move the cursor
to the point where you want the line
segment
to end. The line is displayed
_s you move the
cursor.
Press [ggY_.
R=5,3191_Bgl/I=_.qSi_t_9
To continue
drawing
line segments,
To cancel
Line(, press @.
Drawing a Line
Segment from
the Home Screen
or a Program
repeat
steps
2 and 3.
Line( also draws a line segment
between
the coordinates
(X1 ,Y1) and (X2,Y2). The values nlay be entered
ZLS
expressions.
Line(X1,Y1,X2,Y2)
Line
(0,
To erase
Line(2,
0, 6, 9)11
a line segment,
3, 4, 6, 0)11
enter
Line(X1,Y1,X2,Y2,0)
/,
DRAW Instructions
8-5
Drawing
Horizontal
Drawing a Line
Directly on a
Graph
and Vertical
Lines
To draw
a horizontal
or vertical
displayed,
follow
steps.
1, Select
these
3:Horizontal
line is displayed
line when
or 4:Vertical
that
nloves
from
[_
To continue
To cancel
8-6
DRAW Instructions
to draw
drawing
is
the DRAW menu.
as you nlove
2. Place the cm'sor on the y-coordinate
lines) or x-coordinate
(for vertical
you want the drawn
line to pass.
3. Press
a graph
the cursor.
(for horizontal
lines) through
which
the line on the graph.
lines, repeat steps
2 and 3.
Horizontal or Vertical, press @,
A
Drawing a Line
from the Home
Screen or a
Program
Horizontal
(horizontal
line)
y can be an expression
but
draws
a horizontal
line at Y=y.
not a list.
Horizontal y
Vertical (vertical
line) draws
an expression
but not a list,
Vertical
line,
tile TI-83
to draw
more
separate
each
instruction
Ho_-izor,÷_al
t_al
line at X=x, x can be
_"
To instruct
vertical
a vertical
than
one horizontal
with
a colon
or
( : ).
7: Vet
4: Vertical
......................
DRAW Instructions
8-7
Drawing
Tangent
Drawing
a Tangent Line
Directly
on a Graph
Lines
To draw
these
a tangent
line when
a graph
is displayed,
follow
steps,
1, Select
5:Tangent(
fron]
the
DRAW nlenu.
2. Press [] and [] to move the cm_or to the function
for
which you want to draw the tangent
line. The cmTent
graph's
Y= function
is displayed
in the top-left corner, if
ExprOn is selected.
3. Press [] a_d [] or enter a number
to select the point on
the function
at which you want to draw the tangent line.
4. Press [E_.
In ffunc mode, the X value at which the
tangent
line wa_ drawn
is displayed
on the bottom
of
the screen,
along with the equation
of the tangent
line.
In all other nlodes,
the dy/dx value is displayed.
X=i,gt;_:
Tip: Change the fixed decimal setting on the mode screen
to see fewer digits displayed for X and the equation for Y.
Drawing
a Tangent Line
from the Home
Screen or
a Program
Tangent( (tangent
line) draws a line tangent
to expression
in terms of X, such as Y1 or X2, at point X=value.
X can be
an expression,
expression
is interpreted
as being in Func
nlode,
Tangent(expression,value)
Tangent
8-8
if you want
DRAW Instructions
('gi, 3)|
Drawing
Drawing a
Function
Functions
and Inverses
DrawF (draw
function)
draws
expression
at a function
in
terms of X on the current graph, When you select 6:DrawF
froln the DRAW menu, the TI-83 returns
to the home screen
or the program
editor,
DrawF is not interactive,
DrawF expression
[Ir.at0F
t?1-5
II
Note: You cannot
Drawing an
Inverse of a
Function
use a list in exp'_vssion
......
./_-.._ .(_.
to draw a family
.....
of curves.
Drawlnv (draw inverse) draws the inverse of expression by
plotting X values on the y-axis and Y values on the x-axis.
V_lmn you select 8:Drawlnv from the DRAW menu, the TI-83
returns to the home screen or the program editor. Drawlnv
is not interactive.
Drawlnv works in Func mode only.
Drawlnv expression
Drato Inv
'.?ill
. [email protected]__SI.
Note: You cannot use a list ine_pression to draw a family of curves.
DRAW Instructions
8-9
Shading
Areas
Shading a Graph
on a Graph
To shade an area on a graph, select 7:Shade( fronl the
DRAW menu. The instruction is pasted to the home screen
or to the program editor.
Shade( draws loweffune and uppeffunc
in terms of X on
the current graph and shades the area that is specifically
above lowerfane and below uppe_2fune. Only the areas
where lowerfane < uppeffunc
are shaded.
Xleft and Xright, if included, specify- left and right
boundaries for the shading. Xleft and Xright nmst be
numbers between Xmin and Xmax, which axe the defaults.
patte_
specifies
one of four shading
pattern= 1
pattern= 2
pattern= 3
pattern=4
patres
specifies
patterns.
vertical (default)
horizontal
negative--slope
45 °
positive--slope
45 °
one of eight shading
patres= 1
patres=2
patres=3
patres=4
patres=5
patres=6
patres=7
patres=8
shades
shades
shades
shades
shades
shades
shades
shades
resolutions.
every pixel (default)
evetF- second pixel
every third pixel
eve_- fourth pixel
every fifth pixel
eve_Ty-sixth pixel
evetsz seventh pixel
every eighth pixel
Shade(lowerfanc,uppe_:func[._left._right,patte_,patres])
Shade(X_-8X,
8-10
DRAW Instructions
X-2),
.......
____...;.:(
Drawing
Circles
Drawing a Circle
Directly on a
Graph
To draw
cursor,
1, Select
2, Place
draw.
a circle
follow
directly
these
9:Circle(
on a displayed
graph
using
the
steps,
fronl
the
DRAW menu.
the cursor
at the center
Press [NTEN.
of the circle
you want
3. Move the cursor
to a point on the circumference.
[ggTE_ to draw the circle on the graph.
to
Press
Note: This circle is displayed as circular, regardless of the window
variable values, because you drew it directly on the dispiay. When
you use the Circle( instruction from the home screen or a
program, the current window variables may distort the shape.
To continue
drawing
cancel Circle(, press
Drawing a Circle
from the Home
Screen or a
Program
circles,
@.
repeat
Circle( draws a circle with center
values can be expressions.
steps
2 and 3, To
(X,Y) and radius.
These
Circle(X,Y, radius)
Ciwcle(O,
0, 7)1
Tip: When you use Circle( on the home screen or from a program,
the current window values may distort the drawn circle. Use ZSquare
(Chapter 3) before drawing the circle to adjust the window variables
and make the circle circular.
DRAW Instructions
8-11
Placing
Text on a Graph
Placing Text
Directly on a
Graph
To place
follow
text
these
1, Select
2, Place
on a graph
when
the graph
is displayed,
steps,
0:Text(
from
the cursor
the
where
DRAW menu.
you want
the text
to begin.
3, Enter the characters.
Press @
or [_
[A-LOCK] to
enter lettet\s and 0. You nlay enter TI-83 functions,
variables,
and instructions.
The font is proportional,
so
the exact number
of characters
you can place on the
graph varies. As you type, the characters
are placed
on
top of the graph.
To cancel
Placing Text on a
Graph from the
Home Screen or
a Program
Text(,
press
@,
Text( places
on the current
graph the chara('ters
comprising
value, which can include TI-83 functions
and
instructions.
The top-left
corner of the first character
is at
pixel (row,column),
where row is an integer
between
0 and 57 and column
is an integer
between
0 and 94. Both
row and colnft_firt can be expressions.
Text(row,column,value,value..
,)
value can be text enclosed
in quotation
marks ( " ), or it
can be an expression.
The TI-83 will evaluate
an
expression
and display the result with up to 10 characters.
Text(42,50,"Vt=.
2XX-2X+6
Split Screen
8-12
..... ......
)|
On a Horiz split screen, the nlaxinlunl
On a G-T split screen,
the nlaxinlunl
and the nlaxinlunl
value for column
DRAW Instructions
I
?'I=._:X_-_:X+G
value for row is 25,
value for ro_t_)is 45,
is 46,
Using Pen to Draw on a Graph
Pen draws
directly
Pen from
the home
on a graph
screen
To draw
on a displayed
1. Select
A:Pen from
only, You cannot
graph,
follow
these
[_
to turn
steps.
the DRAW menu,
where you want
on the pen,
3. Move the cursor.
As you move the cursor,
the graph, shading
one pixel at a time,
4. Press
execute
or a progranL
2. Place the cursor
on the point
drawing.
Press [_
to turn
to begin
you
draw
on
off the pen,
For example,
Pen was used to create the arrow
the local minimunl
of the selected
function.
.....
Using Pen to
Draw on a Graph
pointing
to
E.,dL
I
To continue
drawing
on the graph, nlove the cursor
to a
new position
where you want to begin drawing
again, and
then repeat
steps 2, 3, and 4. To cancel Pen, press @.
DRAW Instructions
8-13
Drawing
Points on a Graph
DRAW POINTS
Menu
To display- the DRAW POINTS menu, press [_a] [DRAW] [_.
The TI-83's interpretation
of these instructions
depends
whether
you accessed
this nlenu froth the home screen
the program
editor or directly
froth a graph.
DRAW POINTS
ST0
i : Pt On(
2: Pt Off(
3:
4:
5:
6:
Drawing Points
Directly on a
Graph with
Pt-On(
Turns
on apoint.
Turns off a point.
Toggles a point on or off.
Turns on a pixeL
Turns off a pixel.
Toggles a pixel on or off,
Returns 1 if pixel on, 0 if pixel off,
Pt Change(
Pxl On(
Pxl Off(
Pxl Change(
7: pxl
Test(
To draw a point on a graph, follow these steps.
1, Select 1 :Pt-On( from the DRAW POINTS menu,
2. Move the cursor
the point.
to the position
where you want to draw
3. Press [ggY_ to draw the )oint.
o
R:Ll,_6e0mgl
y:LI.BM]?O.:I?
To continue drawing points, repeat
cancel Pt-On(, press @.
8-14
on
or
DRAW Instructions
steps 2 and 3. To
Erasing Points
with Pt-Off(
To erase
(turn
off) a drawn
point
on a graph,
follow
these
steps,
1. Select
2:Pt-Off(
(point
off) from
the DRAW POINTS
nlenu,
2. Move the cursor
3. Press
_
you want
points,
repeat
steps
2 and 3. To cancel
To change (toggle on or off) a point on a graph, %llow
these steps.
1. Select 3:Pt-Change( (point change)
POINTS menu.
2. Move the cursor
3. Press I_
from the DRAW
to the point you want to change.
to change the point's
To continue changing points, t_peat
cancel Pt-Change(, press @.
Drawing Points
from the Home
Screen or a
Program
to erase.
to ertkse the point.
To continue
ertLsing
Pt-Off(, press @.
Changing Points
with Pt-Change(
to the point
on/off status.
steps 2 and 3. To
Pt-On( (point on) turns on the point at (X=x,Y=y).
Pt-Off(
tutlls the point off. Pt-Change( toggles the point on or off.
mark is optional;
it determines
the point's
appearance;
specify 1, 2, or 3, where:
1 = • (dot;
default)
Pt-On(x,y[,mark])
Pt-Off(x,y[ ,mark
Pt-Change(x,y)
2 = [] (box)
3 = + (cross)
])
Pt.-0n ( 2, 5, 2> :Pt,-
..
Note: If you specified mark to turn on a point with Pt-On(, you must
specify mark when you turn off the point with Pt-Off(. Pt-Change(
does not have the mark option.
DRAW Instructions
8-15
Drawing
Pixels
TI-83 Pixels
A pixel is a square dot on the TI-83 display. The Pxl- (pixel)
instructions
let you turn on, turn off, or reverse a pixel
(dot) on the graph using the cursor. When you select a
pixel instruction from the DRAW POINTS menu, the TI-83
retm'ns to the home screen or the program editor. The
_ixel instl_ctions
are not interactive.
p;
Turning On and
Off Pixels with
Pxl-On( and
Pxl-Off(
jq
PxI-On( (pixel on) turns
where row is an integer
integer
between
PxI-Off( turns
and off.
on the pixel at (row,column),
between
0 and 62 and column
is an
0 and 94.
the pixel
off. Pxl-Change(
toggles
the pixel
on
Pxl-On(row,column)
Pxl-Off(row,column)
Pxl-Change(_'ow,column)
Using pxI-Test(
pxI-Test( (pixel test) returns
1 if the pixel at (row,column)
is turned
on or 0 if the pixel is tunled
off on the curl_nt
graph, row nmst be an integer
between
0 and 62. column
nmst be an integer
between
0 and 94.
pxI-Test(row,colu'rnn)
Split Screen
On a Horiz split screen, the maxinmm
value for row
for PxI-On(, PxI-Off(, Pxl-Change(, and pxI-Test(.
is 30
On a G-T split screen,
the nlaxinlunl
value for row is 50 and
tile nlaxinlunl
value for column
is 46 for PxI-On(, PxI-Off(,
Pxl-Change(,
8-16
DRAW Instructions
and pxI-Test(.
Storing
Graph Pictures
DRAW STO Menu
(Pics)
To display the DRAW STO menu, press [g_ [DRAW] [_,
When you select an instruction fronl the DRAW STO menu,
the TI-83 returns to the home screen or the program editor.
The picture and graph database instructions are not
interactive.
DRAW POINTS STO
1:StorePic
2:RecallPic
3:StoreGDB
4:RecalIGDB
Storing a Graph
Picture
Stores
Recalls
Stores
Recalls
the current picture.
a saved picture.
the current graph datal)ase.
a saved graph database.
You can store up to 10 graph pictures, each of which is an
image of the cmTent graph display-, in picture wuialfles
Pie1 through Picg, or PicO.Later, you can superimpose
the
stored picture onto a displayed graph from the home
screen or a program.
A picture includes drawn elements, plotted functions, axes,
and tick marks. The picture does not include axes labels,
lower and upper bound indicators, prompts, or cursor
coordinates.
Any parts of the display- hidden by these items
m'e stored with the picture.
To store a graph picture,
follow these steps.
1. Select 1:StorePic fronl the DRAW STO menu. StorePic is
DL_ted to the current cursor location.
2. Enter the number (from 1 to 9, or 0) of the picture
variable to which you want to store the picture. For
example, if you enter 3, the TI-83 will store the picture
to Pic3.
5tor.ePio
3
Note: You alsocan select a variable from the PICTURE
secondarymenu (_
4). The variable is pasted next to
8torePic.
3. Press [ggTE_ to display- the current
picture.
graph and store the
DRAW Instructions
8-17
Recalling
Graph Pictures
Recalling a
Graph Picture
To recall
a graph
(Pics)
picture,
1. Select 2:RecallPic
is pasted
ffonl
to the current
follow
these steps,
the DRAW STO menu,
cursor
RecallPic
location,
Enter the number
(from 1 to 9, or 0) of the picture
varial)le
from which you want to recall a picture.
For
example,
if you enter 3, the TI-83 will recall the picture
stored to Pic3.
Reoal
IPio
3
Note: You also can select a variable from the PICTURE
secondary menu (_
4). The variable is pasted next to
RecallPic.
3, Press I_
to display- the current
picture
superimposed
on it,
graph
with
the
Note: Pictures are drawings. You cannot trace a curve that is part of a
picture.
Deleting a Graph
Picture
8-18
To delete graph pictures
from
MEMORY DELETE FROM menu
DRAW Instructions
memo[3z,
(Chapter
use the
18).
Storing
Graph Databases
What Is a Graph
Database.'?
A graph
database
(GDB) contains
the set of elements
that
defines a pm'ticular
graph. You can recreate
the graph froln
these elements.
You can store up to 10 GDBs in variables
GDB1 through
GDB9, or GDB0 and recall them to recreate
graphs.
A GDB stores
•
•
•
•
•
five elements
of a graph.
Graphing
mode
Window variables
Format
settings
All functions
in the Y= editor and the selection
each
Graph style for each Y= function
GDBs do not
Storing a Graph
Database
(GDBs)
To store
a graph
is pasted
StoreGDB
from
to the current
the number
to which
example,
GDB7,
drawn
database,
3:StoreGDB
1, Select
2. Enter
contain
(from
items
or stat
follow
the
these
plot
of
definitions.
steps.
DRAW STO menu.
cursor
status
StoreGDB
location,
1 to 9, or 0) of the GDB variable
you want to store the graph database.
For
if you enter 7, the TI-83 will store the GDB to
7
Note: You also can select a variable from the GDB secondary
menu ([_
3). The variable is pasted next to $toreGDB.
3, Press 1_
specified
to store the current
GDB variable.
database
to the
DRAW Instructions
8-19
Recalling
Graph Databases
Recalling a
Graph Database
(GDBs)
CAUTION: When you recall a GDB, it replaces all existing
Y= functions. Consider storing the cutTent Y= functions to
another database before recalling a stored GDB.
To recall a graph database,
follow these steps.
1. Select 4:RecalIGDB from the DRAW STO menu.
RecalIGDB is pasted to the current cursor location.
2. Enter the number (from 1 to 9, or 0) of the GDB variable
from which you want to recall a GDB. For example, if
you enter 7, the TI-83 will recall the GDB stored to
GDB7,
Reoal IGDB
7
Note: You alsocan select a variable from the GDB secondary
menu (_
3). The variable is pastednext to RecalIGDB.
3, Press [_
to replace the current GDB with the
recalled GDB. The new graph is not plotted. The TI-83
changes the graphing mode automatically,
if necessat T.
Deleting a Graph
Database
8-20
To delete a GDB fronl nlemo_T, use the MEMORY DELETE
FROM menu (Chapter 18).
DRAW Instructions
Screen
Split
Contents
Getting Started: Exploring
tile Unit Circle ................
Using Split Screen
.......................................
Horiz (Horizontal)
Split Screen
..........................
G-T (Graph-Table)
Split Screen ..........................
TI-83 Pixels in Horiz and G-T Mode ......................
'_
TEXAS
T1=83
INSTRUMENTS
','t==in_)J
oX
_'.', l
.._,75 1.2,_3
_,
X=.BO:_h7:_O h
?=.7190761B
9-2
9-3
9-4
9-5
9-6
I oY 1
1.07
1.1177_:
2.337
.97:_9
1.605
.ggg4
J
STATPLOT
TBLSET
FORMAT
CALC
TABLE
Split
Screen
9-1
Getting
Getting
Started:
Started
Exploring
is a fast-paced
the Unit Circle
introduction.
Read the chapter
for details.
Use G-T (graph-table)
split-screen mode to explore the unit circle and its
relationship
to the numeric values for tile connnonly used trigonometric
angles
of 0°, 30 °, 45 °, 60 °, 90 °, and so on.
Press [g6m to display the mode screen.
Press [] [] [] [g_
to select Degree
mode. Press [] [] [g_
to select Par
(parametric)
graphing mode.
Press [] [] [] [] [] [] [g_
to select G-T
(graph-table) split-screen mode.
Press [_ [FORMAT]to display" the format
screen. Press [] [] [] [] [] [] [g_
to
select ExprOff.
Press []
graphing
[ggg_] to
[]
to display" the Y= editor for Par
mode. Press [g6_ _
[]
store cos(T) to XIT, Press [gF_
_
to store sin(T) to YIT.
Press _
editor. Enter
variables.
Train=0
Tmax=360
Tstep=l 5
to display the window
these values for the window
Xmin=-2.3
Xmax=2.3
Xscl=l
Ymin=-2.5
Ymax=2.fi
Yscl=l
Press _.
On the left, the unit circle is
graphed parametrically
in Degree mode
and the trace cursor is activated. When
T=0 (from the graph trace coordinates),
you can see from the table on the right
that the value of XlT (cos(T)) is 1 and YIT
(sin(T)) is 0. Press [] to move the cursor to
the next 15° angle increment. As you trace
around the circle in steps of 15° , an
approximation
of the standard value for
each angle is highlighted in the table.
9-2
Split Screen
li X1,
i
V1T
0
.g
.Bfl6
.zsne ._ss_
T=_O
g:.BSfi02B_
0
1
Using Split Screen
Setting a SplitScreen Mode
To set a split-screen lnode, press [MO0_,and then nlove the
cursor to tile bottol:l line of the l:lode screen.
•
•
Select Horiz (horizontal) to display- the graph screen and
another screen split horizontally.
Select G-T (graph-table)
to display the graph screen and
table screen split vertically.
Sci
Eng
Sci
Eng
Dot
The split screen is activated when you press any key that
applies to either half of the split screen.
Sonle screens m'e never displayed +is split screens. For
example, if you press _
in Roriz or G-T inode, the inode
screen is displayed as a full screen. If you then press a key
that displays either half of a split screen, such as _,
the split screen returns.
VC]mnyou
6-7 mode,
which that
the cursor
displayed.
the half in
press a key or key combination
in either Horiz or
the cursor is placed in the half of the display- for
key applies. For example, if you press _,
is placed in the half in which the graph is
If you press [g_ [TABLE],the cursor is placed in
which the table is displayed.
The TI-83 will remain in split-screen
change back to Full screen mode.
lnode until you
Split
Screen
9-3
Horiz (Horizontal)
Horiz Mode
Split Screen
In Horiz (horizontal)
split-screen lnode, a horizontal
splits tile screen into tc ) and bottom halves.
line
\ViBsin(X z)
,.YzBcos(XZ )
\Y._=
The top half displays the graph.
The bottom
•
•
•
•
•
Moving from Half
to Half in Horiz
Mode
half displays
Home screen (four lines)
Y= editor (four lines)
Stat list editor (two rows)
Window editor (three settings)
Table editor (two rows)
To use the top half of tile split screen:
•
•
Press [g_
or _.
Select a ZOOM or CALC operation.
To use tile bottonl
Full Screens in
Horiz Mode
any of these editors.
half of tile split screen:
•
Press any key or key combination
home screen.
•
•
•
•
Press
Press
Press
Press
that displays the
[] (Y= editor).
[gT_ [g_
(stat list editor).
_
(window editor).
[2_ [TABLE](table editor).
All other screens are displayed
split-screen mode.
as full screens
in Horiz
To return to the Horiz split screen from a full screen when
in Horiz mode, press any- key or key combination
that
displays the graph, home screen, Y= editor, stat list editor,
window editor, or table editor.
9-4
Split
Screen
G-T (Graph-Table)
G-T Mode
Split Screen
In G-T (graph-table) split-screen
mode, a vertical
tile screen into left and right halves.
X
line splits
Y1
Io
,2:
X=Bgq.
The left half displays the graph.
The right half displays the table.
Moving from Half
to Half in G-T
Mode
To use the left half of the split screen:
•
•
Press [g_
or _.
Select a ZOOM or CALC operation.
To use tile right half of the split screen,
Using _
G-T Mode
in
press [:_
[TABLE].
As you lnove tile trace cursor along a graph in the split
screen's left half in G-T mode, the table on the right half
autolnatically scrolls to match tile current cursor values.
x_
g=.B0ZtlTZ0h
Y=,7190761B
X
Vi
1.07 .B77_
1._7_7 ,97:'9
t,l_0g .999h
Note: When you trace in Par graphing mode, both components
of an
equation (XnT and YnT) are displayed in the two columns of the table.
As you trace, the current value of the independent
variable T is
displayed on the graph.
Full Screens in
G-T Mode
All screens other than the graph and the table are
displayed as full screens in G-T split-screen mode.
To return to the G-T split screen from a full screen when in
G-T mode, press any key or key combination
that displays
the graph or the table.
Split
Screen
9-5
TI-83 Pixels
in Horiz and G-T Modes
"*.
Horiz and G-T
Modes
(o,0.',
l
.(°._.h.)?l
€,30,0)
1
o0,9_)_,
_ X
lg
30
_g
60
TI-Sa
Pixels
in
"i
I=o
Note: Each set of numbers in parentheses above represents the row
and column of a corner pixeI, which is turned on.
DRAW POINTS
Menu Pixel
Instructions
For PxI-On(, PxI-Off(, Pxl-Change(,
•
In Horiz mode,
•
In G-T mode,
row
row
nmst
nmst
and pxI-Test(:
be _<30; column
nmst
be _<50; column
nmst
be _<94.
be _<46.
Pxl-On(row,column)
DRAW Menu
Text( Instruction
For the
Text( instruction:
•
In Horiz mode,
•
In G-T mode,
row
row
nmst
nmst
be _<25; column
must
be _<45; column
nmst
be _<94.
be _<46.
Text(row,column,"text")
PRGM I/O Menu
Output(
Instruction
For the
Output(
•
In Horiz mode,
•
In G-T mode,
instruction:
row
row
Output(row,column,
Setting a
Split-Screen
Mode from the
Home Screen or
a Program
nmst
nmst
nmst
nmst
be _<16.
be _<16.
"text")
To set Horiz or G-T from
1. Press [M0_] while
program
editor.
be _<4; column
be _<8; column
a program,
the cursor
follow
is on a blank
these
steps.
line in the
2, Select Horiz or G-T,
The instruction
is pasted to the cursor
location.
The mode
is set when the instruction
is eneountered
during program
execution.
It remains
in effect after execution.
Note: You also can paste Horiz or G-T to the home screen or
program editor from the CATALOG (Chapter 15).
9-6
Split
Screen
10
Contents
Matrices
Getting Started: Systems of Linear Equations
............
Defining a Matrix ........................................
Viewing and Editing Matrix Elements
....................
Using Matrices with Expressions
........................
Displaying and Copying Matrices
........................
Using Math Functions
with Matrices
.....................
Using the MATRX MATH Operations
.....................
'_
TEXAS
T1=83
iNSTRUMENTS
MRTRIX[R]
10-2
10-2
10-4
10-7
10-8
10-9
10-12
8 x4
r_
-_.:l.h_: 1:_
E "1
ro
r 0
E 1.B
r 0
[0
_:.1h11_
0
0
0
.8571h
0
0
0
BB
0
0
2
i, i=3.141592653
J
STATPLOT
TBLSET
FORMAT
CALC
TABLE
Matrices
10-1
Getting
Getting
Started:
Started
Systems
is a fast-paced
of Linear Equations
introduction.
Read the chapter
for details.
Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83, you
can solve a system of linear equations by entering the coefficients as elements
in a matrix, and then using rref( to obtain the reduced row-echelon
form.
1. Press [_.
Press [] [] to display- the
MATRX EDIT menu. Press 1 to select 1: [A],
2.
3.
Press 2 [_
4 [_
to define a 2x4
matrix. The rectangular
cursor indicates
the current element. Ellipses (...) indicate
additional eolunms beyond the screen.
Press 1 [_
to enter the first element.
The rectangular
cursor nloves to the
second colunm of the first row.
MATRIX[R]
[0
2 x4
0
1_1=0
MATRIX[R]
[0
0
2 x4
0
I_Z=0
4.
Press 2 [g_
3 [g_
3 [g_
to complete
the first mw for X + 2Y + 3Z = 3.
5.
Press 2 [_
3 [_
4 [_
3 [_
to
enter the second row for 2X + 3Y + 4Z = 3,
Press [_
[QUIT] to return to the home
screen.
If necessary,
press @
to clear
the home screen.
Press _
[] to
IMRTRIX[A]
2 x4
rre?(|
display the MATRX MATH menu. Press [] to
wrap to the end of the menu. Select B:rref(
to copy rref( to the home screen.
Press [_
1 to select 1: [A] from the
MATRX NAMES menu. Press [] FENTERI.
The
reduced row-echelon form of the matrix is
displayed and stored in Ans.
iX- 1Z=-3
1Y+2Z=3
10-2
Matrices
so
so
X=-3+Z
Y=3-2Z
rref'([Al )
-31
[[1 18 213
]l
Defining
a Matrix
What Is a Matrix?
A matrix
is a two-dimensional
alTay.
You can
display',
define, or edit a matrix
in the matrix editor. Tile TI-83 h_s
10 matrix variables,
[A] through
[J]. You can define a
matrix
directly
in an expression.
A matrix,
depending
on
available
nlelnolT,
may have up to 99 rows or colunms.
You can store only real numbers
in TI-83 matrices.
Selecting a
Matrix
Before you can define or display
a matrix in the editor, you
first nmst select the matrix name. To do so, follow these
steps.
[] to display
the MATRX EDIT menu. The
of any previously
defined
lnatrices
are
1. Press _
dimensions
displayed.
MATH
[el
[D]
[El
[F]
[G]
2, Select
screen
the matrix you want
is displayed.
MATRIX[B]
ro
Accepting or
Changing Matrix
Dimensions
to define.
The MATRX EDIT
I xl
I
The dimensions
of the matrix
displayed
on the top line. The
are 1 xl, You nmst accept
or
time you edit a matrix,
When
(row x column)
are
dimensions
of a new matrix
change the dimensions
each
you select a matrix to define,
the cursor
dimension.
highlighLs
the row
the row
•
To accept
•
To change
the row dimension,
(up to 99), and then press [_.
dimension,
press
enter
[_.
the number
of rows
The cursor moves to the eolunm
dimension,
which you
must accept
or change the same way you accepted
or
changed
the row dimension.
When you press [_,
the
rectangular
cursor
moves to the first matrix
element.
Matrices
10-3
Viewing
and Editing
Displaying Matrix
Elements
Matrix Elements
After you have set the dimensions of the matrix, you can
view the matrix and enter values for the matrix elements.
In a new matrix, 'all values are zero.
Select the matrix from the MATRX EDIT menu and enter or
accept the dimensions. The center portion of the matrix
editor displays up to seven rows and three eolunms of a
matrix, showing the values of the elements in abbreviated
form if necessary. The full vMue of the current element,
which is indicated by the t_ctangular
cursor, is displayed
on the bottonl line.
"t
_:.tht6
MRTRIX[R]
0
8 0 x4
i
i,i=3. 141592653
This is an 8 x 4 matrix. Ellipses
in the left or right colunm
indicate
additional
columns,
i' or _ in the right column
indicate
additional
rows.
Deleting
10-4
a Matrix
Matrices
To delete matrices fronl nlenlory,
FROM seconding- menu ((;hapter
use the MEMORY DELETE
18).
Viewing a Matrix
The
matrix
editor
has two contexts,
viewing
and editing,
In
viewing context,
you can use the cursor
keys to move
quickly from one matrix element
to the next. The full value
of the highlighted
element
is displayed
on the bottom
line,
Select the inatrix fl'oin the MATRX EDIT menu, and then
enter or accept the dimensions.
":1,
}.:DI:I.I_
0
MRTRIX[R]
8 x4
2
I,I=3. 141592653
Viewing-Context
Keys
1
Key
Function
[] or []
Moves the rectangular
current row.
[] or []
Moves the rectangular cursor within the
current coluinn; on the top row, [] moves
the cursor to the colunm dimension; on the
coluinn dimension, [] moves the cursor to
the row dimension.
[gNT_
Switches to editing context; activates
edit cursor on the bottom line.
@
Switches to editing context;
value on the bottoin line.
Any entry
character
Switches to editing context; clears the
value on the bottoln line; copies the
character to the bottom line.
[_
[ggn
[INS]
cursor
within the
the
clears the
Nothing
Nothing
Matrices
10-5
Editing a Matrix
Element
In editing context, an edit cursor is active on the bottom
line. To edit a lnatrix element value, follow these steps.
1. Select the matrix from the MATRX EDiT menu, and then
enter or accept the dimensions.
2. Press [], [], [], and [] to nlove the cursor
element you want to change.
3. Switch to editing context
an entw key-.
by pressing
to the lnatrix
[ggT_, @,
or
4. Change the value of the tnatrix element using the
editing-context
keys described below. You nlay enter an
expression, which is evaluated when you leave editing
context.
Note: You can press @
_
to restore the value at the
rectangular cursor if you make a mistake.
5. Press
IgOr,
[],
MRTRIX[RI
or []
to Inove
to another
element.
8 ×4
r :Ll_ntG ":kl_
13
[ 0
[ :t.B
0
0
BII
0
[ 0
.BgT:th
0
[0
0
3.1_I_
").1ill
MRTRIX[R]
1_
8 x4
i
3, i=2Xz+3|
Editing-Context
Keys
Key
Function
[] or []
Moves the edit cursor within the value,
[] or []
Stores the value displayed on the bottom
line to the nlatrix element; switches to
xqewing context and nloves the rectangular
cut.or within the colunm.
[g_Tgm
Stores the value displayed on the bottom
line to the nlatrix element; switches to
viewing context and moves the rectangular
cm'sor to the next row element.
@
Clears the value on the bottom
Any entrycharacter
Copies the character to the location
edit cursor on the bottom line.
[_
[INS]
[DE[]
10-6
Matrices
Activates
line.
of the
the insert cursor.
Deletes the character
on the bottonl line.
under the edit cursor
Using Matrices
Using a Matrix in
an Expression
with Expressions
To use a matrix in an expression,
following.
•
•
•
Entering a Matrix
in an Expression
you can do any of the
Copy the name from the MATRX NAMES menu.
Recall the contents of the lnatrix into the expression
with [_ [RCL] (Chapter 1).
Enter the matrix directly (see below).
You can enter, edit, and store a matrix in the nlatlJx
You also can enter a nlatrix directly
in an expression.
in an expression,
follow
these
editor.
To enter
a nlatrix
steps.
1. Press
[2_] [ [ ] to indicate
the beginning
of the nlatrix.
2. Press
[2_] [ [ ] to indicate
the beginning
of a row.
3. Enter a value, which can be an expression,
for each
element
in the row. Sepm'ate
the values with conlnlas.
4. Press
5. Repeat
6. Press
[2_] [] ] to indicate
steps
2 through
the end of a row.
4 to enter
[2_] [] ] to indicate
all of the rows.
the end of the nlatrix.
Note: The closing ]] are not necessary at the end of an expression
or preceding -'>.
The resulting
matrix
is displayed
in the form:
[[elementl,l,._,elementl,_l,...,[element.,,_,l,...,element,,_,_]]
Any expressions
executed.
are evaluated
when
the
enttsz is
2.[11 [1,2,31[[_
418"1014'5'161211
Note: The commas that you must enter to separate elements are
not displayed on output.
Matrices
10-7
Displaying
and Copying
Displaying a
Matrix
Matrices
To display- the contents of a matrix on the home screen,
select the nmtrix from tile MATRX NAMES menu, and then
press [_.
lEA, El; 711
Ellipses in the left or fight eolunm indicate additional
colunms. I' or 4 in the right colunm indicate additional
rows. Press [_, [], [], and [] to scroll the lnatrix.
46.0000
I
...116. 0000
...49. 0000
--62. (_iiiI
-96.8...I
%88oo65.00...I
i::47'.
0000
...3, 0000
Copying One
Matrix to Another
-69.04,
136,0...
To copy a matrix,
1. Press [_
follow these steps.
to display the MATRX NAMES menu.
2. Select the name of the lnatrix you want to copy.
3. Press _.
4. Press _
again and select the name of the new
nmtrix to which you want to copy the existing matrix.
5. Press [_
Accessing a
Matrix Element
to copy the lnatrix to the new lnatrix
On the home screen or fronl within a program, you can
store a vMue to, or recM1 a value from, a matrix element.
The element nmst be within the currently defined matrix
dimensions. Select matrix from the MATRX NAMES menu.
[matrixl(row,column)
0-:* [BI (2, 3)-" [BI
[[7
8 91
[B1(2,3)[3
10-8
Matrices
nalne.
2 0110
Using Math Functions
with Matrices
Using Math
Functions with
Matrices
You can use many
of the math
functions
on the TI-83
+ (Add), (Subtract), *
(Multiply)
To add ([_) or subtract ([_) matrices, the dimensions must
be the same, The answer is a matrix in which the elements
are the sum or difference of the individual corresponding
elements.
keybom'd,
tile MATH menu, tile MATH HUM
MATH TEST menu with matrices.
However,
nmst be appropriate.
Each of the functions
new matrix; the original matrL, c remains
the
matrixA
matrixA
+matrixB
- mat)_ixB
To nmltiply
dimension
matrixB.
matrixA
menu, and tile
the dimensions
below creates
a
same.
([_) two matrices
together,
the colunm
of matrixA
nlust match the row dimension
of
*mat_qxB
Multiplying
a matrix
by a value or a value by a matrix
returns
a matrix
in which each element
of matrix
is
nmltiplied
by value,
matrix*value
value*matrix
- (Negation)
Negating
of evetN
a matrix
(D) returns
a matrix
element
is changed
(reversed),
in which
the sign
-matrix
-ira
[RI
-41
[[212; 41-211]
Matrices
10-9
abs( (absolute value, MATH NUM menu) returns a matrix
containing the absolute value of each element of matrix.
abs(
abs(mat_qx)
[°]
14,69'
abs([Cl_[2512369]14]
round(
round( (MATH NUM menu) returns a matrix. It rounds every
element in matrix to #decimals (<_9), If #decimals is
olnitted, the elements are rounded to 10 digits,
rou nd(mat)qx[ ,#decimals
MAT IX[m
2 ×2 1
[ 3,662
-I
(Inverse)
I,'15_
])
[[1.26
2.331
Pound([A],2)
[3.66 4.121
[ Jse the -1 function
([_
) to invert a matrix
valid), matrix
nmst be square.
The determinant
equal
]
("-1 is not
cannot
zero.
matrix-1
MRTRIX[R]
El
E_
_z
2 x2
]
l[m-,
[[-2
[1.5
1-.51 ] ]
To raise a lnatrix to a power, matrix lnust be square. You
can use 2 (_), 3 (MATH menu), or ^power (D) for integer
power between 0 and 2S&
Powers
matrix
matrix
2
3
matrix^power
[[37 54 ]
[81 1181
MRTRIX[R]_
_
10-10
Matrices
2 x2
]
[R]_,5
[R]_ [[1069
[2337
15581 i
34061
Relational
To compare
Operations
and _ (TEST menu), they must have the sanle dimensions,
=
and _ compare
mat_ixA
and mat_ixB
on an element-byelement
basis. The other relational
operations
are not valid
with matrices.
two
matrices
matri._'A=matrixB
returns
t_tums
0 if any comparison
using
the
relational
operations
1 if eveFy" comparison
is false.
=
is true;
matrixA_matrixB
t_tums 1 if at least one comparison
false; it returns 0 if no comparison is false,
it
is
[RI#[B]
[R]=[B]
iPart(, fPart(, int(
iPart( (integer part), fPart( (fractional
part), and
(greatest integer) are on the MATH NUM menu,
iPart( returns
a matrix
element
of matrix,
containing
the integer
int(
part
of each
fPart( returns a matrix containing the fractional part of
each element of matrix.
int( returns a matrix containing the greatest integer of each
element of matrix,
iPart(matrix)
fPart(matrix)
int(matrix)
100.5
47. 151
[[1
3 1
[100 471
¢PaPt([D])
iPaPt([D1)
[[.25
.3331 i
[.5
.15 ]
Matrices
10-11
Using the MATRX
MATRX MATH
Menu
MATH Operations
To display
NAMES
i:
the
MATH
det(
MATRX MATH menu,
EDIT
Calculates
2: T
[_,
_
the determinant.
Transposes
the matrix,
Returns
the matrix dimensions.
Fills all elements
with a constant.
3: dim(
4: Fill(
5:identity(
Returns
Returns
6: randM(
7:augment(
the identity
matrix.
a random
matrix.
Appends
two matrices.
Stores a matrix
to a list.
Stores a list to a matrix.
Returns
the eunmlative
sums of a matrix.
Returns
the row-echelon
form of a matrix.
Returns
the reduced
row-echelon
form.
8: Matr*list(
9: List*matr(
O: cumSum(
A: ref(
B: rref(
Swaps two rows of a matrix.
Adds two rows; stores
in the second
Multiplies
the row by a number.
Multiplies
the row, adds to the second
C: rowSwap(
D: row+(
E: *row(
F: *row+(
det(
press
det((determinant)
of a squm'e matrix.
returns
the determinant
row.
row.
(a real number)
det(matrix)
T
(Transpose)
T (transpose)
returns
a matrix
in which each element
colunm)
is swapped
with the corresponding
element
(colunm,
row) of matrix.
matrix
T
[R]
[R]T
11
[[1[32 2 311
Accessing Matrix
Dimensions with
dim(
dim((dimension)
({rows columns}
[3 11
returns
a list containing
) of mat_qz.
the dimensions
dim(matrix)
Note: dim(mat'rix)->Ln:Ln(1)
returns the number of rows.
dim(mat'rix)->Ln:Ln(2)
returns the number of columns.
dim(
3,111
10-12
Matrices
(row,
[_2,7,11[
-8,
{2 3}
dim([l>+Li:L1
3,111
Creating a Matrix
with dim(
Use dim( with _
dimensions
rows
to create
x columns
a new matrixname
of
with 0 _Lseach element.
{rows,columns}_dim(mat_xname)
{2,2}+di_([E])
[E]
Redimensioning a
Matrix with dim(
Fill(
[
I
I
[0 01
[0
011
Use dim( with _
to redimension
an existing
matrixname
to dimensions
rows x columns,
The elements
in the old matrixname
that m_ within the new dimensions
are not changed.
Matrix elements
deleted.
Additional
created
elements
are zeros.
that m'e outside
the new dimensions
are
{rows,columns}->
dim(matrixname)
Fill(storesv_uetoeve_
elementin
mat_xname.
Fill(v_ue,mat_xname)
FilI(5,[E])
[El
identity(
Done
[[5[5 5]
51]
identity( returns
the identity
dimension
colunms.
matrix
of dimension
rows
x
identity(dimension)
randM(
randM( (create
random
matrix)
returns
a rows x columns
random
matrix
of integers
_>-9 and _<9, The seed value
stored to the rand function
controls
the values (Chapter
2),
randM(rows,eolumns)
I÷r-and: PahdM(2,2
I
[ [0 -71
[88
1]
Matrices
10-13
augment( appends matrixA to matrixB
as new colunms.
matrixA and mahqxB both nlust have tile sanle number of
augment(
[_)WS.
augment(mat) qxA,matrixB)
[ [5,61
[7,811+[BI
_a,.,gr,,ent([Rl,[B[
[1,21 [[1[3,41256]]+JR] ]
[3
Mats,list(
7 811
4
MatrHist( (lnatrix stored to list) fills each listname with
elements from each colunm in mahqx. MatrHist( ignores
extra listname arguments. Likewise, MatrHist( ignores
extra matrix colunms.
MatrHist(matrix,listnomeA,._,listname
MatP_lis[4
5 611
"*
[[R]
[[1
It( 2 31
,Li,LI)
[Rl,LiDone
n)
Lz
i_
{I ii
{3{25}
MatrHist( also fills alistname with elements fronl a specified
column# in matrix. To fill a list vdth a specific colunm from
matrix, you lnust enter column# _ffter matrix.
Mat_list(matrix,column#,listnome)
[R]
It1
2 31 I
5 6111 "*
[a
Lt
{3 6}
Matr_list(
Lt )
Listymatr(
JR]Done
,3,
List)matr( (lists stored to matrL, c) fills matrixna,me colunm by
colunm with the elements fronl each list. If dimensions (ff MI
lists are not equal, Cist_matr(fills each extra matrixna,r_w
row with O.Conlplex lists are not valid.
List_matr(listA,._,list
n,mah_xname)
List.*matP(
10-14
Matrices
{1'2'3}+L_I
2 3}
{4'5'6]'+L_4
5
_
IX,
LB,[CI)
...
[C]
L_",
I
O°nel'
[[1
_
_ll]l
cumSum(
cumSum(
returns
cumulative
sums
of the elements
in
mat_'ix,
starting
with tlle first element.
Each element
cumulative
sum of the colunm
from top to bottom.
is the
cumSum(mat,_ix)
[0]
[[1151361412]]
°ur_Su'_([Dl_[9[46212]]]]
Row Operations
MATRX MATH menu items A th['ough
F m'e row operations.
You can use a row operation
in an expression,
Row
operations
do not change matrix
in nlenloi_yL You can
enter all row numbers
and values as expressions.
You can
select the matrix fronl the MATRX NAMES menu,
ref(, rref(
ref( 0"ow-echelon
fornl) returns
the row-echelon
if)rill of a
real mat'_i:c. The number
of columns
must be greater
than
or equal to the number
of _'ows.
ref(mat,_ix)
rref( (reduced
echelon form
be greater
row-echelon
ff)rm) ret, umls the reduced
rowof a _al matrix', The number
of colunms
must
than
or equal
to the number
of rows,
rref(mat,_ix)
[7
[B]
[ [4
8 9]
5 6] ]
re?([B])
[[1
1.142857143_3
[0 1
...
rre?([B])
[[1
0 -1]
[0 1 2 ]]
Matrices
10-15
rowSwap(
rowSwap(
returns
a matrix,
It swaps
rowA
and rowB
of
matrix,
rowSwap(matrix,
rowA,rowB)
PowSwaP ( [F]
[F]
row+(
[2
[[2[6
,2,4>[
I
5 1 O]
_ 46
3
8 51
791]
row+( (row addition) returns a lnatnx.
rowB of matrix and stores the results
It adds rowA and
in rowB.
row+(mat_x,rowA,rowB)
[[2,5,7118,9,411
+[O]
[[2[8 5
9 71
41
* row(
row+{[D],l,2)[1012
514711111
*row( (row nmltiplieation)
returns a matrix. It nmltiplies
row of matrix by value and stores the results in row.
* row(value,matrix,row)
*row+( (row nmltiplication
and addition) returns a nlatdx,
It nmltiplies rowA of matrix by value, adds it to rowB, and
stores the results in rowB.
* row+(
*row+(value,matrix,rowA,rowB)
*Pow+(3,
[[1
10-16
Matrices
[E], 1,2)
21 3511
I
11
Contents
Lists
Getting Started: Generating
a Sequence
..................
Naming Lists .............................................
Storing and Displaying
Lists .............................
Entering List Names .....................................
Attaching
Fornmlas
to List Names .......................
Using Lists in Expressions
...............................
LIST ©PS Menu ..........................................
LIST MATH Menu ........................................
'_
TEXAS
I I-2
11-3
11-4
11-6
11-7
11-9
11-10
11-17
T1=83
iNSTRUMENTS
cunSu_,( {1,2, 3, 4,
5} )
{1
6 18 15}
J
STATPLOT
TBLSET
FORMAT
CALC
TABLE
Lists
11-1
Getting
Getting
Started:
Started
Generating
is a fast-paced
a Sequence
introduction.
Read the chapter
for details.
Calculate the first eight terms of the sequence i/k-'. Store the results to a use>
created list. Then display the results in fraction form. Begin this example on a
blank line on the home screen.
1,
Press [gfi_ [LIST] []
nlenu,
to display
MRTH
the LIST OPS
3:dim(
4:Fill(
5:se_(
8:cumSu_(
7$_List(
2.
Press 6 to select 6:seq(, which pastes
the current cursor location.
3. Press l [] @
[A] [] [] @
[] 8 [] 1 [] to enter the sequence.
seq( to
[A] [] l
4.
Press F_,
and then press [_ @
to
turn on alpha-lock. Press [s] [E] [Q], and
then press @
to turn off alpha-lock.
Press 1 to complete the list name.
5.
Press F_
to generate the list and store it
in SEQ1. The list is displayed on the home
screen. An ellipsis (...) indicates that the list
continues beyond the viewing window.
Press [] repeatedly- (or press and hold [_)
to scroll the list and view all the list
elements.
Press [gfi_ [LIST] to display the LIST NAMES
menu. Press FENTEm
to p_Bte LSEQ1 to the
current cursor location. (If SEQ1 is not item
1 on your LIST NAMES menu, move the
cursor to SEQ1 before you press F_.)
se_(I/RZ,R,1,8,1
i;S_
_IOPS
.1111111...
MRTH
7. Press [_
to display the MATH menu.
Press 1 to select 1:*Frac, which pastes *Frac
to the current cursor location.
Ise_(i/Ri,R,1,8,1
)+SEQI
{i .25 .1111111._
LSEQI*Frac
8.
_I
11-2
Press F_
to show the sequence in
fraction form. Press [] repeatedly (or press
and hold [_) to scroll the list and view all
the list elements.
Lists
1/4
1,'9 Ix16_.
Naming
Lists
Using TI-83 List
Names L1
through L6
The
TI-83
Creating a List
Name on the
Home Screen
To create
has six list names
in nlenlol_-:
L1, L2, L3, L4, L5,
and L6. The list names L1 through
L6 are on the keyboard
above the numeric
keys [] through
[_. To paste one of
these names to a valid screen, press E_], and then press
the appropriate
key. L1 through
L6 are stored in stat list
editor colunms
1 through
6 when you reset nlenlory,
a list name
on the home
screen,
follow
these
steps.
1. Press [_] [ { ], enter one or more list elements,
and then
press [_
[ }]. Separate
list elements
with conunas.
List
elements
can be real nulnbe_\s,
complex
numbers,
or
expressions.
I<1'2'3'4>
I
2. Press
_.
3. Press
letter
@
[letter from
of the name.
4. Enter
zero to four
A to Z or 0] to enter
letters,
0, or numbers
the first
to complete
the
nanle.
[<10203,4}+TEST
I
5, Press [E_,
The list is displayed
on the next line. The
list name and its elements
are stored
in memory.
The
list name becomes
an item on the LIST NAMES menu.
_:I,2,3,4]'+TEST{I
2 3 4}
21TEI2_""_OPS
MRTH
I
Note: if you want to view a user-created list in the stat list editor,
you must store it in the stat list editor (Chapter 12).
You also
call create
a list nalne
ill these
in the stat
four
places,
•
At the blame= prompt
•
At an Xlist:, Ylist:, or Data List: Dxnnpt
editor
•
At a List:, List1:, List2:, Freq:, Freql:, Freq2:, XList:, or
YList: prompt in the inferential
stat editors
•
On the home
screen using
You can create as many
has space to store.
list editor
in the stat
plot
SetUpEditor
list names
as your
TI-83
memo[3z
Lists
11-3
Storing
and Displaying
Storing Elements
to a List
You can
•
store
Use braces
{4+2t,
•
The
Lists
list elements
and _
in either
of two ways.
on the home
screen.
5-3t } _k G
{4+2t
_,-3t }
Use the stat
maxinmm
list editor
(Chapter
12).
dimension
of a list is 999 elements.
Tip: When you store a complex number to a list, the entire list is
converted to a list of complex numbers. To convert the list to a list of
real numbers, display the home screen, and then enter
real(listname)->listname.
Displaying a List
on the Home
Screen
To display" the elements
of a list on the home selden,
enter
the name of the list (preceded
by L if neeessa_77; see page
11-16), and then press FEET'. An ellipsis indicates
that the
list continues
beyond the viewing
repeatedly
(or press and hold [])
all the list elements.
_IDRTR
{2. 154
11-4
Lists
{2 5 _0}
50,47
....
window.
to scroll
Press []
the list and view
Copying One List
to Another
To copy a list, store it to another
list.
LTEST÷TEST2
LTEST
{123:}}
{123
Accessing
Element
a List
You can store a value to or recall a value fronl a specific
list element. You can store to any element within the
current list dimension or one element beyond.
listname(element)
{1'2'3}÷L_I
23}
4÷L_(4){L_234
L:_ (z.)
}2
Deleting a List
from Memory
To delete lists fronl nlenlol_, including L1through L6,use the
MEMORY DELETE FROM secondatF- menu (Chapter 18).
Resetting nlenlory restores L1through L6. Removing a list
from the stat list editor does not delete it from nlenlol_L
Using Lists in
Graphing
You can use lists to graph a family of creates (Chapter
Lists
3).
11-5
Entering
List Names
Using the
LIST NAMES
Menu
To display- the LIST NAMES menu, press [_
[LIST].
item is a user-created
list name. LIST NAMES menu
Each
items
m'e
sorted automatically
in alphanumerieal
order. Only the first
10 items are labeled, using 1 through 9, then 0. To jump to
the first list name that begins with a particulm" alpha
character
or 0, press @
[letter from A to Z or 0].
T
_
IOF'S
I
MRTH
Tip: From the top of a menu, press [] to move to the bottom. From the
bottom, press [] to move to the top.
Note: The LIST NAMES menu omits list names I_1through 1.6. Enter
L1 through L6 directly from the keyboard (page 11-3).
When
you select
the list name
•
Entering a UserCreated List
Name Directly
from
the LIST NAMES menu,
to the cmTent
cursor
location.
The list name symbol,
precedes
a list nmne when the
name is pasted
where non-list
name data also is valid,
such as the home screen.
LTEST
•
a list name
is pasted
(I
2
3 4}
The L symbol does not precede
a list name when the
name is pasted
where a list name is the only valid input,
such as the stat list editor's
Name-- p_x)mpt or the stat
plot editor's
XList: and YList: prompts.
To enter
an existing
1. Press
[_
list nmne
[LIST] []
directly-,
follow
these
steps.
to display" the LIST OPS menu.
Select B:L, which pastes
L is not always
necessary
L to the current
(page 11-16).
NRMES
[_]_R MRTH
61"CMFISL, Ir'l (
7: _List(
8: Selec.t(
9: augrqent(
81List*F, ate(
R: Mate* 1 ist(
cursor
location.
Note: You also can paste L to the
current cursor location from the
CATALOG (Chapter I5).
=11,
3. Enter the characters
ILT123I
11-6
Lists
that conlprise
I
the list name.
Attaching
Formulas
Attaching a
Formula to a List
Name
to List Names
You call attach
element
attached
a formula
to a list name
is a result of the fornmla.
When
formula
nmst resolve
to a list.
V_llen anything
in the attached
which the fornmla
is attached
so that
each
executed,
list
the
formula
changes,
the list to
is updated
automatically.
•
When you edit an element
of a list that is referenced
in
the fornmla,
the corresponding
element
in the list to
which the fornmla
is attached
is updated.
•
When you edit the fonnula
itself,
to which the fornmla
is attached
all elements
are updated.
in the list
For example,
the fit\st screen
below shows that elements
are stored
to L3, and the fornmla
L3+10 is attached
to the
list name LADD10, The quotation
lnarks designate
the
formula
to be attached
to LADD10. Each element
of LADD10
is the sum of an element
in L3 and 10.
{I°2'3}÷L_I
2 3}[
"L_+IO"+
LADD10
La+IB
I
LRDD10
{11
12 13}
The next screen shows another list, L4.The elements of L4
are the sum of the same formula that is attached to L3.
However, quotation marks are not entered, so the fornmla
is not attached to L4,
On the next line, -6->L3(1):L3 changes
to -6, and then redisplays L3.
the first element in L3
I
{II 12 13}I
-6÷Li(1):Li
{-6 2 3}
W+IO+L4
Tile last screen shows that editing L3updated LADD10, but
did not change L4. This is because the formula L3+10 is
attached to LADDIO,but it is not attached to L4.
LRDDIO {4
L4
{Ii
Note:
12 13}
12 13}
To view a formula
that is attached
to a list name,
use the stat list
editor (Chapter12).
Lists
11-7
Attaching a
Formula to a List
on the Home
To attach
Screen
1. Press @
[.], enter
a list), and press @
or in a
Program
home
a ff)rnmla
screen
from
to a list name
or from
a program,
a blank
follow
the formula
[-] again.
these
(which
line
on the
steps.
must
resolve
to
Note: When you include more than one list name in a formula,
each list must have the same dimension.
2,
Press
_.
3. Enter the name
the fornmla.
of the list to which
•
Press [_,
and then
through
ks.
•
Press [_
[LIST] and select a usm_created
from the LIST NAMES menu.
•
Enter a use_created
11-16).
Press
enter
you want
a TI-83
list name
to attach
list name
kl
list name
directly-
using
t (page
ITNt_RI.
{4, 8,
"5*LI
9}÷L_4
8 9}
'% tLIST
5.LI
LLIST
{28 40
45}
Note: The stat list editor displays a formula-lock symbol next to
each list name that has an attached formula. Chapter 12 describes
how to use the stat list editor to attach formulas to lists, edit
attached formulas, and detach formulas from lists.
Detaching a
Formula from
List
a
You can detach
(cleat')
any- of tht_e ways.
an attached
Lists
fron]
a list in
• Enter ""Olistname on the home screen.
•
Edit any element
attached.
•
Use the stat
of a list to which
list editor
Note: You also can use ClrList
from a list (Chapter 18).
11-8
fornmla
(Chapter
a fornmla
is
12).
or ClrAIIList
to detach a formula
Using
Lists in Expressions
Using a List in an
Expression
You can
use lists
in an expression
in any- of three
When you press [NY_,
any expression
each list element,
and a list is displayed.
•
Use L1-Ls or any user-created
ways.
is evaluated
list name
for
in an expression.
5 16}
20/L1
•
Enter
{10 4 2}
the list elements
20/{2,
•
directly
(step
1 on page
11-3).
5, 10}
{10 4 2}
Use [_
[RCL] to recall the contents
of the list into
expression
at the cursor
location
(Chapter
1).
Rcl Lt
an
"* {2,5,10}I{4
25 i00}
Note: You must paste user-created list names to the Rcl prompt by
selecting them from the LIST NAMES menu. You cannot enter them
directly using L.
Using Lists with
Math Functions
You can use a list to input
functions.
Other chapters
a list is valid. The function
element,
several values ff)r some math
and Appendix
A specify
whether
is evaluated
for each list
and a list is displayed.
When you use a list with a function,
the function
lnust
be valid for every element
in the list, In graphing,
an
invalid element,
such as -1 in _({1,0,-1}), is ignored,
14"({1,O,-1})
I
F'loti Plot_:
\VIBx,r(
{1, F'lot3
O, -I}
)
This returns an error.
Thisskips
graphsX*_(1)
but
X*_(-1).
and X*_(O),
When you use two lists with a two-argulnent
function,
the dimension of each list must be the same, The
function is evaluated for corresponding
elements.
{5 5,7 6}
9}
{i, 2, 3}+{4,
When you use a list and a value with a two-argument
function, the value is used with each element in the list.
{1'2'3}+4{5
6 7}
Lists
11-9
LIST OPS Menu
LIST OPS Menu
To display
NAMES OPS
the
LIST OPS menu,
[LIST]
[_.
Sorts lists in _Lscending order.
Sorts lists in descending order.
Sets the list dimension,
Fills 'all elements with a constant.
Creates a sequence,
Returns a list of cunmlative sums,
Returns difference of successive elements,
Selects specific data points,
Concatenates
two lists,
Stores a list to a nlatrix.
Stores a lnatrix to a list.
Designates the list-name data type,
2:SortD(
3:dim(
4:Fill(
5:seq(
6:cumSum(
7:aList(
8:Select(
9:augment(
O:List_matr(
A:Matr_list(
B:L
SortD(
[_
MATH
1:SortA(
SortA(,
press
SortA( (sort ascending) sorts list elements fron] low to high
values, SortD( (sort descending) sorts list elements from
high to low values. Complex lists are sorted based on
magnitude (modulus).
With one list, SortA( and SortD( sort the elements
listnome and update the list in nlenloi_.
SortA(listname)
of
SortD(listname)
Sor.tR(L_ )
Done
L_
{4 5 6}
{6
With two or more lists, SortA( and SortD( sort keylistname,
and then sort each dependlist by placing its elements in the
same order as the corresponding
elements in keylistname.
All lists nmst have the same dimension,
SortA(k¢ylistname,deperwllistl[,depe_wllist2,...,depe_wllist
SortD(k¢ylistname,deperwllistl[,depe_wllist2,...,depe_wllist
{5'6'4}÷L_5
6
{1,2,3},L_I
2
4}
S°rtR(k_'L_>Done
_
3}
n])
n])
{4 5 6}
{3 1 2}
Note: In the example, 5 is the first element in L4, and 1 is the first
element in L5. After SortA(L4,Ls),
5 becomes the second element
L4, and likewise, 1 becomes the second element of L5.
of
Note: SortA( and SortD( are the same as $ortA( and SortD( on the
STAT EDIT menu (Chapter 12).
11-10
Lists
Using dim( to
Find List
Dimensions
dim((dimension)
of list.
returns
the length
(number
of elements)
dim(list)
diM({1,3,5,7})
Using dim( to
Create a List
4
You can use dim( with _
to create a new listname
with
dimension
length from 1 to 999. The elements
are zeros.
length_ dim(listname)
3÷diFKLz
Lz
Using dim( to
Redimension a
List
You can
listnome
•
) {0 0 0_
use dim with
to dimension
The elements
new
in the old listname
dimension
•
Extra
•
Elements
dimension
[gg_] to redimension
an existing
length from 1 to 999.
that
are within
the
are not changed.
list elements
are filled
in the old list that
are deleted.
by 0.
are outside
the new
length_ d im(listname)
{4'8'6}÷L_4
4÷dim(L1
LI
Fill(
Fill( replaces
8
6
)
{4 8 6 0}
each
element
3÷diM(L1
L1
in listnome
with
) {4 8 6_
value.
Fill(value,listname)
{3'4'5}÷L_3
4 5}
FilI(8,L_)
Done
L_
{8 8 8}
Fill(4+3t,Li_one
Li
{4+or
4+3t
4+3t}
Note: dim( and Fill( are the same as dim( and Fill( on the MATRX
MATH menu (Chapter 10).
Lists
11-11
seq((sequence)
seq(
returns
a list in which
each
element
is the
result of the evaluation
of expression
with regard to
variable
for the values ranging
from begin to end at steps
of increment,
variable
need not be defined
in memory.
increment
can be negative;
the default value for increment
is 1. seq( is not valid within expression.
seq(expression,variable,begin,e_l[,increment])
se_(AZ,
{I
cumSum(
R, 1,11,3)
16
49
100}
cumSum( (cunmlative sunl)
returns the cunmlative
the elements in list, starting with the first element,
elements can be real or complex numbers.
sunls of
list
cumSum(list)
c.umSum( {i,2, 3,4,
5}){I 3 6 10 15}
AList(
aList( returns a list containing the differences between
consecutive elements in list. AList subtracts the first
element in list from the second element, subtracts the
second element from the third, and so on. The list of
differences is always one element shorter than the original
list. list elements can be a real or complex numbers.
AList(list)
{20,30,
45., 70}÷ LD
IST
I
{20 30 45 70}
aList(LDIST)
{10 15 25}
Select(
Select( selects one or more specific
data points fronl a
scatter
plot or xyLine plot (only), and then stores the
selected
data points to two new lists, xlistname
and
ylistname.
For example,
you can use Select( to select and
then analyze
a portion
of plotted
CBL 2/CBL or CBR data.
Select(xlistname,ylistname)
Note: Before you use Select(, you must have selected (turned on) a
scatter plot or xyLine plot. Also, the plot must be displayed in the
current viewing window (page 11-13).
11-12
Lists
Before Using
Select(
Before using Select(, follow these steps.
1. Create two list names and enter the data.
2. Turn on a stat plot, select Le: (scatter plot) or [_- (xyLine),
and enter the two list names for Xlist: and Ylist: (Chapter
12).
3. Use
ZoomStat
to plot
{1,2, 3, 4, 5,6,7,8]
,9,9.5,10}+DIST
I
I{i 2 3 4 5 6 7 ...I
1{15, 15, 15, 13, ll,I
IEg,?,5,3,2,2)÷TIM
I
I{15 15 15 13 11...I
t
Using Select( to
Select Data
Points from a
Plot
the data
(Chapter
_DOnO_z
_1*t_
el.
TgPe: I If"_
_ i_ _
Xlist.:oIsm
YlisL:TIME
Mark: [] ÷ •
J
To select data points fronl a scatter
follow these steps.
3).
. °o
" .
.
° °
%.
plot or xyLine plot,
1. Press [2_] [LIST][] 8 to select 8:Select( from the LIST
OPS menu. Select( is pasted to the home screen.
2. Enter xlistname,
press [], enter ylistname,
and then
press [] to designate list names into which you want
the selected data to be stored.
I
ISeleot(L1,Cz)l
3. Press [g_-gm. The graph screen is displayed
Left Bound? in the bottom-left corner.
a
LeFtBound?
u
with
iI
000
Press [] or [] (if more than one stat plot is selected)
to
move the cursor
onto the stat plot from which you want
to select data points.
Press [] and [] to move the cursor
to the stat
)oint that you want as the left bound.
keFt BOLIhd?
plot
data
_ ua
Lists
11-13
6. Press [NER]. A _ indicator on the graph screen shows
the left bound. Right Bound? is displayed in the bottonlleft corner.
P i:BIST.,TIH{
o a a _
u
U
a
U
uua
RiZlht _OUnd?
Press [] or [] to nlove tile cursor to the stat plot point
that you want for the ri ht bound, and then press [ENY_.
PI:DIST_TIHE
: a
i
aa_
a
Ri_htBound?
m u
a
"
o
u u"_
u
"
[] u
The x-values and y-values of the selected points
stored in xlistname
and ylistname.
A new stat
._:listname and ylistname
replaces the stat plot
which you selected data points. The list names
updated in the stat plot editor.
are
plot of
from
are
11 9 7 s 3
]91ist:Lz
Mark:
[] ÷
.
Note: The two new lists (xlistnanw and ylistname) willinclude the
points you select as left bound and right bound. Also, left-bonnd
x-volne
11-14
Lists
< "l_ight-bound
x-value
must
be true.
augment(
augment( concatenates the elements of listA and listB. The
list elements can be real or complex numbers.
augment(listA,listB)
{1,17,21}+L_
{1 1721}
augment.(L_o{a5,3
8,41})
-,
{1 17 21 25 o0 ...
List_matr(
List*matr( (lists stored to matrix) fills matrixname
colunm
by colunm with the elements from each list. If the
dimensions of all lists are not equal, then List_matr{ fills
each extra matrixname
row with O. Complex lists are not
valid.
List*matr(listl,list2,
{l'2'3}+LX1
. . . ,list n,mat_xname)
2
3}
List*matt(
LB, 1C1 )
LX,
Lists
L'_J,
I
Oone[
11-15
MatrHist(
MatrHist( (matrix stored to lists) fills each listname with
elements from each colunm in mahqx. If the number of
listname argulnents exceeds the number of colunms in
matrix, then MatrHist( ignores extra listr_ame arguments.
Likewise, if the number of colunms in matrix exceeds the
number of listr_ame arguments, then MatrHist( ignores
extra matrix colunms.
Mat_list(mat_x,listnamel,listname2
[4
Matr_li_t(
,Lz,L_)
5 6111
--
....
Lz
[RI,L1
Done
,listnamen)
{2 5}
{3
Math.list( also fills a listname with elements fronl a
specified column# in matrix. To fill a list with a specific
colunm from matrix, you nmst enter a column# after
matrix.
Mat_list(matrix,column#,listnome)
IN]
[[1
2 31 [
5 6111 --
L1
{3 6}
Matt*list(
LI)
[R1,3,
Done
t preceding one to five characters identifies those
characters _ts a use>created
listname, listname may
comprise letter\% 0, and numbers, but it nmst begin with a
letter fi'onl A to Z or 0.
Llistname
Generally, L must precede a user-created
list name when
you enter a use>created
list name where other input is
valid, for example, on the home screen. Without the t, the
TI-83 may misinterpret
a use>created
list name as implied
nmltiplication
of two or more characters.
t need not precede a use>created
list name where a list
name is the only valid input, for example, at the Name=
prompt in the stat list editor or the Xlist: and Ylist: prompts
in the stat plot editor. If you enter • where it is not
necessary, the TI-83 will ignore the enttT.
11-16
Lists
LIST MATH
LIST MATH Menu
min(,
max(
Menu
To display
the
LIST MATH menu,
press
[_
[LIST]
E],
NAMES OPS MATH
i: min(
Returns
2: max(
Returns
Returns
3: mean(
Returns
4: median(
Returns
5: sum(
nnninmm
element
of a list.
nl_ximum
element
of a list.
mean of a list,
median
of a list,
sum of elements
in a list.
6: prod(
7:stdDev(
8: variance(
product
of elements
in list,
standard
deviation
of a list,
the variance
of a list,
Returns
Returns
Returns
min((nlininlunl)
and max((nlaxinlunl)
retul]l the smallest
or
largest element
of listA. If two lists are compared,
it returns
a list of the snmller or larger of each pair of elements
in listA
and listB. For a complex
list, the element
with snmllest
or
largest magnitude
(modulus)
is returned.
min(listA [,listB ])
max(listA[,listB])
mir,({lo2,3},{3,21
,i}>
{I 2 I}II
max({l,2,3},
,i}>
{3 2{3'23}
Note: min( and max( are the same as min( and max( on the MATH
NUM menu.
mean(,
median(
mean( returns
the mean value of list. median( returns
the
median
value of list. The default
value forfreqlist
is 1.
Eachfreqlist
element
counts
the number
of consecutive
occurrences
of the corresponding
element
in list. Complex
lists are not valid.
mean(list[ #¢reqlist])
median(list[ dreqlist ])
mean( {1,2,3}, {3,
2, I} >
I. 666666667
_'_ed
ian ({i, 2, 3} )2
Lists
11-17
sum(, prod(
sum((sununation)
returns
the sunl
of the elements
start and end are optional;
they specify
a range
elements,
list elements
can be real or complex
in list,
of
numbers.
prod( _tma_s
the product
of all elements
of list. start and
end elements
are optional;
they specify- a range of list
elements,
list elements
can be real or complex
nmnbers.
sum(list[,start,ef_l])
prod(list[,start,ef_l])
L_
{I 2 5
sur_(L_ )
8
10}
26
su_KLI,3,5)
Sums and
Products
of
Numeric
You can
23
colnbine
2 5 8
)
10}
400800
Prod(Li,3,5)
sum( or prod( with
upper
Sequences
k_
{I
Prod(L1
seq( to obtain:
upper
expression(x)
x=lower
To evaluate
x=lower
Z 2 (N 1)fl'Oln N=I to 4:
sur_(se_ (2" (N- I ),
N, 1,4, I))
stdDev(,
variance(
15
stdDev( retrains the standard
deviation
of the element._
The default value forfreqlist
is 1, Eachfreqlist
element
counts the number
of consecutive
occurrences
of the
con'esponding
element
in list. Complex
in list.
lists m'e not valid.
variance(
returns
the variance
of the elements
in list, The
default value forfreqlist
is 1, Eachfreqlist
element
counts
the number
of consecutive
occmTences
of the corresponding
element in list. Complex
list.s are not valid.
stdDev(list[freqlist])
stdOev(
,3,
11-18
Lists
vadance(list[freqlist])
{i, 2, 5, -6
-2})
3. 937003937
variance(
-6,3,
-2})
{i,
2,5,
15.5
2
Contents
Statistics
Getting Started: Pendulum Lengihs and Periods .........
Setting Up Statistical Analyses ...........................
Using the Stat List Editor ................................
Attaching Fornmlas to List Names .......................
Detaching Formulas from List Names ....................
Switching Stat List Editor Contexts ......................
Stat List Editor Contexts .................................
STAT EDITMenu ........................................
Regression Model Features ..............................
STAT CALC Menu ........................................
Statistical Variables ......................................
Statistical Analysis in a Program .........................
Statistical Plotting .......................................
Statistical Plotting in a Program .........................
TEXAS
12-2
12-10
12-11
12-14
12-1(;
12-17
12-18
12-20
12-22
12-24
12-2(.)
12-30
12-31
12-37
TI-83
INSTRUMENTS
p Z:LI_RE:VIn
D
0
M
0
M
0
0
g=Nl.g
Y='.OZ7001
J
STAT
PLOT
TBLSET
FORMAT
CALC
TABLE
Statistics
12-1
Getting
Getting
Started:
Started
Pendulum
is a fast-paced
A group of students is
between the length of
pendulum). The group
then suspends it from
of 12 string lengths.*
Press [_DE] [] []
graphing
mode.
2.
Press [g_g]
SetUpEditor
screen.
introduction.
and Periods
Read the chapter
for details.
attempting to determine the lnathelnatical
relationship
a pendulum and its period (one complete swing of a
makes a simple pendulum froln string and washers and
tile ceiling. They record the pendulum's period for each
Length
1.
Lengths
(cm)
Time
6.5
0.51
11.0
0.68
13.2
0.73
15.0
0.79
18.0
0.88
23.1
0.99
24.4
1.01
26.6
1.08
30.5
1.13
34.3
1.26
37.6
1.28
41.5
1.32
(sec)
[] [g_gg] to set Func
5 to select 5:SetUpEditor.
is pasted
to the honm
Press [gfff_. This relnoves lists fronl stat
list editor colunms 1 through 20, and
then stores lists L1through L6 in
eolunms 1 through 6.
SetUeEditof
Done[
Note: Removinglists from the stat list editor doesnot
deletethem from memory.
3.
Press [gf_] 1 to select 1:Edit fronl the
STAT EDIT menu. The stat list editor is
displayed. If elements are stored in 1-1
and I_2,press [] to move the cursor onto
1_1,and then press @
[gNT_ [] []
@
[gg7_ to clear both lists. Press []
to move the rectangular
cut\sor back to
the first row in 1_1.
L1(1)=
*This example is quoted and adapted from Contempo'_mT
P'recal(vdns
Th'mugh Applications,
by the North Carolina School of Science and Mathematics,
by permission of Janson
Publications,
Inc., Dedham, MA. 1-800-322-MATH.
© 1992. Aft rights reserved.
12-2
Statistics
4. Press
6[]
6 _
to store
the first
pendulum
string length (6.5 cm) in 1.1.
The _ctangular
cursor
nloves to the
next row. Repeat
this step to enter each
of the 12 string length values in the table
on page 12-2.
Press [] to inove the rectangular
to the first row in 1.2.
cursor
Press [] 61 _
to store the first time
measurement
(.51 sec) in 1.2. The
LI
.Z
L_:
1
.Z
L_:
Z
26,6
37.ti
L1(1_) =
Lt
26.6
t.0B
3LI.:_
3?.tl
t.Ztl
J..ZB
rectangulm"
cursor moves to the next
row, Repeat
this step to enter each of
the 12 time wdues in the table on
6.
page
12-2.
Press
[]
to display-
Plot1 PloLZ Plot:_
\V1 =11
the Y= editor.
If necessm'y,
press @
to clem" the
fm_ction Y1. As necessmy,
press [], [E_,
and [] to turn off Plot1, Plot2, and Plot3
from the top line of the Y= editor
(Chapter
3). As necessmy,
press [], [_,
and [_
to deselect functions.
".Yz=
_.y_=
xy_=
"_y_=
xY_;=
\Y?=
Press [_
[STAT
PLOT]
1 to select 1:Plot1
fi'om the STAT PLOTS menu. The stat
plot
editor
is displayed
for plot
1.
Press _
to select On, which turns on
plot 1. Press [] _
to select ,,'."
(scatter
plot). Press [] _
[L1] to
specify- ×list:1.1 for plot 1. Press []
[L2] to specify- Ylist:1.2 for plot 1.
Press [] [] _
to select + _ksthe Mark
for each data point on the scatter
plot.
_peO Plo_2 P1o_:_
+-,._
liar-k:
. []
•
Press _
9 to select 9:ZoomStat
fronl
the ZOOM menu. The window
variables
are adjusted
automatically,
displayed.
This is a scatter
time-versus-length
data.
÷ +
÷
and plot 1 is
plot of the
÷
÷
++
+
+÷+
+
Statistics
12-3
Since
thescatter
plotoftime-versus-length
dataappears
tobeapproxhnately
linear,
fit a line to the data.
10. Press _
[] 4 to select
(linear
regression
nlodel)
CALC menu, kinReg(ax+b)
tile home screen.
11. Press [_
[L1]
[] 1 to display
4:LinReg(ax+b)
fronl the STAT
is pasted
to
LinReg(ax+b)
|
_
[L2] [_.
Press
the VARS Y-VARS
[]
FUNCTION secondmT
menu, and then
D_ss 1 to select 1:Y1. Lt L2, and Y1 are
pasted to the home screen
as arguments
to LinReg(ax+b).
12. Press [_
to execute
LinReg(ax+b). The
lineal" regression
for the data in L1 and L2
is calculated.
Values for a and b are
displayed
regression
Residuals
on the home screen. The linear
equation
is stored in Y1,
are calculated
and stored
automatically
in the list name RESID,
which becomes
an item on the LIST
NAMES menu,
13. Press _.
The regression
scatter plot are displayed.
12-4
Statistics
line and the
LinReg
9=_x+b
a=.0230877122
b=.4296826236
Theregression
lineappears
tofit thecentral
portionofthescatter
plotwell.
However,
aresidual
plotmayprovide
moreinformation
about
thisfit.
14.Press
[g_g] 1 to select 1:Edit. The stat
list editor
Press
L3.
E2;
11
is displayed.
[] and [] to lnove
Press [_
displayed
shift right
prompt
is
alpha-lock
the cursor
onto
[INS]. An unnamed
colunm
is
in colunm
3; 1.3, k4, L5, and 1_6
one colunm.
The Name=
displayed
in the entry line, and
is on.
15. Press [2_ [LIST] to display
NAMES menu.
the
1_;
18
;:3.1
2h.h
NaMe=_
2;1
._8
,79
,8B
.99
1,01
LIST
If necessatT, press [] to inove the cursor
onto the list name RESID.
16. Press _
to select RESID and paste it
to the stat list editor's Name= pt_mlpt.
Lt
.2
&5
,B1
11
13.2
,l_B
.73
2h.h
1.01
1_:
1B
.2_:.1
17. Press IgOr. RESID is stored in colunm
of the stat list editor.
Press [] repeatedly
residuals.
to examine
the
_
.79
.EB
.99
3
I_.B
,51
".06911
11
.6B
".0036
13.2
,73
".OOhh
1_:
.79
.01h
1E
.BE
.03h?h
?._:.1
.99
.0Z699
2h._
1.=31
.0lEgit
eCSZD= £ -. 0697527...
Notice that the first three residuals
are negative.
They cotTespond
to the
shortest
pendulum
string lengths
in L1. The next five residuals
are positive,
and
three of the last four are negative.
The latter correspond
to the longer string
lengths
in L1. Plotting
the residuals
will show this pattern
more clearly.
Statistics
12-5
18. Press [2_] [STAT PLOT] 2 to select 2:Plot2
from the STAT PLOTS menu. The stat
plot editor is displayed for plot 2.
19. Press [[email protected]]
plot 2.
to select
On, which
turns
on
Press [] FEffEEN
to select _ (scatter plot).
Press [] [2_] [L1] to specify Xlist:L1 ff)r
plot 2. Press [] [R] [E] [S] [I] [D]
(alpha-lock is on) to specify Ylist:RESID
for plot 2. Press [] FEflT_]to select [] as
the mark for each data point on the
scatter plot.
20. Press [] to display the Y= editor.
Press [] to nlove the cursor onto the
= sign, and then press [g_
to deselect
Y1. Press [] [g_
to turn offplot 1.
21. Press _
9 to select 9:ZoomStat fl'oln
the ZOOM menu. The window variables
are adjusted automatically,
and plot 2 is
displayed. This is a scatter plot of the
residuals.
Pl*t:[O_
P10t?
_uPe:
m k:2 dt_
Xlist:L1
YI ist: RESIO
[] *
Mark:
PI*L1
_
Statistics
Pl*t_
xY1 =. 02308771216
587X+. 4296826135
7287
xYz=
xY?=
xY_=
\Y_=
D
Eli=
Notice the pattern
of the residuals:
a group of negative
residuals,
of positive
residuals,
and then another
group of negative
residuals.
12-6
.
then
a group
Theresidual
patternindicates
acm5Tature
associated
withthisdatasetfor
whichthelinearmodeldidnotaccount.
Theresidual
plotemphasizes
a
downward
curvature,
soamodelthatcm_'es
downwiththedatawouldbe
moreaccurate.
Perhaps
afunction
suchassquare
rootwouldfit.TFFapower
regression to fit a function of the form y = a * xt'.
22. Press [] to display the Y=editor,
Press @
to clear tile linear regression
equation from Y1,Press [] [ggY_ to turn
on plot 1, Press [] [g_gO to turn off plot
2.
",Yz=
,.Y_=
_.y_=
-,y_=
_.y_=
\y;_=
23. Press _
9 to select 9:ZoomStat froin
the ZOOM menu. The window
variables
÷ +
÷
+
are adjusted
automatically,
and the
original
scatter
plot of time-versuslength data (plot 1) is displayed.
_+
÷
÷÷÷
÷
24. Press Fgg_ [] @
[A] to select
A:PwrReg from the STAT CALC menu.
PwrReg is pasted to the home screen.
PuPReg
L1,Lz,Yi|
Press [g_ [L1][] [g_ [L2][]. Press
[] 1 to display the VARS Y-VAR$
FUNCTION secondmT menu, and then
press 1 to select 1:Y1.1.1, 1_2,and Y1 are
pasted to the home screen as arguments
to PwrReg.
25. Press [g_gm to calculate the power
regression. Values for a and b are
displayed on the home screen. The
power regression equation is stored in
Y1. Residuals are calculated and stored
automatically
in the list name RESID,
26. Press _.
The regression
scatter plot are displayed.
PwrReg
_=a*x^b
a=.1922828621
b=.5224982852
line and the
Statistics
12-7
The new function y=.192x _"- appears t( fit the data well. To get nlore
information,
examine a residual plot.
27. Press
[]
to display
Pl*tl
the Y= editor.
_
Pl*t3
19228286213
".,Y 1 ----.
Press
[] _
to deselect
552X%
Y1.
Press [] [NY_ to turn offplot
[] [ggY_ to turn on plot 2.
1. Press
Note: Step 19 defined plot 2 to plot residuals (RESID)
versus string length (11).
28. Press _
9 to select 9:ZoomStat froln
the ZOOM menu. The window variables
are adjusted automaticMly, and plot 2 is
displayed. This is a scatter plot of the
residuMs.
5224982852
\y_=
\Y_=
D
[]
a
El
The new residual plot shows that the residuals are random in sign, with the
residuals increasing in magnitude as the string length increases.
To see the magnitudes
of the residuals,
continue
with these steps.
29. Press _.
Press [] and [] to trace the data.
Observe the values for Y at each point.
With this model, the largest positive
residual is about 0.041 and the smallest
negative residual is about -0.027. All
other residuals are less than 0.02 in
magnitude.
12-8
Statistics
P ;':LI_F;E$'r
II/:_1.5
B
[]
Y:'.OZ?OOJ.
Nowthatyouhaveagoodmodelfortherelationship
between
lengthand
period,
youcanusethemodeltopredict
theperiodforagivenstringlength.
Toprediet
theperiods
forapendulum
withstringlengths
of20cmand50cm,
continue
withthesesteps.
30.Press
[_ [] 1todisplaytheVARS
Y-VARS
FUNCTION
seconda[w
menu,
and
thenpress1toselect
1:Y1.
Y1ispasted
tothehomescreen.
_1
31.Press
[]
20
20 [] to enter
a string
length
II
of
enl,
Press _
to calculate
the predicted
time of about 0.92 seconds.
Based on the residual
expect
the prediction
seconds
to be within
of the actual value.
32. Press
_
[ENTRY]
anMysis,
we would
of about 0.92
about 0.02 seconds
to recall
Press [] [] [] 6 to change
length to 51) enL
the Last EnbTy'.
the string
33. Press _
to calculate
the predicted
time of about 1.48 seconds.
I. 484736865
_11(50)(28!9198781364
Since a string length of 50 cnl exceeds
the lengths
in the data set, and since
residuals
appear to be increasing
_
string length increases,
we would
expect
more etTor with this estimate.
Note: You also can make predictions using the table
with the TABLE SETUP settings Indpnt:Ask
and
Depend:Auto
(Chapter 7).
Statistics
12-9
Setting
Up Statistical
Analyses
Using Lists to
Store Data
Data for statistieM
Setting Up a
Statistical
Analysis
To set up a statistical
chapter
for details.
1. Enter
2. Plot
is stored
4.
data
in lists,
which
you
stat list editor. The TI-83 h_ks
L1 through
L6, to which you
calculations.
Also, you call
you create (Chapter
11).
analysis,
the statistical
follow
into
these
steps.
one or more
Read
the
lists.
the data.
3. Calculate
Graph
the statistical
the regression
5. Graph
Displaying the
Stat List Editor
analyses
can create and edit using the
six list vadal_les
in lnelnory,
can store data ff_r statistical
store data to list names that
the residuals
vm'iables
equation
or fit a model
to the data
for the plotted
list ff)r the given
data.
regression
model.
The stat list editor is a table where you can store, edit, and
xqew up to 20 lists that are in nlenlol_yL Also, you Call create
list nalnes fronl the stat list editor.
To display- the stat list editor, press [g_T], and then select
1:Edit fronl the STAT EDIT menu,
CRLC TESTS
L1
mmm
L_:
._
1
SortO(
ClrList
SetUeEditor
LI(I)=
The top line displays
list names.
L1 through
colunms
1 through
6 after a lnelnolT
reset.
the current
colunm
is displayed
L6 are stored
in
The number
of
in the top-right
The bottom
line is the entry line. All data entry
this line. The characteristics
of this line change
to the current
context
(page 12-17).
corner.
occurs
on
according
The center area displays
up to seven elements
of up to
tht_e lists; it abbreviates
wdues when neeessalT.
The enttT
line displays
the full value of the curt_nt
element.
12-10
Statistics
Using the Stat List Editor
Entering a List
Name in the Stat
List Editor
To enter a list name in tile stat list editor, follow these steps.
1. Display the Name= prompt in the entt T line in either of
two ways.
• Move the cursor onto the list name in the colunm
whet_ you want to insert a list, and then press
[_
[iNS]. Nil unnamed colunm is displayed and the
remaining lists shift right one colunm.
• Press [] until the cut\sor is on the top line, and then
press [] until you reach the unnamed colunm.
Note: If list namesare storedto all 20 columns,you mustremove
a list name to makeroomfor an unnamedcolumn.
The Name= prompt
LI
L:;"
is displayed
and alpha-lock
is on.
1
qame=_
2. Enter a valid list name in any of four ways.
•
Select a name fl'onl file LIST NAMES menu (Chapter
•
•
Enter Cl, C2, Ca, L4, ks, or C6fronl the keyboard.
Enter an existing user-created list name directly from
the key! Joard.
Enter a new user-created
list name (page 12-12).
•
I
I,Iamo=RBC
I
11).
I
I
3. Press [ggtgN or [] to store the list name and its
elements, if any-, in the cutTent colunm of the stat list
editor.
Lt
k:;"
t
To begin entering, scrolling, or editing list elements,
[]. The rectangular
cursor is displayed.
Note: If the
another stat
move to the
names shift
press
list name you entered in step 2 already was stored in
list editor column, then the list and its elements, if any,
current column from the previous column. Remaining
list
accordingly.
Statistics
12-11
Creating a Name
in the Stat List
Editor
To create
1,
a name
in the stat
list editor,
ff)llow
these
steps,
Follow step 1 on page 12-11 to display- the Name=
prompt.
2, Press
[letter from A to Z or 0] to enter the first letter of
the name. The first character cannot be a number.
3, Enter zero to four letters, O, or numbers
new user-created
list name. List names
five characters
to conlplete
the
can be one to
long.
Press [g_
or [] to store the list name in the current
colunm
of the stat list editor. The list name becomes
item
Removing a List
from the Stat List
Editor
on the
[_[ST NAMES menu
(Chapter
an
11).
To remove a list from the stat list editor, move the cursor
onto the list name and then press [DTn. The list is not deleted
from memory;
it is only removed
from the stat list editor.
Note: To delete a list name from memory, use the MEMORY
DELETE:List selection screen (Chapter 18).
Removing
Lists and
All
Restoring L1
through
L6
Clearing All
Elements from a
List
You
Use SetUpEdRor
•
Reset
all user-created
all memotT
•
•
•
lists
list names L1 through
of two ways.
with
no arguments
(Chapter
You can clear all elements
•
Statistics
remove
•
•
12-12
can
editor and restore
through
6 in either
from
the stat
list
L6 to colunms
(page
1
12-21).
18).
from a list in any- of five ways.
Use ClrList to clear specified lists (page 12-20).
In the stat list editor, press [] to move the cursor onto a
list name, and then press @
[ggg_.
In the stat list editor, move the cursor onto each
element, and then press [g_ one by one.
On the home screen or in the program editor, enter
O->dim(listname) to set the dimension of listname to 0
(Chapter 11).
Use ClrAIILists to cleat' all lists in memory (Chapter 18).
Editing a List
Element
To edit
a list element,
follow
1. Move the rectangular
to edit.
2. Press
[_
to move
these
cursor
steps.
onto
the cursor
the element
to the entry
you want
line.
Note: If you want to replace the current value, you can enter a new
value without first pressing _.
When you enter the first
character, the current value is cleared automatically.
3, Edit
tile element
in tile entity- line,
•
Press one or lnore keys to enter the new
you enter the ill,st character,
the current
cleared
automatically.
•
Press [] to move the cta'sor to the character
before
which you want to insert, D_ess [_
[_NS], and then
enter one or more charactegs,
•
Press [] to move the cta'sor to a chm'acter
you want
delete, and then press [ff_] to delete the character.
To cancel any editing and restore
the rectangular
cursor,
press @
ABe
Lt
L2
the
value.
value
original
[_.
When
is
element
to
at
t
_co)=25-1000|
Note: You can enter expressions and variables for elements.
4. Press [gNYE_, [], or [] to update the list. If you entered
all expression,
it is evaluated.
If you entered
only a
variable,
the stored value is displayed
as a list element.
L1
ttl_C
L_:
1
:LO
_C(_)=20
When
updated
you edit
a list element
in nlenloFy
ill the stat
list editor,
the list is
inunediately.
Statistics
12-13
Attaching
Formulas
Attaching a
Formula to a List
Name in Stat List
Editor
to List Names
You can attach a fornmla to a list name in the stat list
editor, and then display- and edit the calculated list
elements. VCl_enexecuted, the attached fommla nmst
resolve to a list. Chapter 11 describes in detail the concept
of attaching fornmlas to list names.
To attach a fonnula to a list name that is stored in the stat
list editor, follow these steps.
1. Press [Kf_T]_
to display the stat list editor.
2. Press [] to move the cursor to the top line.
3. Press [] or [_, if necessm% to move the cm_sor onto the
list name to which you want to attach the fornmla.
Note: If a formula in quotation
marks is displayed on the entry line,
then a formula is already attached to the list name. To edit the
formula, press_,
4. Press @
andthen edit the formula.
[,,], enter the fornmla,
and press @
[,,].
Note: If you do not use quotationmarks,the T1-83calculatesand
displays the same initiallist of answers,but does not attach the
formula forfuture calculations.
I i:i_¢
"II]
tO
L;_
;;
....
L20__ul_5__.
LFIEIC+IO"11
Note: Any user-created
list name referenced
preceded by an L symbol (Chapter 11 ).
in a formula
must be
5. Press IENTERI.
The TI-S3 calculates each list element and
stores it to the list name to which the fornmla is
attached. A lock symbol is displayed in the stat list
editor, next to the list name to which the fornmla is
attached.
lock symboI
/
I=I_C
Lt
tO
;;_:O00
u_1_=15
12-14
Statistics
$ j L>
_:0
_O::!.0
_:
Using the Stat
List Editor When
Formula-
When
Generated
(Chapter
Lists
Are Displayed
you edit
attached
element
ABC
I(,
2_:000
Z$
an element
of a list referenced
in an
fommla,
the TI-83 updates
the co_Tesponding
in the list to which the fornmla
is attached
11).
LI
$
t5
_:0
_:_:0i0
._0
._:
1
ItI_C
2_:000
LI
$
.2
1
>0
;:_:0i0
_c_z_
= 1e
When a list with a formula
attached
is displayed
in the stat
list editor and you edit or enter elements
of another
displayed
list, then the TI-83 takes slightly- longer to accept
each edit or ent_3; than
attached
are in view.
when
no lists with
formulas
Tip: To speed editing time, scroll horizontally
until no lists with
formulas are displayed, or rearrange the stat list editor so that no lists
with formulas are displayed.
Handling Errors
Resulting from
Attached
Formulas
On the home screen, you can attach to a list a formula that
t_ferences
another list with dimension 0 (Chapter 11).
However, you cannot display the fornmla-generated
list in
the star list editor or on the home screen until you enter at
least one element to the list that the formula references.
All elements
of a list t_ferenced
by an attached
fornmla
nmst be valid for the attached
fornmla,
For example,
if
Real number
mode is set and the attached
formula
is
log(l_1), then each element
of 1.1 nmst be greater
since the logarithm
of a negative
number
returns
complex
result,
than
a
O,
Tip: If an error menu is returned when you attempt to display a
formula-generated list in the stat list editor, you can select 2:Goto,
write down the formula that is attached to the list, and then press
_
to detach (clear) the formula. You then can use the stat
list editor to find the source of the error. After making the appropriate
changes, you can reattach the formula to a list.
If you do not want to clear the formula, you can select 1:Quit, display
the referenced list on the home screen, and find and edit the source of
the error. To edit an element of a list on the home screen, store the
new value to list'name(element#)
(Chapter 11).
Statistics
12-15
Detaching
Detaching a
Formula from a
List Name
Formulas
You can detach
four ways,
•
•
•
•
List Names
(clear)
a formula fronl a list name in any of
In the stat list editor, nlove the cursor onto the name of
the list to which a fornmla is attached. Press [gflT_
@
[Ni_. All list elements remain, but the fommla
is detached and the lock symbol disappeat\s.
In the stat list editor, nlove the cursor onto an element
of the list to which a fornmla is attached. Press [gflT_,
edit the element, and then press [ggT_. The element
changes, the fornmla is detached, and the lock symbol
disappears. All other list elements remain.
Use CIrList (page 12-20). All elements of one or more
specified lists are cleared, each formula is detached, and
each lock symbol disappears. All list names remain.
Use ClrAIILists (Chapter 18). All elements of 'all lists in
nlenlory are cleared, M1 fornml_ts m'e detached from 'all
list names, and all lock symbols disappear. All list
nanles
Editing an
Element of a
FormulaGenerated List
from
renlain.
As described above, one way to detach a fornmla fronl a
list name is to edit an element of the list to which the
formula is attached. The TI-83 protects against
inadvertently
detaching the fornmla from the list name by
editing an element of the fornmla-generated
list.
Because of the protection feature, you lnust press [gflT_
before you can edit an element of a formula-generated
list.
The protection feature does not allow you to delete an
element of a list to which a formula is attached. To delete
an element of a list to which a formula is attached, you
nmst first detach the fornmla in any- of the ways described
above.
12-16
Statistics
Switching
Stat List Editor Contexts
The
Stat List Editor
Contexts
stat
list editor
•
View-elements
•
View-nanles
has four
context
context
contexts,
•
Edit-elements
•
Enter-name
context
context
The star list editor is first displayed
in view-elements
context.
To switch through
the four contexts,
select
from the STAT EDIT menu and follow these steps,
Lt
_ L_
1
1,
Press [] to move the cursor
onto a list name. You are
now in view-names
context,
Press [] and [] to xqew list
names stored in other stat list editor columns,
2.
Press [_,
You are now in edit-elements
context,
You
may edit any element
in a list, All elements
of the
cmTent list are displayed
in braces
( { } )in the enhzyline, Press [] and [] to view more list elements.
3.
Press [gNY_ again. You are now in view-elements
context. Press [], [_, [], and [] to view other list
elements. The current element's full value is displayed
in the entt3z line.
4.
Press fNY_ again. You are now in edit-elements
context. You may edit the current element in the entl3z
line,
5,
Press [] until the cursor is on a list name, then press
[_ [INs]. You are now in enter-name
context,
20
2,55?
30
35
Z,SE7
2_
Z5
1:Edit
_c ={5, 10,25000...
LI
5
$ L2
i _5
i
......
I_5._ii_5,
_5
i 35
Asc :|5_10,25000...
_5C
2_5E?
_
_5
LI
$
L&
i 3_
i 35
LIc3)=25000010
AI_5
5
LI
$ L2
i _,5
......
2_5E7
25
i 35
LI(3)=|5000010
5
:i._
2,557
20
25
fist
_5
20
2.557
3_
35
_'1
5
i 15
2.5E7
_
25
_.5£?
i 30
i 35
_ L2
2
6,
Press
2.
7,
Press [], You are now back in _dew-elements
......
@,
You are now in view-naines
context.
Li =" LR_C+10"
_5C
5
:L_
2.5E7
2_
25
LI
im
i 20
i 2,557
i 30
i 35
$
L2
context.
......
LI(I)=15
Statistics
12-17
Stat List Editor Contexts
View-Elements
Context
In view-elements
context,
the enttT
line displays
the list
name, the cmTent
element's
place in that list, and the full
value of the current
element,
up to 12 chm'acters
at a time.
An ellipsis (...) indicates
that the element
continues
beyond
12 characte_\s.
hBC
Lt
5
t5
2._:E7
;'0
_0
$
._
2
tu_)=25000010
To page down the list six elements, press @
[]. To
page up six elements, press @
[]. To delete a list
element, press [DT0.Remaining elements shift up one row.
To insert a new element, press [g_ [INS]. 0 is the default
value for a new element.
Edit-Elements
Context
In edit-elements context, the data displayed
line depends on the previous context.
When you switch
elements context,
is displayed. You
then press [] and
R_(:
LI
in the enttT
to edit-elements
context from xqewthe full value of the cmTent element
can edit the value of this element, and
[] to edit other list elements.
$ L_:
ABe
LI
$
2g010
_0
_g
_0
3E:
2g
_co)=25000
25
A_co_=|5000
When you switch to edit-elements
context fronl viewnames context, the full vMues of 'all elements in the list
are displayed. An ellipsis indicates that list elements
continue beyond the screen. You can press [] and [] to
edit any element in the list.
g
t0
_000
IA_c:£5,
L1
1_;
$
k:;"
-,
Z0
Zg0t0
10, 25000._
L1
1
I0
Z_:000
_c
$
.2
1
ZO
7_010
=I5, 10, 25000...
Note: In edit-elements context, you can attach a formula to a list
name only if you switched to it from view-names context.
12-18
Statistics
View-Names
Context
In view-names
context,
and the list elements,
LI
5
10
15
_O
25
25
_O
_5
€
.2
the
entry
line displays
the list name
I
,Pc =15,10,25000_.
To remove
Remaining
deleted
To insert
Remaining
Enter-Name
Context
a list from the stat list editor, press [3_],
lists shift to the left one colunm.
The list is not
from
memow.
a name in the eutTent colunm,
press [_
eolunms
shift to the right one colunm,
In enter-name
context,
the Name= prompt
the entw line, and alpha-lock
is on.
[_NS],
is displayed
in
At the Name= prompt,
you can create a new list name,
Dkste a list nalne fronl L1 to L6 fronl tile keyboard,
or paste
an existing
list nalne froln the LIST NAMES menu
(Chapter
11). The • s3qnbol is not required
at the Name=
prompt.
_BC
r.
10
_OOO
_O
.1
') i
1_r
_0
-_SOiO
30
Name=_
To leave enter-name context without entering a list name,
press @.
The stat list editor switches to xqew-names
context.
Statistics
12-19
STAT EDIT Menu
STAT EDIT Menu
To display
the
STAT EDIT menu,
press
[_,
EDIT CALC TESTS
i: Edit..,
Displays the stat list editor.
2: SortA(
Sorts a list in ascending order.
3: SortD(
Sorts a list in descending order.
4: ClrList
Deletes all elements of a list.
5: SetUpEditor
Stores lists in the stat list editor.
Note: Chapter 13: Inferential Statistics describes the STAT TESTS
menu items.
SortA(,
SortD(
SortA( (sort ascending)
sorts list elements
fl'om low to high
values, SortD( (sort descending)
sorts list elements
fl'om
high to low values, Complex
lists are sorted based on
magnitude
(modulus).
SortA( and SortD( each can sort in
either of two ways.
With one listname,
SortA( and SortD( sort the elements
in listname
and update
the list in memory.
With two or more lists, SortA( and SortD( sort
keylistname,
and then sort each dependlist
by placing
its elements
in the same order as the corresponding
elements
in keylistname,
This lets you sort two-variable
data on X and keep the data pairs together,
All lists
nmst have the same dimension.
The sorted lists are updated
in nlen]ot_yL
SortA(listname)
SortD(listname)
SortA(k¢ylistname,depe_MJistl[,depezwllist2,...,depezMlist
SortD(k_ylistname,depe_Mlistl[,depe_wllist2,...,depe_Mlist
{5 4 3}I
,{1,2,3}+L4
{5, 4,33 +L {i
_ 2 3} I
I
_ortR (L_, L4 >Done
n])
n])
{3 4 5}
{3 2
_
L_
I}
Note: SortA( and SortD( are the same as SortA( and SortD( on the
LIST OPS menu.
CIrList
ClrList clears (deletes)
from memotT the elements
of one
or more listnames.
Clrkist also detaches
any fornmla
attached
to a listname.
ClrList
listname
l ,listname2,...,listname
n
Note: To clear from memory al! elements of all list names, use
OIrAIILists (Chapter 18).
12-20
Statistics
SetUpEditor
With SetUpEditor
you can set up the stat
list editor
display- one or more listnames
in the order that
specify-. You can specify
zero to 20 listnames.
to
you
SetUpEditor
[listnamel,listname2,...,listname
n]
SetUpEditor
names fron]
with one to 20 listnames
removes
the stat list editor and then stores
all list
listnames
the stat
list editor
colunms
in the specified
in
order,
beginningincoluinnl.
SetUPEditor
RESI
D,L_,L_,TIME,LOH
G,RI23
_E_ID
.00692
Done
L_
._
_ t
2
12
".001_ h
.OOBh _
",OOIB 6
",0106
t_
I_
16
RESZD<V=
-. 0013125_.
TIME
Lgn6
_123
120
30
s6
B2
?h
Is
It0
I1_
......
_6
98
I_
130
h
TIHE(!) =_
If you enter a listname
that is not stored
in lnelnory
already,
then listname
is created
and stored in memory;
becoines
an item on the LIST NAMES menu,
Restoring L1
through L6 to the
Stat List Editor
SetUpEditor with no listnames
removes
all list names
the stat list editor and restores
list names
kl through
the stat list editor columns
1 through
6.
it
fronl
ks in
SetUPEditor
Done
|
Lt
11
13.2
1_;
1B
2_.1
:*h,h
L1(I:_=6,5
L2
._1
,6B
,7_
,79
.BB
,99
1,01
._
1
_"
t
Lh
L5
[L6
$ h
1LI
h
5
6
[i6
Lh(1)=
Statistics
12-21
Regression
Model
Features
Regression
Model Features
STAT CALC menu items 3 through
C are regression
models
(page 12-24). The automatic
residual
list and automatic
_gression
equation
features
apply to all regression
models,
Diagnostics
display
mode applies
to some
regression
models.
Automatic
Residual List
Vclmn you execute
a regression
model, the automatic
residual
list feature
computes
and stores
the residuals
the list name RESID. RESID becomes
an item on the
LIST NAMES menu
OPS
The TI-83
elements.
(Chapter
11).
MRTH
uses the fommla
The next section
RESID = Ylistname
Automatic
Regression
Equation
to
below to compute
RESID list
describes
the variable
RegEQ.
- RegEQ(Xlistname)
Each regression
nlodel has an optional
argulnent,
regequ,
which you can specify- a Y= variable such as Y1. Upon
for
execution,
the regression
the specified
Y= variable
to
2, -5_÷t_l
equation
is stored automatically
and the Y= function
is selected.
-2
LinReg(ax+b)
Lz,Y_I
I
Lir_Re9
b= I.333333333
Regardless
of whether
the regression
equation
variable
RegEQ, which
secondmT
XY
E L_
[
nou _
,,,1=
B -2X+l.
13333333
you specify-
a Y= variable
no_
333333
I
for regequ,
always is stored to the TI-83
is item 1 on the VARS Statistics
EQ
menu.
TEST
PTS
3-'b
Note: For the regression
equation, you can use the fixed-decimal
mode setting to control the number of digits stored after the decimal
point (Chapter I ). However, limiting the number of digits to a small
number could affect the accuracy of the fit.
12-22
Statistics
Diagnostics
Display Mode
When
you execute
computes
coefficient)
sonle
t_gression
nlodels,
the TI-83
and stores
diagnostics
values for r (correlation
and r2 (coefficient
of determination)
or for N2
(coefficient
of determination).
r and r2 are computed
models.
and stored
LinReg(ax+b)
LinReg(a+bx)
LnReg
ExpReg
R2 is computed
and stored
QuadReg
for these
regression
PwrReg
for these
t_gression
CubicReg
models.
QuartReg
The r and r2 that are computed
for LnReg, ExpReg, and
PwrReg are based on the linearly
transformed
data. For
example,
for ExpReg (y=ab^x),
r and r2 are computed
on
In y=ln a+x(ln b).
By- default,
these values are not displayed
with the results
of a regression
model when you execute
it. However,
you
can set the diagnostics
display mode by executing
the
DiagnosticOn or DiagnosticOff instruction.
Each instruction
is in the CATALOG (Chapter
15).
det(
DiagnostioO_
vDiagnostioOn
CATALOG
diM(
Note: To set DiagnosticOn or DiagnosticOff from the home
screen, press _
[CATALOG], and then select the instruction for the
mode you want. The instruction is pasted to the home screen. Press
to set the mode.
When
DiagnosticOn
the results
when
is set,
di_nostics
you execute
OiagnostioOnoone
L_Reg(a×+b)
m'e displayed
a regression
LinReg
_=_x+b
L,,
a=-2
b=1.333333333
ni=.9230769231
n=-.9607689228
When DiagnosticOff
is set, di_nostics
are not
with the results
when you execute
a regression
Diagno_tioO¢_one
L_Reg(ax+b)
with
model.
displayed
model.
LinReg
_=ax+b
LI,
a=-2
b=1.333333333
Statistics
12-23
STAT
CALC
STAT CALC
Menu
Menu
To display
EDIT
the
CALC
1:1
Var
Stats
2:2
Var
Stats
3:Med
STAT CALC menu,
press
[KY_] [_.
TESTS
Calculates
1-vmiable
statistics,
Calculates
2-vmiable
statistics.
Calculates
a lnedian-lnedian
line,
Fits a linear model to data.
Med
4: LinReg(ax+b)
5:QuadReg
6: CubicReg
7: QuartReg
8: LinReg(a+bx)
9: LnReg
O: ExpReg
A: PwrReg
B: Logistic
C: SinReg
Fits
Fits
a quadratic
model to data,
a cubic model to data.
Fits
Fits
a quartic
model to data,
a linear model to data.
Fits
Fits
Fits
Fits
Fits
a logarithmic
model to data,
an exponential
model to data,
a power
model to data,
a logistic model to data,
a sinusoidal
model to data,
For each STAT CALC menu item, if neither
Xlistname
nor
Ylistname
is specified,
then the default
list names m'e kl
and k2. If you do not specifyfreqlist,
then the default
is 1
occurrence
of each list element.
Frequency of
Occurrence for
Data Points
For most STAT CALC nlenu itenls,
data occurrences,
or frequencies
you can specify
(freqlist).
Each element
infreqlist
indicates
corresponding
data point or data
you are analyzing.
how many
pair occurs
a list of
times the
in the data
set
For example,
if 1_1={15,12,9,14} and LFRlaQ={1,4,1,3}, then
the TI-83 interprets
the instruction
1-Vat Stats 1.1, LFREO to
mean that 16 occurs once, 12 occurs
four times, 9 occurs
once, and 14 occurs
three times.
Each element
element
nmst
infreqlist
be > 0.
nmst
be _>0, and at least
one
Nonintegerfreqlist
elements
m'e valid. This is useful when
entering
frequencies
expressed
as percentages
or parts
that add up to 1. However,
iffreqlist
contains
noninteger
frequencies,
Sx and Sy are undefined;
wdues m'e not
displayed
for Sx and $y in the statistical
results,
12-24
Statistics
1-Var Stats
1-Var Stats (one-variable
statistics) analyzes data with one
measm'ed variable. Each element infreqlist
is the
frequency of occurrence
for each corresponding
data point
in Xlistname.
freqlist elements nmst be real numbers > 0.
1-Var Stats [Xlistnamefreqlist]
_iVaP
2-Var Stats
Stats
LI,L
2-Var Stats (two-variable statistics) analyzes paired data.
Xlistname
is the independent variable. Ylistname
is the
dependent variable. Each element infreqlist
is the
frequency of occutTence for each data pair
(Xlistname, Ylistname),
2-Var Stats [Xlistname,_Tistnome_freqlist]
Med-Med
Med-Med (nmdian-n]edian)
(ax+b)
to the data using the median-nmdim_
line (resistmlt
line)
technique,
calculating
the sunul]aYy points xl, yl, x2, y2, x3,
and y3. Med-Med displays
values for a (slope)
and
b (y-intercept).
fits the model
equation
y=ax+b
Med-Med[Xlis_ame,_is_ame_v_ist,regequ]
_=ax+b
_ed-Med
LinReg
(ax+b)
L_,L_,Yz
a=.875
Med-Med
b=1.541666667
I
LinReg(ax+b) (linear regression) fits the model equation
y=ax+b to the data using a least-squares fit. It displays values
for a (slope) and b (y-intercept); when DiagnosticOn is set, it
also displays values for r2and r,
LinReg(ax+b) [Xlistname,Ylistname_freqlist,regequ]
QuadReg
(axZ+bx+c)
QuadReg (quadratic regression)
fits the second-degree
polynomial y=ax2+bx+c to the data. It displays values for a,
b, and c; when DiagnosticOn is set, it also displays a value
for R2. 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_freqlist,regequ]
Statistics
12-25
CubicReg
(ax3+bx2+cx+d)
CubicReg
(cubic
regression)
fits the third-degree
polynomial
y=ax:_+bx2+ex+d
to the data. It displays
wdues
for a, b, c, and d; when DiagnosticOn
is set, it also displays
a wdue for R2. For four points, the equation
is a polynomial
fit; for five or more, it is a polynomial
four points are requil_d.
CubicReg
Qua_Reg
(ax4+bx3+cx2+
dx+e)
[Xlistname,_istnamedCreqlist,regequ
At least
]
QuartReg (quartic
regression)
fits tile fourth-degree
polynomial
y=ax4+bx:%cx2+dx+e
to the data. It displays
values for a, b, c, d, and e; when DiagnosticOn
is set, it also
displays
a wdue for R 2. For five points, the equation
is a
polynomial
fit; for six or more, it is a polynomial
regression.
At least five points
are required.
OuartReg
LinReg
(a+bx)
regression.
[Xlistname,YlistnamedCreqlist,regequ]
LinReg(a+bx) (linear regression)
ills the model equation
y=a+bx to the data using a least-squalls
fit. It displays
values
for a (y-intercept)
and b (slope); when DiagnosticOn
is set, it
also displays
values for r2 and r.
LinReg(a+bx)
LnReg
(a+b In(x))
[Xlistname,_istnamedCreqlist,regequ
LnReg (logarithmic
regression)
y=a+b ln(x) to the data using
]
fits the model equation
a least-squares
fit and
transformed
values ln(x) and y. It displays
b; when DiagnosticOn
is set, it also displays
and r.
values for a and
values for r2
LnReg [Xlistname,YlistnamedCreqlist,regequ]
ExpReg
(ab x)
ExpReg (exponential
regression)
fits the model equation
y=ab _ to the data using a least-squares
fit and transformed
values x and ln(y). It displays
values for a and b; when
DiagnosticOn
is set, it also displays values for r2 and r.
ExpReg
12-26
Statistics
[Xlistname,YlistnamedCreqlist,regequ]
PwrReg (power l_gression) fits the model equation y=ax b to
the data using a least-squares fit and transformed values
ln(x) and ln(y). It displays wdues for a and b; when
DiagnosticOn is set, it 'also displays values for r2 and r.
PwrReg
(axb)
PwrReg [Xlistname,Ylistname_freqlist,regequ]
Logistic
c/(l+a*e
-bx)
Logistic fits the model equation y=c/(l+a*e
-bx) to tile data
using an iterative least-squares
fit. It displays values for a, b,
and c.
Logistic
SinReg
a sin(bx+c)+d
[Xlistname,Ylistname_reqlist,regequ]
SinReg (sinusoidal
regression)
fits the model equation
y=a sin(bx+e)+d
to the data using an iterative
least-squares
fit. It displays
values for a, b, c, and d. At least fore" data
points m'e required.
At least two data points per cycle m'e
required
in order to avoid aliased
frequency
estimates.
SinReg
[iterations,Xlistname,I_istname,period,regequ]
iterations
will iterate
is the nlaxinlonl
number
of times the algorithm
to find a solution.
The value for iterations
can
be an integer
The algorithm
_>1 and _<16; if not specified,
nlay find a solution
before
the default is 3.
iterations
is
l_a('hed.
Typically,
lm'ger values for iterations
result in
longer execution
times and better accuracy
for SinReg,
and
vice versa.
A period
guess is optional.
If you do not specify-period,
the
difference
between
time values in Xlistname
must be equal
and the time values nmst be ordered
in ascending
sequential
order. If you specify-period,
the algorithm
nlay
find a solution
nlore quickly,
or it nlay find a solution
when
it would not have found one if you had omitted
a value for
period.
If you specify period,
the differences
between
time
values in Xlistname
can be unequal.
Note: The output of SinReg is always in radians, regardless of the
Radian/Degree
mode setting.
A SinReg
example
is shown
on tile next
page.
Statistics
12-27
SinReg Example:
Daylight Hours in
Alaska for One
Year
Compute
the regression
daylight in Alaska durin
se_(X,
X, 1,361,30
)+LI : {5.5,8, ii, 1
3.5, 16.5, 19, 19.5
,17, 14.5, 12.5,8.
5_6.5,5.5}+Lz
{5.5 8 Ii 13.5
model
for the number
[liar
of
Notz _lotx
orr
IT_Pe:_I..
_ _
-_
li<,listiE
16Jlist:Lz
Mark:
SinReg
of hours
one year.
° []
.
LI,Li,VI1
SinReg
_=a*sin(bx+c)+d
a=6.770292445
b=.8162697853
o=-1.215498579
d=12.18138372
With noisy data, you will achieve better convergence
results when you specify- an accurate estimate for period.
You can obtain aperiod guess in either of two ways.
•
•
Plot the data and trace to determine the x-distance
between the beginning and end of one complete period,
or cycle. The illustration above and to the right
graphically depicts a complete period, or cycle.
Plot the data and trace to determine the x-distance
between the beginning and end of N complete periods,
or cycles. Then divide the total distance by N.
M'ter your fit_t attempt to use SinReg and the default value
for iterations
to fit the data, you may find the fit to be
approximately
correct, but not optimal. For an optimal fit,
execute SinReg 16,Xlistname,I_istfzame,2_
I b where b is
the value obtained froln the prexqous SinReg execution.
12-28
Statistics
Statistical
Variables
The statistical
variables
are calculated
and stored
as indicated
below,
To
access these variables
ff)r use in expressions,
press _,
and select
5:Statistics.
Then select the VARS menu shown in the colunm
below under
VARS menu. If you edit a list or change
vm'iables
m'e clem'ed.
Variables
the type
of analysis,
1-Var
Stats
2-Var
Stats
all statistical
Other
VARS
menu
mean of x values
_
_
XY
SUnl of x values
Ex
Ex
E
sunl of X2values
Yx2
Yx2
E
Sx
Sx
XY
_x
Gx
XY
n
n
XY
_
XY
2y
1;
sample
standard
population
nulnber
deviation
standard
of x
deviation
of x
of data points
mean of y values
sunl of y values
sunl
of y2 values
sample
standard
population
dexqation of y
standard
deviation
of y
sunl of X * y
'Fy2
y
Sy
XY
_y
XY
Zxy
Z
lninimuln
of x values
minX
minX
XY
lnaxilnuln
of x values
maxX
max)(
XY
lninimuln
of y values
minY
XY
lnaxilnum
of y values
maxY
1st quartile
median
3rd quartile
regression/fit
polynomial,
coefficients
coefficients
Logistic, and SinReg
correlation
coefficient
coefficient
of determination
regression
equation
sulnl:laI T points (Med-Med only)
Q1 and Q3
XY
Q1
PTS
Med
PTS
Q3
PTS
a, b
EQ
a, b, c,
d, e
EQ
r
EQ
r2, R2
EQ
RegEQ
EQ
xl, yl, x2,
y2, x3, y3
PTS
The first quartile (Q1) is the median of points between
minX and Meal (median). The third quartile (Q3) is the
median of points between Med and maxX.
Statistics
12-29
Statistical
Entering Stat
Data
Analysis
in a Program
You can enter statisticM data, calculate statistical results,
and fit models to data from a program. You can enter
statistical data into lists directly within the program
(Chapter 11),
: {1,2,3}÷LI
PROGRRM:
: {-I, -2, STRTS
-5}÷Lz
Statistical
Calculations
To perform
these steps,
a statistical
1, On a blank
calculation
]
calculatkm
from
a program,
line in the progrmn
editor,
select
from the $TAT CALC menu.
follow
the type of
2, Enter the names of the lists to use in the calculation.
Separate the list names with a conlnla,
3, Enter a conulla and then the name of a Y= variable, if you
want to store the regression equation to a Y= variable.
PROGRRM:STRT5
:{1,2,3}÷LI
:{-I,-2,-5}÷L1
:LinReg(ax+b)
12-30
Statistics
LI
Statistical
Plotting
Steps for Plotting
Statistical Data in
Lists
You call plot
types of plots
modified box
plot. You can
statistical data that is stored in lists. The six
available m'e scatter plot, xyLine, histogram,
plot, regulm" box plot, and normal probability
define up to three plots.
To plot statistical
data in lists, follow these steps.
1, Store the stat data in one or more lists.
2, Select or deselect
¥= functions
as appropriate.
3, Define the stat plot.
4. Turn on the plots you want to display.
5, Define the v_ewing window.
6, Display and explore
(Scatter)
the graph.
Scatter plots plot the data
coordinate pairs, showing
( + ), or dot ( • ). Xlist and
You can use the same list
points fronl Xlist and Ylist as
each point as a box ( o ), cross
Ylist nmst be the sanle length.
for Xlist and Ylist,
"t]';i'Off
÷
T'_Pe:_m_,._
Xlist.;_t-Vli__L:Lz
÷
+÷
:+_
Mark: [] []
(xyLine)
÷
k____
÷
.........
xyLine is a scatter
plot in which the data points
are plotted
and connected
in order of appearance
in Xlist and Ylist.
You nlay want to use SortA( or SortD( to sort the lists
beffwe you plot them (page 12-20).
_Pe:
-L_ _
J_
Y,IisL:LI_
Vlist:Lz
Mark:
[] *
.
Statistics
12-31
Histogram plots
(Histogram)
one-variable
data. The Xscl window
variable
value determines
the width of each bar, beginning
at Xmin.
ZoomStat
adjusts Xmin, Xmax, Ymin, and Ymax to include all
values, and 'also adjusts Xscl. The inequality
(Xmax - Xmin) / Xscl _<47 must be true. A value that occurs
on the edge of a bar is counted
in the bar to the right.
m
0f'€
i
;
X list,;"Ct
Fr.e_:
(ModBoxplot)
Ip_in=_B.4Bt30B
I
ModBoxplot
(modified
box plot)
like the regular box plot, except
Interquartile
Range beyond the
Range is defined
_s the difference
quartile
Q3 and the first quartile
plotted
individually
beyond
the
(5 or + or ,) you select. You can
are called outliers.
The prompt
ff)r outlier points
is the maximunl
point (maxX)
(minX). When outliers
exist,
display x=. When no outliers
prompts
for the end of each
and Q3 define the box (page
plots one-variable
data,
points that are 1.5 *
quartiles.
(The Interquartile
between
the third
Q1.) These points are
whisker,
using the Mark
trace these points,
which
is x=, except
when the outlier
or the minimunl
point
the end of each whisker
will
exist, minX and maxX are the
whisker.
O1, Med (median),
12-29).
Box plots are plotted
with respect
to Xmin and Xmax, but
ignore Ymin and Ymax. When two box plots are plotted,
the
first one plots at the top of the screen and the second
plots
in the middle.
When three a_ plotted,
the first one plots at
the top, the second
in the middle,
and the third at the
bottonL
Lt
1
+
2: Plot2...On
,'D,-L2
1
3: P 1 ot3...O_f
L1
LZ
4.&P lotsO_
12-32
Statistics
+
Boxplot
(Boxplot)
(regular
box
plot)
plots
one-variable
data.
The
whiskers
on the plot extend
fronl tile nlininlunl
data point
in the set (minX) to the first quartile
(Q1) and from the third
quartile
(Q3) to the nlaxinmln
point (maxX). The box is
defined by Q1, Med (median),
and Q3 (page 12-29).
Box plots are plotted
with respect
to Xmin and Xmax, but
ignore Ymin and Ymax. When two box plots are plotted,
the
first one plots at the top of the screen and the second
plots
in the middle.
When three ale plotted,
the first one plots at
tile top, tile second
in tile middle,
and the third at the
bottonl.
L,t
li q
2: P lot2...0n
le
3: Plot3...Of'f"
44,P 1otsOtPt"
(NormProbPIot)
,a ....
NormProbPIot (normal probability plot) plots each
observation X in Data List vel\sus the corresponding
quantile z of the standard nonnM distribution,
If the plotted
points lie close to a straight line, then the plot indicates
that the data are normal.
Enter
a valid
list nalne
in the Data List field.
Select
X or Y
for the Data Axis setting.
•
If you select
the z-values
X, tile TI-83 plots
on the y-axis.
tile data
on tile x-axis
and
•
If you select
the z-values
Y, the TI-83 plots
on the x-axis.
the data
on the y-axis
and
[PandHorp_(35,
)÷L_
2,90
7
36
Plot1 p1OI:;_
m
0f'f"
T_Pe:
Data
Data
Mar'k:
P 3:Lh
-L_ b-_ 31_
_.- a]b I
Crst.--: L _
Axis:@
Y
= *
II
N=')E.E:1321E
?=.?hEIBB19
Statistics
12-33
Defining the
Plots
To define
a plot,
1, Press [_
displayed
follow
these
steps.
[STAT PLOT]. The STAT PLOTS menu
with the current
plot definitions,
2, Select the plot you want to use, The stat
displayed
for the plot you selected,
3, Press _
statistical
Select
options
Statistics
is
you select
On or Off,
the type of plot.
checked
Each
type prompts
for the
in this table.
Plot Type
XList
YList
Mark
Freq
Data
List
Data
Axis
_L_ Scatter
_
_i
_
rl
[]
[]
xyLine
_
121
_
[]
[]
[]
Zn_ Histogram
_
[]
[]
_
[]
[]
o,.
_
[]
_
_
[]
[]
_:_> Boxplot
_
[]
[]
_
[]
[]
[__
[]
[]
_
[]
_
lTI
ModBoxplot
NormProbPIot
Enter
12-34
editor
to select On if you want to plot the
data imnlediately.
The definition
is stored
whether
4,
plot
is
list names
or select
options
for the plot
•
Xlist (list name
containing
independent
•
Ylist (list name
containing
dependent
•
Mark (aor
•
Freq (frequency
•
Data List (list nanle for NormProbPIot)
•
Data Axis (axis
type,
data)
data)
+ or.)
list for Xlist elements;
on which
to plot
default
Data List)
is 1")
Displaying Other
Stat Plot Editors
Each stat plot has a unique stat plot editor. The name of
the current stat plot (Plot1, Plot2, or Plot3) is highlighted in
the top line of the stat plot editor. To display the stat plot
editor for a different plot, press [], [], and [] to lnove the
cursor onto the name in the top line, and then press [_.
The stat plot editor for the selected plot is displayed, and
the selected name remains highlighted.
_" _
Xlist:L1
Vlist:Lz
Mark: [] *
Turning On and
Turning Off Stat
Plots
L_
PlotsOn and PlotsOff allow you to turn on or turn off stat
plots from the home screen or a program. With no plot
number, PlotsOn turns on M1plots and PlotsOff turns off 'all
plots. With one or more plot numbers (1, 2, and 3), PlotsOn
turns on specified plots, and PlotsOff turns off specified
plots.
PlotsOff [1,2,3]
PlotsOn [1,2,3]
PlotsOf'f"
Note: You also can turn on and turn off stat plots in the top line of the
Y= editor (Chapter 3).
Statistics
12-35
Defining the
Viewing Window
Stat plots are displayed on the current graph. To define the
xqewing window, press _
and enter values for the
window variables. ZoomStat redefines the xqewing window
to display all statistical data points.
Tracing a Stat
Plot
When you trace a scatter plot or xyLine, tracing begins at
the first element in the lists.
VClmnyou trace a histogram, the cursor nloves fronl the
top center of one colunm to tile top center of tile next,
starting at the first colunm.
When you trace a box plot, tracing begins at Med (the
median). Press [] to trace to Ol and minX. Press [] to trace
to O3 and maxX.
When you press [] or [] to move to another plot or to
another Y= function, tracing moves to the current or
beginning point on that plot (not the nearest pixel).
The ExprOn/ExprOff format setting applies to stat plots
(Chapter 3).When ExprOn is selected, the plot number and
plotted data lists are displayed in the top-left corner.
12-36
Statistics
Statistical
Plotting
Defining a Stat
Plot in a Program
in a Program
To display a stat plot fronl a program,
then display the graph.
define the plot, and
To define a star plot from a program, begin on a blank line
in the program editor and enter data into one or more lists;
then, follow these steps.
1. Press [g_ [STATPLOT]to displw tile STAT PLOTS menu.
T"tPE
MARK
i3:Plot3(
i4.PlotsOgg
5:Plot.sOn
Select the plot to define, which pastes
Plot3( to the cursor location.
Plot1(, Plot2(, or
PROGRAM:PLOT
:{I,2,3,4}+LI
:{5,6,7,8}+Lz
:Plot2(I
Press[_[STATPLOT][_todisplaytheSTATTYPE
nlenu,
PLOTS _
._Soatter
z: x_Line
MARK
5:Bo>,'g
Iot
S:HorMProbPlot
Select
plot
the type of plot,
type
to the cm'sor
which
pastes
the name
of the
location.
PROGRAM:PLOT
:{1,2,3,4}+LI
:{5,6,7,8}+Lz
:Plot2(SoatterI
Statistics
12-37
5_
Press
[].
Enter
the list names,
separated
by eonunas.
6, Press [] [_
[STAT PLOT] [] to display the
STAT PLOT MARK menu. (This step is not necessaqyyou selected
3:Histogram
or 6:Boxplot
in step 4.)
Select the type of nlark (D or + or °) for each data
The selected
mm'k symbol is pasted to the cursor
location.
Press
[]
_
to complete
: {I02,3,4}÷LI
: {5, 6, 7,8}÷Lz
: Plot2(Soattet-,
PROGRAM: PLOT
Displaying a Stat
Plot from a
Program
To displayinstruction
(Chapter
line,
L
3),
::
DisParaF-h
Statistics
point.
a plot from a program,
use the DispGraph
(Chapter
16) or any of the ZOOM instructions
PROGRR_I: PLOT
: {1,2,3,4}÷LI
: ,.5,6, _, 8}+Lz
: Plot2(ScatteP,
I,Lz,=)
12-38
the command
if
L
PROGRRM:PLOT
:{1,2,3,4}÷Lt
:_506,7,8}÷Lz
:Plot2(ScatteP,L
I,Lz,.)
::_°°MStat
3
Contents
and Distributions
InferentialStatistics
Getting Started: Mean Height of a Population
Inferential
Star Editors ...................................
STAT TESTS Menu ......................................
Inferential
Statistics
Input
I)eseriptions
............
..................
13-2
13-6
13-9
13-26
Test and Interval Output Variables .......................
Distribution
Functions
...................................
13-28
13-29
Distribution
13-35
'_
Shading
TEXAS
.....................................
T1=83
iNSTRUMENTS
z=.ee:l.
I_=._?e:_
J
STATPLOT
TBLSET
FORMAT
Inferential
CALC
Statistics
TABLE
and
Distributions
13-1
Getting
Getting
Started:
Started
Mean Height of a Population
is a fast-paced
introduction.
Read the chapter
for details.
Suppose you want to estimate the mean height of a population of women given
tile random sample below. Because heights among a biological population tend
to be normally distributed, a t distribution confidence interval can be used
when estimating the mean. The l0 height wdues below are the first l0 of 90
wdues, randonfly generated from a normally distributed population with an
assumed mean of 165.1 cm. and a standard dexqation of 6.35 cm.
(randNorm(165.1,6.36,90)
with a seed of 789).
Height
169.43
168.33
159.55
(in cm.)
169.97
of Each
159.79
of 10 Women
181.42
Press [gTKg][gNT_ to display the stat list
editor.
Press [] to nlove the cursor
onto L1, and
then press [_] [,NS]. The Name= prompt
is
displayed
on the bottom
line. The [] cursor
indicates
that alpha-lock
is on. The
existing
list name eolunms
shift to the
171.17
162.64
1
167.15
159.53
.I
L_
I
.1
L;'
1
L_
3
HaMe==
right.
Note: Your stat editor may not look like the one
pictured here, depending on the lists you have
already stored.
Enter [H] [G] [H] [T] at the Name= prompt,
and then press [gNT_. The list to which
you will store the women's
height data is
created.
Press [] to move the cursor
onto the first
row of the list. HGHT(1)=is displayed
on the
bottom
line.
Press 169 [] 43 to enter the first height
value. As you enter it, it is displayed on the
bottom line.
Press [gNT_. The value is displayed in the
first row, and the rectangular
cursor
nloves to the next row.
Enter the other nine height values the
sanle
way,
13-2
hfferential
Statistics
and
Distributions
HGHT
mmm
H6HT(1) =
HGHT
1_9.7B
171.17
16Y.tg
H6HT(11)=
.1
4.
Press [gY_ [] to display the STAT TESTS
menu, and then press [] until 8:Tlnterval is
highlighted.
EDIT CRLCIII_
2ST-Test,,
3:2-SamPZTest
4:2-Sar4eTTest_
7:ZIntervM,.,"[_tlTInterval...
5.
Press _
to select 8:Tlnterval. The
inferential stat editor for Tlnterval is
displayed. If Data is not selected for Inpt:,
press [] [ggY_ to select Data.
TlntervM
InPt:_
Stats
List:HGHT
Fre_:1
C-Level:.99
Calculate
Press [] and [H] [G] [a] [T] at the List:
prompt (alpha-lock is on).
Press [] [] [] [email protected] enter a 99 percent
confidence level at the C-Level: prompt.
6.
Press [] to move the cursor onto Calculate,
and then press IgOr. The confidence
intet¢TM is calculated, and the Tlnterval
results are displayed on the home screen.
Interpret
Tlnterval
(159.74,173.94)
R=166.838
Sx=6.907879237
n=lO
the results.
The first line, (159.74,173.94), shows that the 99 percent confidence inte_xal for
the population mean is between about 159.74 cm. and 173.94 cm. This is about
a 14.2 cm. spread.
The .99 confidence level indicates that in a vet3z lm'ge number of samples, we
expect 99 percent of the intervals calculated to contain the population mean.
The actual mean of the population sampled is 165.1 cm. (introduction;
page
13-2), which is in the calculated interval.
The second line gives the mean height of the sample N used to compute this
intet_'al. The third line gives the sample standard deviation Sx. The bottom line
gives the sample size n.
Inferential
Statistics
and
Distributions
13-3
To obtain a more precise bound on the population mean _tof women's heights,
increase the sample size to 96. Use a sample mean ._ of 163.8 and sample
standard deviation Sx of 7.1 calculated from the larger random sample
(introduction;
page 13-2). This time, use the Stats (sunullal_y
statistics) input
option.
Press [g_g] [] 8 to display" the inferential
star editor for Tlnterval.
Press [] [g_N to select Inpt:Stats. The
editor changes so that you can enter
sunullal_ statistics as input.
8.
Press
[] 163 [] 8 [N?_
to store
Press
7 [] 1 [ggY_
Press
90 [NTgN to store
to store
163.8 to _.
7.1 to Sx.
96 to n.
Press [] to move the cursor onto Calculate,
and then press [g_N to calculate the new
99 percent confidence interval. The results
are displayed on the home screen.
TInterual
InPt:Data I¢_
5:166.838
Sx:G.90787923Z_
n:10
C-Leuel:.99
Calculate
TInterual
InPt:Data _
R:IG3.8
Sx:7.1
n:90
C-Leuel:.99
Calculate
TInterual
(161.83,165.77)
R=163.8
Sx=7.1
n=90
If the height distribution
among a population of women is normally distributed
with a nlean [J of 165.1 cm. and a standard deviation _ of 6.35 cm., what height
is exceeded by only 5 percent of the women (the 95th percentile)?
10. Press
@
to clear
the home
Press [2_] [DISTR] to display
(distributions)
menu.
13-4
hfferential
Statistics
screen.
the DISTR
and
Distributions
DRAW
normalcd?(
3:invNorm(
4:tPd?(
5:tod¢(
6:XZpd?(
74XZod¢(
11.Press
3 to
invHorr_(.
1_ 6.35)
invNorm( to the home
paste
screen.
Press_
95_
.95 is the area,
lS5_
1_
6_ 35_
1G5.1 is p, and 6.35 is o.
The result is displayed
women
are taller than
on the home
175.5 cm.
I
screen;
Now graph and shade the top 5 percent
it shows
Ymin=-.02
Ymax=.08
Yscl=0
13. Press [_ [DISTR]
DRAW menu.
that
five percent
Xres=l
STR Llli'_l_
ShadeNoPm
3: ShadeX
4: ShadeF
14. Press
home
Press
_
to paste
screen.
[_
[ANS] []
ShadeNorm(
1 _
[EE l 99_
of the
gINDOg
XMin=145
Xmax=185
Xsol=5
YMin=-.82
YMax=.88
Yscl=O
XPes=1
to display the DISTR
[]
175.5448285
of the population.
12. Press [_
and set the window
variables to these values.
Xmin=145
Xmax=185
Xscl=5
95,165.
to the
165[_
1
D6[]asD.
(
z(
(
invHor.M(. 95,165.
1,6.35)
175. 5448285
ShadeNoPFKRns,
1E
99, 165. 1,6.35)I
Ans (175.5448205
from step 11) is the
lower bound.
1E99 is the upper bound.
The
normal
curve is defined
by a mean p of
165.1 and a standm'd
deviation
o of 6.35.
15. Press
[gfff_
to plot
and shade
the normal
eui%re.
Area is the area
above
low is the lower
bound.
bound,
the 95th percentile.
up is the upper
firca=.OB
low='l
Inferential
Statistics
and
7_:._:LI_:
up,=:LEBB
Distributions
13-5
Inferential
Displaying the
Inferential Stat
Editors
Stat Editors
When you select a hypothesis test or confidence intetsTal
instruction from the home screen, the appropriate
inferential statistics editor is displayed. The editors yaw
according to each test or interval's input requirements.
Below is the inferential stat editor for T-Test.
T-Test
InPt:_
Stats
List:L1
Fne_:l
_:_
<_
Calculate
>_n
Orau
Note: When you select the ANOVA( instruction, it is pasted to the
home screen. ANOVA( does not have an editor screen.
Using an
Inferential Stat
Editor
To use an inferential stat editor, follow these steps.
1. Select a hypothesis test (Jr confidence intet_'al from the
STAT TESTS menu. The appropriate
editor is displayed.
2. Select Data or Stats input, if the selection
The appropriate
editor is displayed.
is available.
3. Enter real numbers, list names, (Jr expressions
argument in the editor.
for each
4. Select the alternative hypothesis (€, <, or >) against
which to test, if the selection is available.
5. Select No or Yes for the Pooled option, if the selection
available.
6. Select Calculate (Jr Draw (when Draw is available)
execute the instruction.
•
When you select Calculate, the results
on the honle screen.
•
When you select Draw, the t_sults
graph.
is
to
are displayed
are displayed
in a
This chapter describes the selections in the above steps for
each hypothesis test and confidence intetwal instruction.
13-6
hfferential
Statistics
and
Distributions
Select Data or
Stats input
Stats
Sete_ an alternative
hypothesis
Enter values for
arguments
Calculate
Selecting
Stats
Data or
Select Calculate
or Draw output
Omau
Most inferential
stat editors
prompt
you to select one of
two types of input. (1-PropZlnt
and 2-PropZTest,
1-PropZlnt
and 2-PropZlnt, x2-Test, and LinRegTTest do not,)
•
Select
Data to enter
the data
•
Select Stats to enter
and n, as input.
sunmm_
lists
_s input.
statistics,
To select Data or Stats, move the cursor
Stats, and then press [ggY_.
Entering
the
Values for
Arguments
such
as 2, Sx,
to either Data or
Inferential
stat editors
require
a value for ever7 argument.
If you do not know what a pm'ticulm" argument
symbol
represents,
see the tables on pages 13-26 and 13-27.
When you enter values in any inferential
stat editor, the
TI-83 stores them in nlenlory
so that you can run many
tests or intetnT'als without
having to reenter
evet3z vMue.
Selecting
an
Alternative
Hypothesis
(_ < >)
Most of the inferential
prompt
you to select
stat editors
one of three
•
The first is a _ Mternative
the Z-Test.
•
The second
is a < alternative
for tile 2-SampTTest.
•
The third is a > alternative
the 2-PropZTest.
To select an alternative
appropriate
alternative,
Inferential
for the hypothesis
tests
alternative
hypotheses.
hypothesis,
such
hypothesis,
hypothesis,
as p¢p0 for
such
such
as pl<_t2
as pl>p2
hypothesis,
nlove the cursor
and then press [ggY_.
Statistics
and
Distributions
for
to the
13-7
Selecting
the
Pooled Option
Pooled (2-SampTTest
whether
the vmiances
or Draw
for a Hypothesis
Test
m'e to be pooled
only)
Select No if you do not want the vmiances
Population
vm'iances
can be unequal.
•
Select Yes if you want
wu'iances
m'e assumed
the wu'iances
to be equal.
option,
move
specifies
for the
•
To select the Pooled
then press [_T_].
Selecting
Calculate
and 2-SampTInt
calculation,
pooled.
pooled.
the cursor
Population
to Yes, and
Alter you have entered all arguments in an inferential star
editor for a hypothesis test, you nmst select whether you
want to see the calculated results on the home screen
(Calculate) or on the graph screen (Draw).
•
•
Calculate c_dculates the test results and displays the
outputs on the home screen.
Draw draws a graph of the test results and displays the
test statistic and p-value with the graph. The window
variables m'e adjusted automatically
to fit the graph.
To select Calculate or Draw, nlove the cursor to either
Calculate or Draw, and then press IgOr. The instruction
inunediately
executed.
Selecting
Calculate
for a
Confidence
Interval
is
Alter you have entered
all arguments
in an inferential
star
editor for a confidence
inte_'al,
select Calculate to display
the results.
The Draw option is not available.
When you press [g_EN, Calculate
calculates
the confidence
inte_w'M results
and displays
the outputs
on the home
screen.
Bypassing
Inferential
Editors
the
Stat
To paste
a 1wpothesis
test
or confidence
inte_-'al
instruction
to the home screen without
displaying
the
corresponding
inferential
stat editor, select the instruction
you want from the CATALOG menu. Appendix
A describes
the input syntm, c for each hypothesis
test and confidence
inte_nTal instruction.
12-Sar,_PZTest
(
I
Note:You can pastea hypothesis
testorconfidenceinterval
instruction to a command line in a program. From within the program
editor, select the instruction from either the CATALOG (Chapter I5)
or the STAT TESTS menu.
13-8
hfferential
Statistics
and
Distributions
STAT TESTS
Menu
STAT TESTS
Menu
To display the STAT TESTS menu, press [gT_] [_. When you
select an inferential statistics instruction, the appropriate
inferential stat editor is displayed.
Most STAT TESTS instructions
store some output varial_les
to memory. Most of these output variables are in the TEST
secondmT menu (VARS menu; 5:Statistics). For a list of
these varial)les, see page 13-28.
EDIT CALC TESTS
1:Z Test,..
Test for 1 p, known
2:T Test,.,
Test for i p, unknown
3:2 SampZTest...
Test compming 2 #'s, known _'s
4:2 SampTTest,..
Test compming 2 #'s, unknown
_'s
5:1 PropZTest...
Test for 1 proportion
6:2 PropZTest,..
Test compming 2 proportions
7:Zlnterval,.,
Confidence intmwal for 1 #, known
8:Tlnterval,.,
Confidence intmwal for 1 #, unknown
9:2
Conf. int. for diff. of 2 p's, known o's
Conf. int. for diff. of 2 #'s, unknown o's
Confidence int. for 1 proportion
Confidence int. for diff. of 2 props
Chi-squm'e test for 2-way tables
Test compming 2 o's
t test for regression slope and p
One-way analysis of variance
SampZlnt.,.
0:2 SampTlnt.,.
A:I PropZlnt.,.
B:2 PropZlnt.,.
C:X2 Test,,.
D:2 SampFTest...
E: LinRegTTest,..
F: ANOVA(
Note: When a new test or interval is computed, all previous output
variables are invalidated.
Inferential Stat
Editors for the
STAT TESTS
Instructions
In this chapter, the description of each STAT TESTS
instruction shows the unique inferential stat editor for that
instruction with example arguments.
•
•
Descriptions of instructions that offer the Data/Stats
input choice show both types of input screens.
Descriptions of instructions
that do not ofl_r the
Data/Stats input choice show only one input screen.
The description
that instruction
•
•
then shows the unique output
with the example results.
screen for
Descriptions of instructions that offer the
Calculate/Draw output choice show both types of
screens: calculated and graphic results.
Descriptions of instructions that offer only the Calculate
output choice show the calculated results on the home
screen.
Inferential
Statistics
and
Distributions
13-9
Z-Test
Z-Test (one-sample z test; item 1) performs a hypothesis
test for a single unknown population mean _ when the
population standard deviation cris known. It tests the null
hypothesis H0: g= P0 against one of the alternatives below.
•
•
•
H_,:_!¢P0 (vt:_to)
H_,:_<_00a:<_to)
H_,:_>_0 (_t:>_to)
In tile example:
L1={299,4 297.7 301 298.9 300.2 297}
Data
Z-Test
Inet:_
Input:
Calculated
results:
Stats
0.:3
List:L1
Fre_:l
_:#_
_
Calculate
>_o
Draw
Stats
Z-Test
InPt:Oata
v.n : 300
0:3
_: 299. 0333
n:6
v.:#v.n_
>_n
Calculate
Draw
Z-Test
v.<300. 0000
z= -. 7893
P=. 2150
_=299.
0333
mx= 1. 5029
Z-Test
u<300.0000
z=-.7893
e=.2150
R=299.0333
ir,=6.
I n=6.0000
0000
[email protected]
[email protected]
Drawn results:
:=-.7B9_ _=._I_
Note:
All examples
on pages13-10
through
t3-25
assume
a fixed-
decimal mode setting of 4 (Chapter 1 ). If you set the decimal mode to
Float or a different fixed-decimal
setting, your output may differ from
the output
13-10
Inferential
Statistics
in the examples.
and
Distributions
T-Test
T-Test (one-sample
t test;
item
2) performs
a hypothesis
test for a single unknown
population
mean p when the
population
standard
deviation
_ is unknown.
It tests the
null hypothesis
H0:P=P0 against
one of the alternatives
below.
•
•
H_,:PCPo (p:¢po)
H_,:P<Po (p:<po)
•
H_,:P>Po (,u:>_.to)
In the example:
TEST={91.9 97.8 111.4 122.3 105.4 95}
Input:
Data
T-Test
InPt:_
_n:105
List:TEST
FPe_:l
_:_
<_n
Calculate
Stats
>_n
DPau
Stats
T-Test
InPt:Oata
p0:105
7,:103. 9667
Sx: 11.4669
n:6
Calculate
T-Test
_#105.0000
t=-.2207
P=.8340
R=103.9667
Sx=II.4669
T-Test
,,lo5.00oo
t=-.,_20_
Calculated
results:
P=. 8340
2= 100 • 9667
Sx= 1 I. 4669
in=6.
OPau
in=6.0000
0000
Drawn results:
t= -,i:_:07
_=,g3h
Inferential
Statistics
and
Distributions
13-11
2-SampZTest
2-SampZTest
(two-sample
z test;
item
3) tests
the equality
of the means of two populations
(Pl and #2) based on
independent
samples
when both population
standard
deviations
(_1 and a_,) are known. The null hypothesis
H0:#1=p2
is tested
against one of the alternatives
below.
•
H_,: _[l<_t2 (pl:<p2)
•
H_,: #1>P2 (pl:>p2)
In the
example:
LISTA={154
LISTB={108
109 137 116 140}
115 126 92 146}
Data
Input:
2-SamPZTest
InPt =I_
¢I: 15.5
¢2:13.5
ListI:LISTR
List2:LISTB
FPe_l:l
_Fre_2:l
_I:#_2
Calculate
<_2
Stats
results:
2-SaMPZTest
P:. 695
z= I. 4795
P=. 0695
_1=131.0000
RI=131. 0000
Rz=117.4000
l.n i =5. 0000
2z=I17.4000
I
i
1_Sx,=18.6145
r,z=5.0000
S×z=20.1941
ni=5.0000
i
inz=5.0000
//
Drawn resutts:
z=l.h795
13-12
Inferential
=-LI:#p.2 <p.2 I_
Calculate
Dr-a,,J
_
Drau
2-SaMmZTest
Calculated
Stats
2-SaMPZTest
InPt:Data
¢I: 15.5
¢2:13.5
RI: 131
hi:5
R2:117.4
_n2:5
Statistics
_=.Ofigg
and
Distributions
2-SampTTest (two-sample t test; item 4) tests the equality
of the lneans of two populations
(_l 1 and g2) based on
independent
samples when neither population standard
deviation ((_1or (_2)is known, The null hypothesis
n0:_11=_12
is tested against one of the alternatives
below.
2-SampTTest
•
H_,: _11<_l2 (_1:<_2)
•
H_,: _11>_12
(_1:>_2)
In the example:
8AMPl={12.207 16.869 25,05 22,429 8,456 10,589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
Input:
Data
2-SamPTTest
InPt:liI_11_Stats
ListI:SRMPI
List2:SRMP2
Fre_l:l
Fre_2:l
SPooled:l_
9es
I Calc.ulate Draw
Calculated
results:
Stats
2-SaMPTTesL
Inet: Data !i_rul_lEl
1 : 15. 9333
SxI :6. 7014
nl:6
_2:9.4998
Sx2: I. 9501
i.n2:6
I
_LI:_
<_2 >_2
PooI_:[_
Yes
Calculate
Draw
2-SamPTTest
2-SamPTTest
t=2.2579
P=.0659
d_=5.8408
RI=15.9333
$_z=9.4998
t=2.2579
P=.0659
d€=5.8408
RI=15.9333
_2z=9.4998
Sxz=1.9501
ni=6.0000
I nz=6.0000
SXI=6"7014
m =6. 00e
I r,z=6. 0000
Drawn resutts:
Inferential
Statistics
and
Distributions
13-13
1-PropZTest (one-proportion
z test; item B) computes a test
for an unknown proportion
of successes (prop). It takes as
input the count of successes in the sample x and the count
of observations
in the sample n. 1-PropZTest tests the null
hypothesis H0:prop=p0 against one of the alternatives
below.
1-PropZTest
•
•
•
H_,:prop€p0 (prop:¢p0)
H_,:prop<p0 (prop:<po)
H_,:prop>p0 (prop:>po)
I
1-ProPZTest
pill
Input:
I
.5
x: 2848
I
n: 4848
I
eroI=Ei1"_,'1
<ell >Pal
Caloulate
Draw
l-ProeZTest
ProP#.
Calculated
results:
5000
z=. 8810
P=. o783
_=. 5069
in=4e4e.
0088
Drawn results:
13-14
Inferential
Statistics
and
Distributions
2-PropZTest (two-proportion
z test; item 6) computes a test
to compare the proportion
of successes
(Pl and P2) fronl
two populations. It takes _ksinput the count of successes in
each sample (x 1and x2) and the count of observations
in
each sample (nl and n2). 2-PropZTest tests the null
hypothesis H0:pl=p2 (using the pooled sample proportion
_) against one of the alternatives
below.
2-PropZTest
•
•
•
Input:
Calculated
results:
H_,:pl;eP2 (pl:_p2)
H_,:pl<P2 (pl:<p2)
H_,:pl>P2 (pl:>p2)
2-PPoeZTest
xi:45
hi:61
x2:38
n2:62
el:I
<e2 >e2
Calculate
Draw
B2-ProeZTest
e1#ez
z=1.4773
P=.1396
@i=.7377
@z=.6129
4#=.6748
|
nI=61.0000
nl=62.0000
-I
Drawn results:
Inferential
Statistics
and
Distributions
13-15
Zlnterval (one-sample z confidence intetsTal; item 7)
computes a confidence interval for an unknown population
mean p when the population standard deflation cris
known. The computed confidence intet_-'al depends on the
user-specified
confidence level,
Zlnterval
In the example:
L1={299.4 297.7 301 298.9 300.2 297}
Data
ZInterval
In_t:l_ellI_Stats
Input:
Calculated
results:
List:L1
Fre_:l
C-Level:.9
Calculate
-BZInterval
(297.02,301.85)
R=299.0333
Sx=1.5029
|n=6.0000
13-16
Inferential
Statistics
and
Stats
ZInterval
Inet:Data
_:3
R: 299. 0333
n:6
C-Legel :. 9
Calculate
Zlnterval
(297.02,301.05)
I
Distributions
Tlnterval
Tlnterval
(one-sample
t confidence
inte_nTal; item
8)
computes
a confidence
interval
for an unknown
population
mean p when the population
standard
deviation
_ is
unknown.
The computed
confidence
inte_wTal depends
on
the user-specified
confidence
level.
In the
L6={1.6
Input:
example:
1.7 1.8 1.9}
Data
Tlnterval
InPt:llL_u1_Stats
List:L_
Fre_:l
C-Level:.95
Calculate
Stats
T Interva I
InF.t:Data
_: 1.75
Sx:. 1291
n:4
C-Level: .95
Caloulate
-B-
Calculated
results:
TInterval
(1.5446,1.9554)
R=1.7500
Sx=.1291
TInterval
(1.5446, i.9554)
R=1.7500
Sx=.1291
|n=4.0000
|n=4.0000
Inferential
Statistics
and
Distributions
13-17
2-SampZInt (two-sample z confidence inte_wTal;item 9)
c()mputes a confidence inte[wTal for the difference between
two population means ({11-_12) when both population
standard deviations (or1 and a_) are known. The computed
confidence inte_'al depends on the user-specified
confidence level.
2-SampZlnt
In the
example:
LISTC={154
LISTD={108
Input:
109 137 116 140}
115 126 92 146}
Data
2-SamPZlnt
InPt:[._Z
Stats
_i:15.5
_2:13.5
ListI:LISTC
List2:LISTD
Fre_l:l
SFre_2:l
C-Level:.99
Calculate
2-SamPZInt
(-10.08,37.278)
21=131.0000
2z=117.4000
Calculated
results:
Sxi=18.6145
Sxz=20.1941
$ni=5.0000
n2=5.0000
|
Inferential
Statistics
and
C-Level:.99
Calculate
2-SamPZlnt
(-10.08,37.278)
21=131.0000
2_=117.4000
m=5.0000
inz=5.0000
|
13-18
Stats
2-SamPZ I nt
InPt:Data
_I: 15.5
¢2:13.5
21:131
ni:5
22:117.4
_n2:5
Distributions
2-SampTInt
2-SampTInt
(two-sample
t confidence
inte[wTal; item O)
c()mputes
a confidence
inte[wTal for the difference
between
two population
means (Pl-P2)
when both population
standard
deviations
(a 1 and _) are unknown.
The
computed
confidence
interval
depends
on the userspecified
confidence
level.
In the
example:
SAMP1={12.207
SAMP2={11.074
16.869 25.05 22,429 8.456 10.589}
9.686 12.064 9.351 8,182 6.642}
Stats
2-SaP/PT I r=t
Data
Input:
2-SamPTlnt
InPt:_
ListI:SRMPI
List2:SRMP2
Fne_l:1
Fne_2:l
C-Level:.95
$Pooled:l:_
Stats
Sxl :6. 7014
nl:6
R2:9.4998
Sx2:1.9581
_n2:6
Yes
C-Level :. 95
Pooled:l:_ Yes
Calculate
Calculate
Calculated
results:
2-SamPTlnt
(%5848,13.452)
d¢=5.8408
Ri=15.9333
Rz=9.4998
SxI=6.7014
$Sxz=1.9501
|
2-SamPT
Int
( -.5849, 13. 452)
df=5.8408
_i =15. 9333
R1=9.4998
SxI=6. 7014
_Sx1=1.9501
|
i
ni=6.0000
nz=6.0000
ni=6.8000
nz=6.0000
|
Inferential
Statistics
and
Distributions
13-19
1-PropZInt (one-proportion
z confidence inte_'al; item A)
computes a confidence interval for an unknown proportion
of successes. It takes as input the count of successes in the
sample x and the count of obse_'ations
in the sample n.
The computed confidence intetnTal depends on the userspecified confidence level.
1-PropZlnt
input:
1-PPoeZlnt
x: 2848
n: 4848
C-Leve I :.99
Caicuiate
-Bl-ProeZlnt
(.4867,.5272)
A=.5069
Calculated
results:
|n=4040.0000
13-20
Inferential
Statistics
and
Distributions
2-PropZInt
2-PropZlnt
(two-proportion
z confidence
inte_'al;
item
B)
computes
a confidence
intet_'al
for the difference
between
the proportion
of successes
in two populations
(Pl-P2)- It
takes a_n input the count of successes
in each sample
(Xl and x2) and the count of observations
in eaeh sample
(n 1 and n2), The computed
confidence
intetnTal depends
on
the user-specified
confidence
level.
2-Pt-oPZ Int
xi:49
nl:61
x2:38
Input:
n2: 62
C-Leve I :.95
Calculate
-I
Calculated
results:
2-PPoeZInt
(.0334,.3474)
#I=.8033
#z=.6129
ni=61.0000
|nz=62.0000
Inferential
Statistics
and
Distributions
13-21
z2-Test (chi-squm'e test; item C) computes a chi-squm'e test
for association on the two-way table of counts in the
specified Observed lnatrix. The null hypothesis H 0 for a
two-way table is: no association exists between row
variables and colunm variables. The Mternative hypothesis
is: the vm'iables are related.
z2-Test
Before computing a zZ-Test, enter the obsetnTed counts in a
matrix. Enter that matrix variable name at the Observed:
prompt in the z2-Test editor; default=[A]. At the Expected:
prompt, enter the matrix variable name to which you want
the computed expected counts to be stored; default=[B].
[ 5.0000
19.000
MATRIX[R]
J.3.000
3 x2
]
Note: Press _
select 1 :[A] from
EDIT menu.
[] [] 1 to
the MATRX
Matrix editor:
[ i0. o000
t,.000
Xi-Test
Observed:[R]
Exeected:[B]
Calculate
Draw
Input:
Note: Press_
display
[B]
[[8.0000
XZ-Test
XZ=3.3750
P=.1850
d€=2.0000
Calculated
results:
Inferential
Statistics
and
[B] _
[B].
16.000.
[ :888816.000...i
Drawn results:
13-22
matrix
Distributions
to
2-SampFTest
2-SampVTest
(two-sample
V-test;
item
D) computes
an
V-test to compare
two normal population
standard
deviations
((31 and
(32). The population
means and standard
deflations
are all unknown.
2-$ampFTest,
which uses the
ratio of sample variances
Sxl_/Sx2 _, tests the null
hypothesis
H0:(31=(32 against one of the alternatives
below.
•
H_,: (315(32 (G1:_(52)
•
H_,:(31<(32
H_,:(31>(32
•
In the
Calculated
results:
((51 :>(52)
example:
SAMP4={
SAMPS={
Input:
((51 :<(52)
7 -4 18
-1 12 -1
17
-3
-3
3
-5
-5
1 10 11-2}
5 2-11
-1-3}
Data
2-SamPFTest
InPt:_
SLats
ListI:SRMP4
List2:SRMP5
FPe_l:l
FPe_2:l
_i:_
<z2 >z2
Caloulate
OPaw
Stats
2-Sar/PFTest
InPt: Data_
Sx i :8. 7433
hi: 10
Sx2: 5. 9007
n2: II
zl:_
<_2 >z2
Calculate
Dra_,J
2-SaMPFTest
zl #zz
2-SameFTest
zl#zz
F=2. 1956
P=. 2364
S× _=8. 7433
Sxz=5. 9007
_nl =10. 0000
F=2. 1955
P=. 2365
Sxl =8. 7433
Sx z =5. 9007
_i
=5. 0000
z= -.2727
n_=lO. 0000
nz=l I.0000
2
in _ = 1 I. 0000
Drawn results:
Inferential
Statistics
and
Distributions
13-23
LinRegTTest
LinRegTTest
(linear
regressk)n
t test;
item
E) computes
a
linear regression
on the given data and a t test on the value
of slope _ and the correlation
coefficient
p for the equation
y=(x +_x. It tests the null hypothesis
H0:_=0 (equivalently,
p=O) against one of the alternatives
below.
•
Hr,: _€0 and
pC0 ([3 & p:_0)
•
H_,: _<0 and
p<0 (9 & p:<0)
•
H_,: _>0 and
p>0 (9 & P:>0)
The regression
equation
is automatically
stored to
(MARS Statistics EQ secondary
menu).
If you enter
variable
name at the RegEO: prompt,
the eMeulated
regression
equation
is automatically
stored
to the
Y= equation.
In the example
below, the regression
is stored
to Y1, which is then selected
(turned on).
In the
specified
equation
example:
L3={38 56 59
L4={41 63 70
Input:
RegEQ
a Y=
64 74}
72 84}
LinRegTTest
Xlist:L_
91ist:L4
Fre_:l
B & P:_
<0
RegEQ:_
Calculate
>0
lJ-
Calculated
results:
LinRegTTest
_=a+bx
B_O and
p_O
t=15.9405
P=5.3684E-4
",371B-3. 6596+i.
69X
xYz=
d€=3.8888
4a=-3.6596
xY4=
PloLt
xVs=
xY_=
PloI:Z
PloL3
19
$b=i.1969
s_1.9820
P_=.9883
P=,9941
When
LinRegTTest
is executed,
the list of residuals
is
created
and stored
to the list name RESID automatically.
RESID is placed on the LIST NAMES menu.
Note: For the regression
equation, you can use the fix-decimal
mode
setting to control the number of digits stored after the decimal point
(Chapter I). However, limiting the number of digits to a small number
could affect the accuracy of the fit.
13-24
Inferential
Statistics
and
Distributions
ANOVA(
ANOVA(
(one-way
analysis
of variance;
item
F) computes
a
one-way
analysis
of variance
for COlnparing
the means of
two to 20 populations.
The ANOVA procedure
for
COlnparing
these means involves
analysis
of the variation
in the sample
data. The null hypothesis
H0:#1=#2 ..... #k is
tested
against the alternative
H_,: not all p 1---#l_are equal.
ANOVA(listl,list2[,...,list20])
In the
example:
L1={7 4 6 6 5}
L2={6 5 5 8 7}
L3={4 7 6 7 6}
RNOVR(LI,Lz,L_)I
Input:
ll-
Calculated
results:
One-_au
RNOVR
F=.olll
P=.7384
Factor
d_=2.0000
SS=.9333
_MS=.4667
Error
d_=12.0000
SS=18.0000
MS=1.5000
I_xP=1.2247
Note:
SS is sum of squares
Inferential
and MS is mean square.
Statistics
and
Distributions
13-25
Inferential
Statistics
Input Descriptions
The tables in this section describe the inferential statistics inputs discussed
this chapter. You enter values for these inputs in the inferentiM stat editors.
The tables present the inputs in the same order that they appear in this
chapter.
in
Input
Description
_0
Hypothesized
testing.
G
The known population
number > 0.
List
The name of the list containing
Freq
The name of the list containing the frequency values for the
data in List. Default=l. All elements must be integers ->0.
Calculate/Draw
Determines the type of output to generate for tests and
intervals. Calculate displays the output on the home screen.
In tests, Draw draws a graph of the results.
_, Sx, n
Sumlnary statistics (mean, standard deviation,
size) for the one-sample tests and intervals.
_1
The known population standard deviation fronl the first
population for the two-sample tests and intervals. Must be
a real number > 0.
_2
The known population standard deviation fronl the second
population for the two-sample tests and intervals. Must be
a real number > 0.
List1, List2
The names of the lists containing the data you are testing
for the two-salnple tests and intervals. Defaults are L1 and
L2,respectively.
Freql, Freq2
The names of the lists containing the frequencies for the
data in List1 and List2 for the two-salnple tests and
intervals. Defaufis=l. All elements must be integers _>0.
_1, Sxl, nl, _2,
Sx2, n2
Sununary
Pooled
Specifies whether variances are to be pooled for
2-SampTTest and 2-SampTInt. No instructs the TI-83 not to
pool the variances. Yes instructs the TI-83 to pool the
variances.
13-26
Inferential
value of the population
standard
mean that you are
deviation;
must be a real
the data you are testing.
and sample
statistics (mean, standard deviation, and sample
size) for sample one and sample two in the two-salnple
tests and intervals.
Statistics
and
Distributions
Input
Description
P0
The
real
The
and
x
expected sample proportion for 1-PropZTest. Must be a
nmnber, such that 0 < I90 < 1.
count of successes in the sample for the 1-PropZTest
1-PropZlnt. Must be an integer _>0.
n
Tile count of observations
in the sample for the
1-PropZTest and 1-PropZlnt. Must be an integer > O.
xl
The count of successes fronl sample one for the
2-PropZTest and 2-PropZlnt. Must be an integer _>0.
x2
The count of successes froln sample two for the
2-PropZTest and 2-PropZlnt. Must be an integer _>0.
nl
The count of observations
in sample one for the
2-PropZTest and 2-PropZlnt. Must be an integer > 0.
n2
The count of observations
in sample two for the
2-PropZTest and 2-PropZlnt. Must be an integer > 0.
The confidence level for the inteP_-al instructions. Must be
>_0 and <100. If it is _>1, it is assumed to be given as a
percent and is divided by 100. Default=0.95.
C-Level
Observed
(Matrix)
The matrix name that represents the colunms and rows for
the obseP_'ed values of a two-way table of counts for the
z2-Test. Observed nmst contain 'all integers _>0. Matrix
dimensions nmst be at least 2x 2.
Expected (Matrix)
The matrix name that specifies where the expected values
should be stored. Expected is created upon successful
completion of the z_Test.
Xlist, Ylist
The names of the lists containing the data for LinRegTTest.
Defaults are L1 and L2, respectively.
The dimensions of
Xlist and Ylist nmst be the same.
RegE(:l
The prolnpt for the name of the Y= variable where the
cMculated regression equation is to be stored. If a
Y= variable is specified, that equation is automatically
selected (turned on). The default is to store the regression
equation to the RegEQ variable only.
Inferential
Statistics
and
Distributions
13-27
Test and Interval
Output Variables
The inferential
variables
statistics
are calculated
as indicated
below.
variables
for use in expressions,
press [_,
5 (5:Statistics),
the VARS menu listed in the last column
below.
these
select
Variables
Tests
Intervals
To access
and then
LinRegTTest,
ANOVA
VARS
Menu
p-value
p
p
TEST
test
z, t, Z2_ F
t, F
TEST
df
TEST
statistics
degrees
of freedom
df
df
sample
sample
mean of x values
1 and sample 2
21,22
21, 22
TEST
sample
standard
deviation
of x
for sample
1 and sample
2
Sxl,
Sx2
Sxl,
Sx2
TEST
nulnber
of data points
1 and sample 2
nl, n2
nl, n2
TEST
SxP
SxP
/3
/3
TEST
pooled
standm'd
for
for sample
deviation
SxP
TEST
estimated
sample
proportion
estimated
population
sample
1
proportion
for
/31
/31
TEST
estimated
population
sample
2
proportion
for
/32
/32
TEST
lower,
upper
TEST
2
_
XY
Sx
Sx
XY
n
n
confidence
mean
interval
pair
of x values
sample
standm'd
nulnber
of data
standard
error
deviation
of x
points
about
the
line
XY
s
TEST
a, b
EQ
correlation
coefficient
r
EQ
coefficient
of determination
r2
EQ
regression
equation
RegEQ
EQ
regression/fit
13-28
coefficients
Inferential
Statistics
and
Distributions
Distribution
DISTR menu
Functions
To display
DISTR
the
DISTR menu,
press
[_
[DiSTR],
DRAW
Normal
Normal
Inverse
i: normalpdf(
2: normalcdf(
3:invNorm(
probability
distribution
cunmlative
densityprobability
normal
distribution
Student-t
probability
density
Student-t
distribution
probability
Chi-square
probability
densityChi-square
distribution
probability
F probability
densityF distribution
probability
Binomial
probability
Binomial
cunmlative
densityPoisson
probability
Poisson
cunmlative
density
Geometric
probability
Geometric
cunmlative
density-
4:tpdf(
5:tcdf(
6: z2pdf(
7: x2cdf
8: Fpdf(
9: Fcdf(
O: binompdf(
A: binomcdf(
B: poissonpdf(
C: poissoncdf(
D: geometpdf(
E: geometcdf(
Note: -1E99 and IE99 specify infinity. If you want to view the area left
of upp¢rbound,
for example, specify lowerbound_1E99.
normalpdf(
norwmalpdf( computes
the probability
density
function
(pdf) for the normal distribution
at a specified
x value, The
defaults
are mean p=O and standard
deviation
cr=l. To plot
the normal
distribution,
p_k_te normalpdf( to the Y= editor.
The probability
density
function
(pdf) is:
1
- (x-")=
f(x)=_e
2_
,_>0
4"z_c_
normalpdf(x[,p,o])
Pl,:,tl
P10L2
Plot3
",V1 Bnor.r_alPdf" (X,
35,2>
Note:
Xmin
Xmax
Ymin
Ymax
For this example,
= 28
= 42
=0
= .25
Tip: For plotting the normal distribution,
you can set window variables
Xmin and Xmax so that the mean p falls between them, and then
select 0:ZoomFit
from the ZOOM menu.
Inferential
Statistics
and
Distributions
13-29
normalcdf(
normalcdf( computes
between
lowerbound
nlean u and standard
and 6= 1.
the normal distribution
probability
and upperbound
for the specified
deviation
or. The defaults
are u =0
normalcdf(_werbound,upperbound[,p,_])
noPmalod_(-iE99,
36,35,2)
.6914624678
invNorm(
invNorm( computes
the inverse
cumulative
normal
distribution
function
for a given area under the normal
distribution
cut_'e specified
by mean p and standard
de_iation
cr. It calculates
the x value associated
with an
area to the left of the x value. 0 _<area _<1 must be true.
The
defaults
are p =0 and or=1.
invNorm(area[,p,_])
invNorr_(. 6914624
678,35,
2)
36. ee0000e4
tpdf(
tpdf( computes
the probability
density- function
(pdf) %r
the Student-t
distribution
at a specified
x value, df (degrees
of freedom)
must be >0. To plot the Student-t
distribution,
paste tpdf( to the Y= editor,
function
(pdf) is:
F [(df + 1)/2]
f(x)
probability
(1 + x2/df)
- (if + 1)/2
x/_f
dJ)
Pl_{:[ P1¢_: Plo{. _
",YI BtPd{'(X,
2)
I
Note: For this example,
Xmin = -4.5
Xmax = 4.5
Ymin = 0
Ymax = .4
13-30
Inferential
density-
=
F(df /2)
tpdf(x,
The
Statistics
and
Distributions
tcdf(
tcdf( computes the Student-t distribution probability
between lowo'bound
and uppe_"bound for the specified
(degrees of freedom), which nmst be > O.
df
tcdf(lowerbound,uppe'rbou.rwl,d]_
tc.d_" ( •9657465644
-2, 3, 18)
x2pdf(
z2pdf( computes
the probability
density
function
(pdf) ff)r
the X2 (chi-square)
distribution
at a specified
x value, df
(degrees
of freedoln)
nmst be an integer
> 0, To plot the X 2
distribution,
paste x2pdf( to the Y= editor, The probability
density function
(pdf) is:
f(x)
1
=
r(df
(1/2)df/2
x/f/:)
- 1e - x/:), x _>0
/2)
:2pdf(x,dj)
P1,;,tl PloLZ Plot_
\YI B:KZPdf'(X, 9)
",VZ I_I;_
Z Pdla (X _F)
Note:
Xmin
Xmax
Ymin
Ymax
xYs=
\Y_=
\Y_=
xY_=
\Y_=
x2cdf(
For this example,
=0
= 30
= -.02
= .132
x2cdf( computes
the Z z (chi-square) distribution probability
between lowerbound and upperbound
for the specified df
(degrees of freedom), which nmst be an integer > O.
z2cdf(lowe'rbound,upperbound,dj)
_Zc.d_(O,
19. 023,9
.9750019601
Inferential
Statistics
and
Distributions
13-31
Fpdf(
Fpdf(
computes
the probability
density-
function
(pdf)
for
the F distribution
at a specified
x value, numerator
df
(degrees
of freedonl)
and denominator
dfnmst
be integers
> O. To plot the F distribution,
paste Fpdf( to the Y= editor.
The probability
density
function
(pdf) is:
f(X)
F[(n+d)/2]
= F(n/2)F(d/2)
where
(d)n/2xn/2
n = numerator
d = denominator
F pdf(x,numero
tor dr, denominator
Plot:l, plot:i: Plo_,3
_._1BFPdf
Fcdf(
l(l+,_a_./d)(n+d)/2,X>
(X,
24,
dJ_
Note: For this example,
19
Xmin
Xmax
Ymin
Ymax
== 05
=0
= 1
Fcdf( computes
the F distribution
probability
between
lowerbound
and uppe'rbound
for the specified
nume_-ator
df (degrees
of freedon0
and denominator
dr. numerator
dfand
denominator
df nmst be integers
>0.
F cdf(lowerbound,upperbound,numerator
denominator
dJ)
Fodf'(O, 2. 4523,24
,19)
-,
• 9_ 49989576
13-32
degrees
of freedom
degrees
of fi'eedom
Inferential
Statistics
and
Distributions
dr,
0
binompdf(
binompdf(
computes
a probability
at x ffw the discrete
binomial
distribution
with the specified
numtrials
and
probability
of success
(1)) on each trial, x can be an integer
or a list of integers.
O_<p_<lnmst be true. numtrials
nmst be
an integer
> O. If you do not specify x, a list of probabilities
from 0 to numtrials
is returned.
The probability
density
function
(pdf) is:
f(
X
( _7/,
)=/xiP
x
n-x
(l-p)
where
,
X
=O,1,...,n
n = numtrials
binompdf(numtrials,p[,x
])
binomPd¢(5,. 6, {3
,4,5})
{. 3456 .2592 .0...
binomcdf(
binomcdf( computes a cunmlative probability at x ff)r the
discrete binomial distribution
with the specified numtrials
and probability of success (p) on each trial, x can be a real
nmnber or a list of real nmnbers. O_<p_<
1 nmst be true.
numtrials
nmst be an integer > O. If you do not specify- x, a
list of cunmlative probabilities
is returned.
binomcdf(numtrials,p[,x
])
binomcd¢(5,. 6, {3
,4,5})
{,66304
.92224
...
poissonpdf(
poissonpdf(
computes
a probability
at x ff)r the discrete
Poisson
distribution
with the specified
mean {l, which nmst
be a real nmnber
> O. x can be an integer
or a list of
integers.
The probability
density function
(pdf) is:
f(x)
= e - _ ,uX/x!,
x = 0,1,2,...
poissonpdf(p,x)
PoissonPd¢(6,10)
.0413030934
Inferential
Statistics
and
Distributions
13-33
poissoncdf(
poissoncdf(
computes
a eunmlative
discrete
Poisson
distribution
which nmst be a real number
probability
at x for the
with the specified
mean _l,
> O. x can be a real number
or a list of real numbers.
poissoncdf(p,x)
eoissonod¢(.126,
{0,1,2,3})
{.8816148468
.9...
geometpdf(
geometpdf( computes
a probability
at x, the number
of tlle
trial on which the first success
occurs,
for the discrete
geometric
distribution
with the specified
probability
of
success
p. 0_<p_<l nmst be true. x can be an integer
or a list
of integers.
The probability
density
function
(pdf) is:
f(x)
= p(1 - p)X - 1, x = 1,2,...
geometpdf_,x)
geo_eted?(.4,6)
.031104
geometcdf(
geometcdf( computes a cunmlative probability at x, the
number of the trial on which the first success occurs, for
the discrete geometric distribution
with the specified
probability of success p. O_<p_<
1 must be true. x can be a
real number or a list of real numbers.
geometcdf_,x)
geo_etod¢(.5,{l,
2,3J)
{.5
13-34
Inferential
Statistics
.75
and
.875}
Distributions
Distribution
DISTR DRAW
Menu
Shading
To display
the DISTR DRAW menu, p_ss
_
[DISTR] [].
DISTR DRAW instructions
draw vmious types of density
functions,
shade the area specified
by lower'bound
and
uppc'rbound,
and display- the computed
area vMue.
To clem" the drawings,
menu (Chapter
8).
select
l:CIrDraw
from
the DRAW
Note: Before you execute a DISTR DRAW instruction, you must set
the window variables so that the desired distribution fits the screen.
DISTR
i:
DRAW
ShadeNorm(
2:Shade
t(
3:Shadez2(
4:ShadeF(
Shades
normal
Shades
Student-t
distribution.
Shades
Shades
)_ distribution.
F distribution,
distribution,
Note: -1E99 and IE99 specify infinity. If you want to view the area left
of upperbowad,
for example, specify lowe'rbownd_1E99.
ShadeNorm(
ShadeNorm( draws the normal density function specified
by mean u and standard deviation a and shades the m'ea
between lowc'rbound and upperbound.
The defaults are
u=0 and a= 1.
ShadeNorm(lowerboural,uppc'rbound[,g,c_])
Note: For this example,
Xmin = 55
Xmax = 72
Ymin = -,05
Ymax = ,2
Inferential
Statistics
and
Distributions
13-35
Shade_t(
Shade_t(
draws
the density
function
distribution
specified
by df (degrees
shades the area between
lowe_rbound
for the Student-t
of freedom)
and
and upperbound.
Shade_t(lowerbound,upperbound,dJ_
Note: For this example,
Xmin = -3
4)IShade-t(-l'IE99'
Xmax = 3
Ymin = -,lS
Ymax = .S
Shadex2(
Shadex2( draws the density function
for the Z 2 (chi-square)
distribution
specified by df (degrees
of freedom)
and shades
the area between
lowerbou_l
and uppe_rbound.
Shadex2(lowerbound,uppe_'bound,dj)
IShadeXZ
(0,
4, 10)I
I
Note:
Xmin
Xmax
Ymin
For this example.
=0
= 35
= -.025
Ymax = .1
ShadeF(
ShadeF(
draws the density
function
for the F distribution
specified
by numerator
df (degrees
of freedom)
and
denominator
dfand
shades the area between
lowed'bound
and upperbour_l.
ShadeF
(lowe'rbound,upperbound,numerator
denominator
ShadeF()i 1,2,
dr,
d_
10, 15
Note:
Xmin
Xmax
Ymin
For this example,
=0
= S
= -.25
Ymax = .9
13-36
Inferential
Statistics
and
Distributions
14
Contents
Financial
Functions
Getting Started: Einaneing
a Car. ........................
Getting Started: Computing
Compound
Interest ..........
Using the TVM Solver ....................................
Using the Financial
Functions
...........................
Calculating
Time Value of Money (TVM) .................
Calculating
Cash Flows ..................................
Calculating
Amortization
................................
Calculating
Interest Conversion
..........................
Finding Days between Date_)efil_N
Paynlent Method .....
Using tile TVM Variables .................................
TEXAS
I4-2
14-3
14-4
14-5
14-6
14-8
14-9
I4-I2
14-13
14-14
T1=83
INSTRUMENTS
N=360.00
I_=IB.00
PV=100000.00
-PMT=-I507.09
FV=0.00
P/V=12.00
C/Y=12.00
PMT:L_
BEGIN
STAT
PLOT
TBLSET
FORMAT
CALC
TABLE
Financial
Functions
14-1
Getting
Getting
Started:
Started
Financing
a Car
is a ftkst-paced introduction.
Read the chapter
for details.
You have found a cat" you would like to buy-. The car costs 9,1)00. You can
afford payments of 250 per month for four years. What annual percentage rate
(APR) will make it possible for you to afford the car?
Press[_[][][][][_to
setthe
fixed-deeimalmode
seging to 2. The TI-83
will display all numbers with two decimal
places.
Sci Ehg
_I_3456789
Degree
Pol Se_
Dog
Horiz
2. Press [_ [FINANCE]to display" the
FINANCE CALC menu.
G-T
VRRS
Solver...
gum_I%
gvm_PV
tvm_N
tvm_FV
,nev(
3.
Press [_
to select I:TVM Solver. The
TVM Solver is displayed.
Press 48 [_
to store 48 months to N.
Press [] 9000 [gNT_ to store 9,000 to PV.
Press [] 2S0 [gNT_ to store -250 to PMT.
(Negation indicates cash outflow.) Press 0
[ggg_ to store 0 to FV. Press 12 F_tggl to
store 12 payments per year to P/Y and 12
compounding
periods per year to O/Y.
Setting PlY to 12 will compute an annual
percentage rate (compounded
monthly)
for I%.Press [] [gNT_ to select PMT:END,
which indicates that payments are due at
the end of each period.
4.
14-2
Press [] [] [] [] [] [] to move the cursor
to the I%prompt. Press @
[SOLVE] to
solve for I%.What APR should you look
for?
Financial
Functions
N=0.00
I%=0.00
PV=0.00
PMT=0.00
FV=0.00
P/Y=l.O0
C/V=l.00
PMT:L_
BEGIN
N=48.00
I%=0.00
PV=9000.00
PMT=-250.00
FV=0.00
P/Y=12.00
C/Y=12.00
PMT:[__[LL_
BEGIN
N=48.00
"1%=14.90
PV=9000.00
PMT=-250.00
FV=0.00
P/Y=12.00
C/Y=12.00
PMT:L:[II_BEGIN
Getting
At what
2,000
Started:
annual
interest
Computing
rate,
Compound
compounded
monthly,
will
Interest
1,250 accumulate
to
in 7 years?
Note: Because there are no payments when you solve compound interest problems, PMT
must be set to 0 and PlY must be set to 1.
Z.._tvVRR5
M Solver
_,_PMt
3: tw,_l%
4: tvM_PV
5: tur,,_N
6: tvr.__FV
74nPv(
Press [_
[FINANCE]
to display- the
FINANCE CALC menu.
Press [_
to select I:TVM Solver. Press 7
to enter the number of periods in years,
Press [] [] [] 12S0 to enter the present
value as a cash outflow (investment).
Press [] 0 to specify- no payments. Press
[] 2000 to enter the future value as a cash
inflow (return), Press [] 1 to enter
payment periods per year, Press [] 12 to
set compounding periods per yea[" to 12.
N=7
1%=0
PV=-1250
PMT=O
FV=2000
P/9=I
C/Y=12
PMT:L_IiE BEGIN
Press [] [] [] [] [] to place the cursor
the 1%prompt.
N=7
1%=|
PV=-1250
PMT=O
FV=2000
P/Y=1
C/Y=I2
PMT:I=_I_ BEGIN
Press @
[SOLVE] to solve for I%, the
annual interest
['ate.
on
.N=7.O0
1%=6.73
PV=-1250.00
PMT=0.00
FV=2000.00
P/Y=l.00
C/Y=12.00
PMT:_
BEGIN
Financial
Functions
14-3
Using the TVM Solver
Using the TVM
Solver
The TVM Solver displays the time-value-of-money
(TVM)
variables. Given four variable wdues, tile TVM Solver solves
for the fifth variable.
The FINANCE VARS menu section
(page 14-14) describes
the five TVM variables
(N, I%, PV, PMT, and FV) and PlY and
C/Y,
PMT: END BEGIN in the TVM Solver corresponds
to the
FINANCE CALC menu items Pmt_End (pa3qnent at the end
of each period) and Pmt_Bgn (payment at the beginning of
each period).
To solve for an unknown
TVM vm'iable, follow these steps.
1, Press [2ffa][FINANCE] _
to display the TVM Solver. The
screen below shows the default values with the fixeddecimal mode set to two decimal places,
N=0.00
Ia=0.00
PV=0.00
PMT=O,00
FV=0.00
P/V=I.00
C/V=I.O0
PMT:[__II_
BEGIN
2. Enter
the known
vMues
for four TVM variables.
Note: Enter cash inflows as positive numbers and cash
outflows as negative numbers.
Enter
same
C/Y.
4.
Select
a value for P/Y, which automatically
enters the
wdue for C/Y; if PW € CIY, enter a unique value for
END or BEGIN to specify-
5. Place the cursor
want to solve.
on the
the pa3qnent
TVM vm'iable
method.
for which
you
Press @
[SOLVE].The answer is computed,
displayed in tile TVM Solver, and stored to the
appropriate TVM variable, An indicator square in the left
colunm designates the solution variable.
N=360.00
I%=1B.00
PV=100000.00
PMT=-I507.09
FV=0.00
P/Y=I2.00
CXY=12.00
PMT:I:IIIIBEGIN
14-4
Financial
Functions
Using the Financial
Functions
Entering Cash
Inflows and Cash
Outflows
When
FINANCE CALC
Menu
To display
using
the TI-83
financial
functions,
CALC
the
enter
FINANCE CALC menu,
press
[_
[FINANCE].
VARS
i : TVM Sol ver.,.
2 : tvm
Pmt
3: tvm
I%
4:tvm
PV
5:tvm
N
6:tvm
FV
7:npv(
8:irr(
9: bal(
O:EPrn(
A:EInt(
B:_Nom(
C:_Eff(
D:dbd(
E: Pmt
End
F: Pmt
Bgn
Displays
Conlputes
Conlputes
Computes
Colnputes
Computes
Computes
Computes
Computes
Computes
Computes
Computes
Computes
tile TVM Solver.
the amount
of each payment.
the interest
rate per year,
the present
value.
the nulnber
of paylnent
periods,
the future value,
the net present
value,
the internal
rate of l_tum.
the amortization
sched, balance,
the amort, sched, principal
sum,
the amort, sched, interest
sum.
the nominal
interest
rate,
the effective
interest
rate.
Calculates
the days between
two dates,
Selects ordinary
annuity
(end of period).
Selects annuity- due (beginning
of period),
[ _se these functions
to set up and perform
calculations
on the home screen,
TVM Solver
you lnust
cash inflows
(cash received)
as positive
numbers
and cash
outflows
(cash paid) as negative
numbel\_.
The TI-S3
follows this convention
when computing
and displaying
answers.
TVM Solver displays
tile TVM Solver (page
Financial
financial
14-4).
Functions
14-5
Calculating
Calculating Time
Value of Money
Time Value of Money
I _se tilne-value-of-lnoney
(TVM)
(TVM) functions
(menu
through
6) to analyze financial
instruments
such
annuities,
loans, mortgages,
leases, and sa_ings.
items
2
as
Each TVM function
takes zero to six arguments,
which
must be real numbers.
The wdues that you specify as
arguments
for these functions
m'e not stored
to the TVM
variables
(page 14-14).
Note: To store a value to a TVM variable, use the TVM Solver (page
14-4) or use _
and any TVM variable on the FINANCE VARS
menu (page 14-14).
If you enter less than six arguments,
the TI-83 substitutes
previously
stored TVM vm'iable value for each unspecified
argument.
tvm_Pmt
If you
enter
place
the argmnent
any argunlents
with
a TVM function,
or arguments
tvm_Pmt
computes
the amount
tvm_Pmt
[(N,I %,PV,FV, P_,
In the example
nlust
in parentheses,
of each
payment.
C/Y) ]
N=360
I%=8.5
Pg=IO0000
PMT=O
FV=O
P/?=I2
C/V=12
PMT:I_I[ BEGIN
Note:
you
a
above, the values
tvm_Pmt
-768 91
tvm_Pr_t (360, 9: 5)
I
I
-840.85
are stored
to the TVM
variables in the TVM Solver. Then the payment (tyro_Pint)
is
computed on the home screen using the values in the TVM Solver.
Next, the interest rate is changed to 9.5 to illustrate the effect on the
payment amount.
14-6
Financial
Functions
tvm_]%
tvm_I% computes
the annual inte[_st
rate.
tvm_1%[(N,PV,PMT, FV, P/Y, C/Y) ]
10000, I
tvm_l%(48,
-250,0,
tvm_PV
12)
9
24
Rns÷l%
9124
tvm_PV computes
the present
tvm_PV[(_I%,PMT,
FV, P/Y,C/Y)]
vMue.
360÷N:II÷I%:-100
÷PMT:O÷FV:12÷P/
tvm_PV
I
tvm_N
12.00
1o5oo6.351
tvm_N computes
the number
tvm_N[(I%_V_MT,
of paylnent
periods.
FV, P/Y,C/Y)]
6÷I%:9000÷PV:-351
O÷PMT:O+FV:3÷P/V
tvm_N
tvm_FV
l
3.00
36.47
tvm_FVcomputesthe
_turevMue.
tvm_FV[(_I%,PV, PMT_X,C/Y)]
6÷N:8÷I%:-5500÷P
V:0÷PMT:l÷P/_.00
tvm_FV
8727.81
Financial
Functions
14-7
Calculating
Calculating a
Cash Flow
Cash Flows
Use
the cash
flow
functions
(menu
items
7 and 8) to
analyze the value of money over equal time periods.
You
can enter unequal
cash flows, which can be cash inflows
outflows.
The syntax
descriptions
for npv( and irr( use
these arguments.
•
interest
rate is the rate by which to discount
flows (the cost of money)
over one period.
the
•
CFO is the initial
nunlber.
be a real
•
CFList
is a list of cash
c_sh flow CFO.
•
CFFreq is a list in which each element
specifies
the
frequency
of occurrence
for a grouped
(consecutive)
cash flow amount,
which is the corresponding
element
of CFList.
The default is 1; if you enter values, they
nmst be positive
integers
< 10,000.
For example,
2000
cash
express
2000
;
I
flow
flow
at time
0; it nmst
alnounts
this uneven
cash
2000
T
after
flow
cash
the initial
in lists.
4000
1
or
I
4000
I
- 3000
CFO = 2000
CFList
CFFreq
npv(, irr(
= {2000,-3000,4000}
= {2,1,2}
npv( (net present value) is the sunl of the present values
for the cash inflows and outflows. A positive result for npv
indicates a profitable investment.
npv(interest
rate,CFO,CFList[,CFFreq])
irr( (internal rate of return) is the interest rate at which the
net present value of the cash flows is equal to zero,
irr(CFO,CFList[,CFFreq])
1000
0
1
2000
1
-2500
{1000,-2500,0,501
00,3000_+L1
I
<1000.00
14-8
Financial
Functions
5000
-2500 ....
nPv(6,-2000,Lt)
2920.65
irP(-2000,L1)
27.88
3000
Calculating
Amortization
Calculating an
Amortization
Schedule
Use
the amortization
functions
(menu
bal(
bal( computes
tile balance
ff)r an amortization
schedule
using stored wdues ff)r I%, PV, and PMT. npmt is the
number
of the payment
at which you want to calculate
a
balance.
It nmst be a positive
integer
< 10,000. roundvalue
specifies
the internal
precision
the calculator
uses to
calculate
the balance;
if you do not specify roundvalue,
then the TI-83 uses the cmTent
Float/Fix decimal-mode
calculate
balance,
sum of principal,
an amortization
schedule.
items
and sum
9, 0, and A) to
of interest
for
setting.
bal(npmt[,roundvalue])
IO0000÷PV:
EPrn(, Elnt(
8.5÷I%
bal (12)
I_.O0
99244.07
EPrn( computes
the sunl of the principal
during a specified
period for an amortization
schedule
using stored values for
I%, PV, and PMT. pmtl
is the starting paylnent,
pmt2 is the
ending payment
in the range, pmtl
and pmt2 nmst be
positive
integers
< 10,000. roufwlvalue
specifies
the internal
precision
the calculator
uses to calculate
the principal;
if you
do not specify- _vu.rwlvalue,
the TI-83 uses the current
Float/Fix deeinml-mode
setting.
Note: You must enter values for 1%, PV, PMT, and before computing
the principal.
EPrn(pmtl,pmt2[,rou_wlvalue])
Elnt( computes
the stun
of the interest
period for an amortization
schedule
I%, PV, and PMT. pmtl
is the starting
ending payment
in the range, pmtl
during
a specified
using stored values for
paylnent,
pmt2 is the
and pmt2 nmst be
positive
integers
< 10,000. roundvalue
specifies
the
internal
precision
the calculator
uses to calculate
the
interest;
if you do not specify- roundvalue,
the TI-83 uses
the emTent
Float/Fix deeinml-mode
setting.
Elnt(pmt
l ,pmt2[
,roundvalue
360÷N:
100000÷PV:
8.5÷1%:
-768.91÷P
MT:I2÷P/V
12.00
I
])
EF'Po (I, 12)755._ 93
EInt(l,12)_8470.99
Financial
Functions
14-9
Amortization
You want
Example:
Calculating an
Outstanding
Loan Balance
percent
APR. Monthly
payments
are 800, Calculate
the
outstanding
loan balance
after each payment
and displaythe results
in a graph and in the table,
to buy
a home
with
a 30-year
mortgage
at S
1, Press [_].
Press [] [] [] [] _
to set the
fixed-decimal
mode setting to 2, Press [] [] [] _
select Par graphing
mode,
Sci
to
I
Eng
II_34567891
Degree
_Pol
I
Se_
Dot
I
SiMi
hi, I e^8'
Horiz
G-T
2, Press [_
[FINANCE]
_
I
to display
the TVM Solver.
3. Press 360 to enter number
of payments.
Press [] 8 to
enter the interest
rate. Press [] [] [] 800 to enter the
paynmnt
amount.
Press [] 0 to enter the future value of
tile mortgage.
Press [] 12 to enter the payments
per
year, which also sets the compounding
periods
per year
to 12. Press [] [] _
to select PMT:END,
N=360.00
I%=8.00
PV=0.00
PMT=-800.00
FV=0.00
P/Y=12.00
C/Y=12.00
PMT:[_:IIL_
BEGIN
4. Press
Press
[] [] [] [] [] to place the cul_or on tile PV prompt.
@
[SOLVE] to solve for the present value.
N=360.00
I%=8.00
PV=109026.80
PMT=-800.00
FV=0.00
PIV=I2.00
C/Y=12.00
PMT:I:I_I_BEGIN
5, Press [] to display
stat plots. Press _
[FINANCE] 9 _[_
pI,:,I:I
pl,:,l:._
\X1 "r_T
YIT_baI(T)
14-10
Financial
Functions
plol:_
tile parametric
Y= editor. Turn off all
to define X1T as T. Press [] [g_
to define Y1T as bal(T).
6. Press _
to display- the window
tile values below.
Tmin=0
Xmin=0
Tmax=360
Xmax=360
Tstep=12
Xscl=50
variables.
Enter
Ymin=0
Ymax=125000
Yscl=10000
7, Press _
to draw the graph and activate the trace
cursor. Press [] and [] to explore the graph of the
outstanding bahmce over time. Press a number and then
press [gNY_ to xqew the balance at a specific time T.
1T=T
Y1T=b_I(T)
S, Press [g_
TblStart=0
ATbI=12
[TBLSET] and enter
the vMues
below.
9, Press [g_ [TABLE] to display the table of outstanding
balances (Y1T).
Tim
O,00
tZ.00
,"4
t -,a"
IaL0O
10907::7
YtT
10Bl11_
tlIEII00
E0.O0
31L00
rIB.00
I;0,00
lO60E:I,
1Oh9O_:
1031_g2
T-?_2{_00
72.00
10_:29g
10.Press [g0_ [] [] [] [] [] [] [] [] [] [V_Y_ to select G-T
split-screen mode, in which the graph and table are
displayed sinmltaneously.
Press _
the table.
to display- XIT (time) and YIT (balance)
_0.00
72,00
1.0Eg
1,0E5
96.00
t0B,0
.._.Eh.00
99_h
97510
t.OEg
T=132
X=132
?=93621.91
in
_
Financial
Functions
14-11
Calculating
Calculating
Interest
Conversion
an
,Nom(
Interest
Conversion
Use the interest conversion functions Onenu items B and
C) to convert interest rates from an annual effective rate to
a nominal rate (_Nom() or from a nominal rate to an annual
effective rate (_Eff().
_Nom( computes
the nominal
interest
rate. effective
and compounding
periods
nmst be real numbers.
compounding
periods
nmst be >0.
_Nom(effective
rate,compounding
_Nor_( 15.87,
,Eft(
14-12
Financial
periods)
4)15.00
)Elf( computes
compounding
compounding
the effective
periods
must
periods
must
_Eff(nominal
rate,compounding
_E€€(8,12)
Functions
rate
8.30
interest
be real
be >0.
rate. nominal
nulnbers.
periods)
rate and
Finding Days between Dates/Defining
dbd(
Use
the date
Payment Method
dbd( (menu
function
item
D) to calculate
the
number
of days between
two dates using the actual-daycount method,
datel and date2 can be numbers
or lists of
numbers
calendar.
within
the range
of the
dates
on the standard
Note: Dates must be between the years I950 through 2049.
dbd(date
l ,date2)
You can
enter
•
•
datel
and date2
in either
of two formats.
MM.DDYY (United States)
DDMM.YY (Europe)
The decimal placement
differentiates
the date formats,
dbd( 12. 3190, 12.3
192)
731.00
Defining the
Payment Method
Pmt_End and Pmt_Bgn (menu items E and F) specify- a
transaction
_k_an ordinmy7 annuity
or an annuity
due. VC]mn
you execute
either conunand,
the TVM Solver is updated.
Pint_End
Pmt_End (payment
end) specifies
an ordinmTy- annuity-,
where payments
occur at the end of eaeh payment
period.
Most
loans
are in this
catego[%
Pint_End
is the default.
Pmt_End
On the TVM Solver's PMT:END
PMT to ordinmTy- annuity.
Pmt_Bgn
BEGIN line, select
Pmt_Bgn (payment
beginning)
specifies
where payments
occur at the beginning
period.
Most leases are in this catego_7.
END to set
an annuity
due,
of each payment
Pmt_Bgn
On the TVM Solver's PMT:END
set PMT to annuity
due.
BEGIN line, select
Financial
Functions
BEGIN to
14-13
Using the TVM Variables
FINANCE VARS
Menu
To display
the FINANCE VARS menu,
press _
[_. You can use TVM variables
in TVM functions
values to them on the home screen,
CALC VARS
1: N
Total number
of payment
2:1%
Annual interest
rate
3: PV
Present
value
4:
5:
6:
7:
PMT
FV
P/Y
C/Y
[FINANCE]
and store
periods
Payment
amount
Future value
Number
Number
of payment
periods
per year
of compounding
periods/year
N, [%, PV, PMT,
FV
N, I%, PV, PMT, and FV are the five TVM wu'iables. They
t_present the elements of eonunon financial transactions,
as described in the table above. I%is an annual interest rate
that is converted to a per-period rate based on the values
of P/Y and C/Y.
PlY and C/Y
PW is the number of payment
financial transaction.
C/Y is the number
salne transaction.
periods
of compounding
per year in a
periods
per year in the
When you store a value to P/Y, the value for C/Y
automatically
changes to the same value. To store a unique
value to g/Y, you nmst store the value to C/Y after you have
stored a value to PlY.
14-14
Financial
Functions
5
Contents
CATALOG,Strings,
HyperbolicFunctions
Browsing tile TI-83 CATALOG ...........................
Entering and Using Strings ...............................
Storing Strings to String Variables
.......................
String Functions
and Instructions
in the CATALOG
Hyperbolic
Functions
in tile CATALOG ..................
......
15-2
15-3
15-4
15-6
15-10
T1=83
TEXAS INSTRUMENTS
m
CATALOG
_abs(
and
angle(
QNOUA(
Ans
augnenL(
AxesO_¢
J
STAT
PLOT
TBLSET
FORMAT
CATALOG,
Strings,
BALe
TABLE
Hyperbolic
Functions
15-1
Browsing
the TI-83 CATALOG
What Is the
CATALOG?
The CATALOG is an alphabetical
list of all functions and
instructions
on the TI-83. You also can access each
CATALOG item fronl a menu or the keyboard, except:
•
•
•
•
The six string functions (page 15-6)
The six hyperbolic functions (page 15-10)
The solve( instruction without the equation solver editor
(Chapter 2)
The inferential stat functions without the inferential stat
editors (Chapter 13)
Note:The only CATALOG programming commandsyou can execute
from the home screen are GetCalc(, Get(, and Send(.
Selecting an Item
from the
CATALOG
To select a CATALOG item, follow these steps.
1. Press F_a] [CATALOG]
to display the CATALOG.
i*abs(
and
angle(
RNOVR(
Rn_
iCRTRLOG
augment(
Axes0€€
The _ in the first colunm
is the selection
cursor.
2. Press [] or [] to scroll the CATALOG until the selection
cursor points to the item you want.
•
•
•
To jump to the first item beginning with a particular
letter, press that letter; alpha-lock is on.
Items that begin with a number are in alphabetical
order according to the first letter 'after the number.
For example, 2-PropZTest( is among the itenls that
begin with the letter P.
Functions that appear as symbols, such as +, -1, <,
and g(, follow the last item that begins with Z. To
jump to the first s3qnbol, !, press [@
3. Press [ggY_ to paste the item to the current
Iabs(1
screen.
I
Tip: From the top of the CATALOG menu, press [] to move to the
bottom. From the bottom, press [] to move to the top.
15-2
CATALOG, Strings,
Hyperbolic
Functions
Entering
What
and Using Strings
Is a String?
A string
is a sequence
On the TI-83,
•
It defines
text
to be displayed
•
It accepts
input
Characters
Entering a String
of characters
quotation
marks,
applications.
from
Count
•
Count each instruction
cos(, as one character;
instruction
or function
number,
letter,
and space
to form
as one character,
a string
follow
on a blank line on the home
these steps.
1, Press
@
[,] to indicate
2, Enter
the characters
that
the beginning
comprise
Use any combination
names, or instruction
•
To enter
•
To enter several
alpha characters
[A-LOCK] to activate
alpha-lock.
@
space,
[-] to indicate
screen
or in a
of the string.
the string.
•
3, Press
a string.
or function
name, such as sin( or
the TI-83 interprets
each
name as one character.
To enter
program,
ablank
within
primaFy"
in a program,
that you combine
•
enclose
has two
in a p_x)gram.
the keyboard
are the units
each
that you
a string
of numbers,
letters,
function
names to create the string.
press
@
[_],
in a row,
press
[_
the end of the string.
"string"
4. Press [ENY_. On the home screen,
the string is displayed
on the next line without
quotations.
An ellipsis (...)
indicates
that the string continues
beyond
the screen,
To scroll the entire string, press [] and EO"RBC,D, 1234
EFGH
5678
RBCD 1234
EFGH ...
Note: Quotation marks do not count as string characters.
CATALOG,
Strings,
Hyperbolic
Functions
15-3
Storing
Strings
String Variables
to String Variables
The
TI-83
has
10 variables
You can use string
instructions.
to which
variables
with
you can
string
store
functions
strings.
and
To display the VARS STRING menu, follow these steps.
1, Press _
to display- the VARS menu, Move the cursor
to 7:String.
_
Y-VRRS
ndo_z..
2: Zoom.
3: GDB...
4: Picture...
5: Statistics_.
6: Table...
WString...
2, Press_
to displaytheSTRING secondarymenu,
5:Str3
Str4
Str5
Str6
,Str7
15-4
CATALOG,
Strings,
Hyperbolic
Functions
Storing a String
to a String
Variable
a string
to a string
1. Press
@
[,], enter
2. Press
_.
To
store
3. Press _
4.
Select
which
variable,
the string,
7 to display
the string
you want
follow
these
and press
steps.
@
[-].
the VARS STRING menu.
variable
to store
(from $trl
the string.
to $tr9, or $tr0)
to
4:Str.4
5:StP5
6:_tr6
74Str-7
The string variable
is D_sted to the current
location,
next to the store symbol (-)).
cursor
Press _
to store the string to the string variable.
On
the home screen, the stored string is displayed
on the
next line without
quotation
marks.
"HELL0"eStP2
HELLO
Displaying
the
Contents
of a
String
Variable
To display the contents
of a string variable
on the home
screen, select the string variable
from the VARS STRING
menu, and then press [gNT_. The string is displayed.
I
St.r2
HELLO
CATALOG,
Strings,
Hyperbolic
Functions
15-5
String Functions
Displaying String
Functions and
Instructions in
the CATALOG
and Instructions
String
functions
in the CATALOG
and instructions
m'e available
only fronl
the CATALOG. The table below lists the string functions
and instructions
in the order in which they appem" among
the other CATALOG menu items. The ellipses
in the table
indicate
the presence
of additional
CATALOG items.
CATALOG
+ (Concatenation)
Equ)String(
expr(
Converts
Converts
inString(
Returns
a chm'acter's
length(
Returns
a string's
String)Equ(
sub(
Converts
Returns
a string to an equation,
a string subset
as a string,
To concatenate
two or more
1, Enter
stringl,
2, Press
[],
3, Enter
string2,
necessmT,
stringl
4, Press
15-6
CATALOG,
number.
chm'acter
length.
follow
name.
which
can be a string
or string
name,
press
[] and enter
to display-
Hyperbolic
steps,
or string
string3,
If
and so on,
, ,
the strings
as a single
string.
: 5tr
To select a string function
or instruction
current
screen, follow the steps on page
Strings,
these
can be a string
+string2+string3,
[_
strings,
place
which
1 +"LMHOP"
"HIJK
"+StPl
HIJK
LMNOP
Selecting a String
Function from
the CATALOG
an equation
to a string,
a string to an expression.
Functions
and paste
15-2.
it to the
Equ*String(
Equ*String( converts to a string an equation that is stored
to any- VARS ¥-VARS variable. Yn contains the equation.
Strn (from Strl to Strg, or Str0) is the string variable to
which you want the equation to be stored as a string.
Equ*Stdng(Yn,Strn)
expr(
"3X"÷Y1
E_u*String(gt,
Done
St
rl)
Done
expr( converts
an expression
the chm'acter
and executes
string contained
in string
to
it. string
can be a string or a
stringvariable.
expr(string)
,,l+2+XZ,,)
l_X:"5X"+Strl
x_r(Strl)÷R
inString(
10
I0
7
exPr(
inString( returns the chm'acter position in string of the first
character of substring, string can be a string or a string
variable, start is an optional character position at which to
start the search; the default is 1.
inString(string,subst,ring[
inStr
,start])
ing ( "PQRSTU
V", "STU" )
4
inStr ing ( "RBCRBC
,
Note:
RBC ,4)
4
If st:_ing does not contain
snbst:Hng,
or start
is greater than the
lengthof string, inString( returns O.
CATALOG,
Strings,
Hyperbolic
Functions
15-7
length(
length(
returns
can be a string
the number
or string
of chara('ters
in st'ring,
string
variable.
Note: An instruction or function name, such as sin( or cos(, counts as
one character.
length(string)
WXYz"WXYZ"eStrl
length(Strl)
String*Equ(
4
String*Equ( converts
st'ring into an equation
and stores
equation
to Yn. st'ring can be a string or string vmiable,
String*Equ(
is tlle inverse
of Equ*String(.
String*Equ(st'ring,Yn)
I
String*E_u(Str2,
'.?z)
Plot1
Done
Plot;"
Plot3
,,yl=
",YzB2X
15-8
CATALOG,
Strings,
Hyperbolic
I
I
Functions
tlle
sub( returns
sub(
a string
that
is a subset
of an existing
st'ring.
string
can be a string or a string variable,
begin is the
position
number
of the first character
of the subset,
length
is the number
of characters
in the subset.
sub(st_ng,b_in,length)
I
sub(StP5,4,2)
ABCDEFG"RBCDEFG"÷SLP5
DE
Entering
Function
a
to
Graph during
Program
Execution
Inapmgram,
youcanentera
programexecutionusin
Nnctiontographdunng
theseconunands.
PROGRRM:INPUT
:InPut
"ENTRY ='' ,
StP3
:String*E_u(Str3
,Y_)
:DisPGraPh
PPYmINPUT
ENTRY=3XI
/
/
/
Note: When you execute this program, enter a function to store to Y3
at the ENTRY= prompt.
CATALOG,
Strings,
Hyperbolic
Functions
15-9
Hyperbolic
Functions
Hyperbolic
Functions
The
hyperbolic
in the CATALOG
functions
are available
only
from
the
CATALOG, The table below lists the hyperbolic
functions
in
the order in which they appear among the other CATALOG
menu items. The ellipses in the table indicate
the presence
of additional
CATALOG items.
CATALOG
sinh(, cosh(,
tanh(
c0 s h (
c 0 s h-1 (
Hyperbolic
Hyperbolic
cosine
arccosine
s i nh (
si nh-1 (
Hyperbolic
Hyperbolic
sine
arcsine
t a nh (
t a nh- 1(
Hyperbolic
Hyperbolic
tangent
arctangent
sinh(, cosh(, and tanh( are the hyperbolic
functions.
valid for real numbers,
expressions,
and lists.
Each
sinh(value)
cosh(value)
tanh(value)
sinh(.5)
.5210953055
cosh( {.25,. 5, I} )
{1.8314131
sinhd(, cosh-l(,
tanh-l(
1.12
sinh-l( is the hyperbolic arcsine function, cosh-l( is the
hyperbolic arccosine function, tanh-l( is the hyperbolic
m'ctangent function. Each is valid for real nulnbers,
expressions, and lists.
sinh- l(value)
cosh- 1(value)
sinh -1(value)
sinh-1({O,l})
I
{0 .881373587}I
tanh-1(-.5)
-.5493061443
15-10
CATALOG,
Strings,
Hyperbolic
Functions
is
6
Contents
Programming
Getting Started: Volume of a Cylinder ....................
Creating and Deleting Programs
.........................
Entering Colnmand
Lines and Executing
Programs
Editing Programs
........................................
Copying and Renaming
Programs
........................
PRGM CTL (Control)
Instructions
.......................
PRGM I/O (Input/Output)
Instructions
...................
('ailing Other Programs
as Subroutines
..................
'_
TEXAS
......
16-2
16-4
16-5
16-6
16-7
16-8
16-16
16-22
T1=83
INSTRUMENTS
PROGRRM: CYL INDER
:PromPt R, H
:_R zH÷V
:O ise "VOLUME
IS
.,.j
:I
J
STATPLOT
TBLSET
FORMAT
CALC
TABLE
Programming
16-1
Getting
Getting
Started:
Started
Volume
is a fast-paced
of a Cylinder
introduction.
Read the chapter
for details.
A program is a set of connnands that the TI-83 executes sequentially, as if you
had entered them fl'om the keyboard. Create a program that prompts for the
radius R and the height H of a cylinder and then computes its volume.
Press [E_
[] [] to display the
PRGM NEW menu.
EXEC EDIT [{L_
BBCreate
Press [_
to select 1:Create New. The
Name= prompt is displayed, and alpha-lock
is on. Press [c] [Y] [L][I] [N] [D] [E] [R], and
then press [g_-gm to name the prograin
CYLINDER.
Flew
PIROGRRM:CYLINDER
You are now in the program editor. The
colon ( : ) in the first colunm of the second
line indicates the beginning of a command
line.
Press [E_
[] 2 to select 2:Prompt from
the PRGM I/O menu. Prompt is copied to
the command line. Press @
[R] []
@
[H] to enter the variable names for
radius and height. Press [_.
Press [g_ Ix] @
[R] [] @
[H] [g?_
@
[v] [_
to enter the expression
_R2H and store it to the variable V.
16-2
Programming
PROGRRM: CYL INDER
Press J_
[] 3 to select 3:Disp fronl the
PRGM I/O menu. Disp is p_ksted to the
conunand line. Press J_ [A-LOCK]["] [V]
[O]
[L]
[U]
[M]
[E][_]
[I]
[S]
["]@1_
@
[V] _
to set up the program to
display" the text VOLUME IS on one line and
the calculated value of V on the next.
6.
Press J_
screen.
PROGRAM:CYLINBER
l:ProMPt R,H
I
:=RZH+V
_DisP "VOLUME
IS
:i v
[QUIT]to display tile home
7. Press [gff_ to display- the PRGM EXEC
menu. The items on this menu are the
names of stored programs.
_EOIT
NEW
LINOER
Press [g_
to paste prgmCYLINBER to the
cmTent cursor location. (If CYLINDER is
not item 1 on your PRGM EXEC menu,
move the cursor to CYLINDERbefore you
press [ggT_. )
Prg_CYLINOER|
Press [ggT_ to execute the prograln. Enter
1.8 if)r the radius, and then press [g_.
Enter a for the height, and then press
[g_.
The text VOLUME iS, the value of V,
and Done are displayed.
PPgMCYLINDER
R=?1.5
H=?3
VOLUME
IS
21.20575041
I
Bone
Repeat steps 7 through 9 and enter
different values for R and H.
Programming
16-3
Creating
and Deleting
Programs
What Is a
Program.'?
A prograln
Creating a New
Program
To create a new program,
is a set of one or more
connnand
lines.
Each
line contains
one or more instructions.
When you execute
a
prograln,
the TI-83 perk)tins
each instruction
on each
connnand
line in the salne order in which you entered
them. The number
and size of programs
that the TI-83 can
store is limited only by available
lnelnolT.
1. Press _
k)llow these steps.
[] to display tile PRGM NEW menu.
EXEC EDIT IIL=I_
HBCreate
New
2. Press _
is displayed,
to select 1:Create New. The Name= proInpt
and alpha-lock is on.
3. Press a letter fi'oln A to Z or 0 to enter tile first
character of tile new program nalne.
Note: A program name can be one to eight characterslong. The
first character must be a letter from A to Z or e. The second
through eighth characters can be letters, numbers, or e.
4. Enter zero to seven letters, numbers,
the new prograln nalne.
5, Press ITNYERI,
Tile prograin
6. Enter one or more prograln
editor is displayed.
commands
7. Press [_ [QUIT]to leave the progranl
to the holne screen.
Managing
Memory and
Deleting a
Program
or 0 to conlplete
(page 16-5).
editor and return
To check whether
adequate
nlenlol_y- is available
for a
prograln
you want to enter, press [_
[MEM], and then
select 1:Check RAM froln the MEMORY menu (Chapter
18).
To increase
available
nlenlolTy- , press [_
[MEM], and then
select 2:Delete froln the MEMORY menu (Chapter
18).
To delete a specific prograln,
press [_
[MEM], select
2:Delete froln the MEMORY menu, and then select 7:Prgm
froln the DELETE FROM seeondalT
menu (Chapter
18).
16-4
Progranuning
Entering
Command
Entering a
Program
Command Line
Lines and Executing
Programs
You emn enter on a eonulland lille any instruction or
expression that you could execute from the home screen. In
the program editor, each new eonunand line begins with a
colon. To enter more than one instruction or expression on a
single eonunand line, separate each with a colon.
Note: A command line can be longer than the screen is wide; Iong
command lines wrap to the next screen line.
While ill the program editor, you call display and select
fronl menus. You can return to the prograln editor fronl a
menu in either of two ways.
•
Select a menu item, which pastes the item to the
cmTent conunand line.
•
Press @.
When you complete
CUrSOr
nloves
a eolnmand
tile next
to
line, press [NY_. The
eonulland
lille,
Progralns can access variables, lists, lnatrices, and strings
saved in nlenlol_yL If a prograln stores a new wdue to a
variable, list, lnatrix, or string, the prograln changes the
value in nlenlory during execution.
You e an call another
and page 16-22).
Executing a
Program
prograln
as a subroutine
(page 16-15
To execute a program, begin on a blank line on the home
screen and follow these steps.
1. Press [_
to display- the PRGM EXEC menu.
2. Select a pmgraln nalne froln the PRGM EXEC lnenu
(page 16-7). prgmname is pasted to the home screen
(for example, prgmCYUNDER).
3. Press [_
to execute the program. While the program
is executing, the busy indicator is on.
L_Bt Answer (Ans) is updated during prograln execution.
Last EntlT is not updated as each eonulland is executed
(Chapter 1).
The TI-83 checks for errors during prograln execution.
does not check for errors msyou enter a progranL
Breaking a
Program
To stop
nlenu
prograln
execution,
press
[_.
The
It
ERR:BREAK
is displayed.
•
To return
•
To go where
to the honle
screen,
the interruption
1:Quit.
select
occurred,
select
Programming
2:Goto.
16-5
Editing
Programs
Editing a
Program
To edit
a stored
1. Press
[V_
program,
ff)llow
[] to display-
these
the PRGM
steps.
EDIT menu.
2. Select a program
name froln the PRGM EDIT menu (page
16-7), Up to the first seven lines of the program
are
displayed.
Note: The program editor does not display a ¢ to indicate that
a program continues beyond the screen.
3, Edit
the program
conlnland
lines.
•
Move tile cursor
to the appropriate
then delete,
ove_wvrite, or insert.
•
Press @
to clear all program
eomnmnd
line (the lending colon
enter a new progrmn
eonmmnd.
location,
eominands
remains),
and
on the
and then
Tip: To move the cursor to the beginning of a command line, press
[_; to move to the end, press _ lB. To scroll the cursor down
seven command lines, press @
[_. To scroll the cursor up seven
command lines, press @
[_.
Inserting and
Deleting
Command
Lines
To insert a new eonnnand
line anywhere
in the progranl,
place the cursor
where you want the new line, press [_
[tNs], and then press [_T_.
A colon indicates
a new line.
To delete a conlnland
line, place the cursor
on the line,
press @
to clear all instructions
and expressions
on
the line, and then press [ff_ to delete the eonlnland
line,
including
the colon.
16-6
Programming
Copying
and Renaming
Copying and
Renaming a
Program
Programs
To copy
all conunand
program,
Program
follow steps 1 through
5 for Creating
a New
(page 16-4), and then follow these steps.
lines
fronl
one progranl
into
a new
1. Press [_
[RCL]. Rcl is displayed
on the bottom
line of
the prograln
editor in the new program
(Chapter
1).
2. Press
_
[] to display-
the PRGM
3. Select a nalne fronl
the menu.
tile bottom
line of the program
EXEC menu.
prgmname
editor.
is pasted
to
4. Press [ENt_. All colnnland
lines fl'om the selected
program
are copied into the new program.
Copying programs
applications.
h_s
at least
•
You can create a template
that you use Kequently.
•
You can rename
a new program.
a program
two
convenient
for groups
by copying
of instl_ctions
its contents
into
Note: You also can copy all the command lines from one existing
program to another existing program using RCU
Scrolling the
PRGM EXEC and
PRGM EDIT
Menus
The
TI-S3 sorts PRGM EXEC and PRGM EDIT menu
automatically
into alphanumerical
order. Each
labels the first 10 itenls using 1 through
9, then
items
menu
0.
only
To jump to the first prograln name that begins with a
particular alpha character or O, press @
[letter from A
to Z or 0].
Tip: From the top of either the PRGM EXEC or PRGM EDIT menu,
press [] to move to the bottom. From the bottom, press [] to move to
the top. To scroll the cursor down the menu seven items, press @
[]. To scroll the cursor up the menu seven items, press @
[].
Programming
16-7
PRGM CTL (Control)
PRGM CTL Menu
Instructions
To display the PRGM CTL (program control)
[_
from the prograln editor only.
CTL I/0
i: If
2: Then
3: Else
EXEC
4: For(
5: While
6:
7:
8:
9:
O:
A:
B:
C:
menu, press
Repeat
End
Pause
Lbl
Geto
IS>(
DS<(
Menu(
D: prgm
E: Return
F: Stop
G: DelVar
H: GraphStyle(
Creates a conditional test.
Executes conlnlands when If is true,
Executes eonnnands when If is false,
Creates an incrementing loop.
Creates a conditional loop.
Creates a conditional loop.
Signifies the end of a block.
Pauses program execution,
Defnes a label.
Goes to a label.
Increments and skips if greater than.
Decrements
and skips if less than.
Defines menu items and branches.
Executes a program as a subroutine.
Returns from a subroutine.
Stops execution.
Deletes a wuiable from within program.
Designates the graph style to be drawn.
These menu items direct the flow of an executing program.
They make it eaksy to repeat or skip a group of commands
during program execution. When you select an item from
the menu, the name is pasted to the cursor location on a
conlnland line in the program.
To return to the program
press @.
Controlling
Program Flow
OF
If N=I and M:l:Goto
Programming
selecting
an item,
Program control instructions tell the TI-83 which
command to execute next in a program, If, While, and
Repeat check a defined condition to determine which
command to execute next, Conditions frequently use
relational or Boolean tests (Chapter 2), as in:
If A<7:A+I->A
16-8
editor without
Z
[ _se If for testing
and branching.
If condition
then the command
inunediately
following
condition
is true (nonzero),
then the next
executed.
If instructions
can be nested.
is false
(zero),
If is skipped.
If
command
is
:If condition
:command
:command
(if true)
Program
PROGRAM:
: O÷R _
:Lbl
COUNT
output
PrgmCOUNT
IR IS
::OisP
A+l÷A._ M T_-,,
i_ _,,,
: If' R_2
I: Stop
1:Goto
If-Then
R IS
Z
Then following
an If executes
condition
is true (nonzero).
group of commands.
a group of commands
if
End identifies
the end of the
:If condition
:Then
:command
:command
:End
(if true)
(if true)
:co_and
Program
PROGRRM:TEST
:I÷X:IO÷Y
:I_ X<IO
:Then
:2X+3÷X
:2Y-3÷Y
l:End
I:OisP X,Y
output
PPgmTEST
Programming
O0_!
16-9
If-Then-Else
Else following
If-Then executes
condition
is false (zero).
group of commands.
a group
End identifies
of commands
if
the end of the
:If condition
:Then
:command
:command
:Else
(if true)
(if true)
:command
:command
:End
:command
(if false)
(if false)
Pro_lram
PROGRRM" TESTELSE
:InPut
"X=",X
: Ii_ X<B
: Then
: Xz÷y
: Else
: X÷Y
: End
: OisP
For(
output
_:_TESTELSE
{5 5}
X=-5
Done
{-5 25}
Done
{X,Y}
For( loops and inc[_ments.
It increments
begin to e_d by increme_t,
increment
is 1) and can be negative
(end<begin).
or lnininmnl
value not to be exceeded.
end of the loop.
For( loops
variable
fron]
is optional
(default
end is a nlmKinlunl
End identifies
the
can be nested.
:For(variable,begin,end[,increme_t])
:command
(while end not exceeded)
:command
(while e_d not exceeded)
:End
:command
Pro_lram
PROGRRM: SQURRE
: For(R, 0, 8, 2)
output
::EDi,
Ip RZ
PPgf_SQURRE
16-10
Programming
Oon40e643616
While
While performs a group of commands while condition is
true. condition is frequently a relational test (Chapter 2).
condition is tested when While is encountered.
If
condition is true (nonzero), the program executes a group
of commands,
End signifies the end of the group, When
condition is false (zero), the p_)gram executes each
command following End. While instructions can be nested.
:While condition
:command (while condition
:command (while condition
:End
:command
Program
PROGRAM:
: O÷l
:While
: J+l÷J
: I+l÷I
: End
I:DisP
Repeat
is true)
is true)
Output
LOOP
_,.,_
,_9mLOOP
J=
Done6
,J
Repeat repeats
a group of commands
until condition
is
true (nonzero).
It is similar to While, but condition
is tested
when End is encountered;
therefore,
the group of
commands
is always
executed
at least once. Repeat
instructions
can be nested.
:Repeat condition
:command
(until
:command
(until
:End
:command
condition
condition
Program
PROGRRM: RLOOP
I:0÷I
:O÷J
>
:Repeat
I_6
:J+l÷J
: I+l÷I
:End
F DisP .J= , J
is true)
is true)
Output
,_r-cJrqRLOOP
Programming
Done6
16-11
End
End identifies
the end of a group
of commands.
You nmst
include
an End instruction
at the end of each For(, While, or
Repeat k)op. Also, you nmst paste an End instruction
at the
end of each If-Then group and each If-Then-Else
group.
Pause
Pause suspends
execution
of the program
so that you can
see answers
or graphs,
During the pause, the pause
indicator
is on in the top-right
corner. Press _
to
resume
execution.
Pause without
a value temporarily
If the DispGraph or Disp instruction
the appropriate
screen
is displayed.
pauses the pr()gram.
has been executed,
Pause with value displays value on the current
screen, value can be scrolled.
home
Pause [value]
Program
PROGRRM: PRUSE
: 10+X
: "XZ+2"÷y1
:DisP
"X=",
X
: Pause
: DisPGraF-h
I: Pause
l:OisP
16-12
Programming
output
PPgF_PRUSE
X=
10
Lbl, Goto
Lbl (label)
and Goto (go to) are used
together
for
branching.
Lbl specifies
the label for a conlnland,
two characters
(A through
Z, 0 through
label can be one or
99, or 0).
Lbl label
Goto causes
encountered.
the program
to branch
to label when
Goto is
Goto label
output
Pro_lram
PROGRRM:
CUBE
: Lbl 99
: Input
R
: If' R._100
: Stop
:Dise
R -_
IPegmCUBE
?31105
I:Pause
I:Goto
IS>(
Done
27
8
99
IS>( (inc_ment
and skip) adds 1 to variable.
If the answer
]s > value (which
can be an expression),
the next
command
is skipped;
if the answer
is _<value, the next
command
is executed,
variable
cannot
be a system
variable,
:lS>(variable,value)
:command
(if answer
:command
(if answer
_<value)
> value)
Program
Output
I
IPROGRRM:::::
DispDi-_pT÷RIs>(R;'6)NOT>
ISKIP6
> 6"
_r_mISKIP
Done
Note: IS>( is not a looping instruction.
Programming
16-13
DS<( (decrement
DS<(
and skip)
subtracts
1 fronl
variable.
If the
answer is < value (which
can be an expression),
the next
command
is skipped;
if the answer
is _>value, the next
command
is executed,
variable
cannot
be a system
variable,
:DS<(variable,wdue)
:command (if answer
:command (if answer
_>value)
< value)
Pro_lram
:DS\ (A, 6>
:DisP
"> DSKIP
6"
PROGRRM::
I+R
:DisP
'NOT > 6
I
Note: DS<( is not a looping instruction.
Menu( sets
Menu(
up branching
within
If Menu( is
a program.
encountered
during prograln
execution,
the menu screen
displayed
with the specified
menu items, the pause
indicator
is on, and execution
pauses
until you select a
menu item.
is
The lnenu title is enclosed
in quotation
lnarks ( " ). Up to
seven pairs of menu items follow. Each pair conlprises
a
text item (also enclosed
in quotation
marks)
to be
displayed
as a menu selection,
and a label item to which to
branch
if you select the corresponding
menu selection.
Menu("title","te:ct
l",label
l ,"te:ct2",label2
....
)
Program
:Menu(
TOSS
DICE
","FRIR
OICE",R,
PROGRR_,!: TOSSDICE
;WEIGHTED
DICE
,
The progranl
above pauses
until you select
select 2, for example,
the menu disappears
program
continues
execution
at Lbl B.
16-14
Programming
DICE
i
1 or 2. If you
and the
prgm
[ _se prgm to execute other programs as subroutines
(page
16-22). When you select prgm, it is pasted to the cut, or
location. Enter characters to spell a program name. Using
prgm is equivalent to selecting existing programs fronl the
PRGM EXEC menu; however, it allows you to enter the
name of a program that you have not yet created.
prgmname
Note: You cannot directly enter the subroutine
name when using RCL.
You must paste the name from the PRGM
EXEC menu (page I6-7).
Return
Return quits the subroutine and returns execution to the
calling program (page 16-22), even if encountered
within
nested loops. Any loops are ended. An implied Return
exists at the end of any- program that is called as a
subroutine. Within the main program, Return stops
execution and retut_ls to the honle screen.
Stop
Stop stops execution of a program and returns to the home
screen. Stop is optional at the end of a program.
DelVar
DelVar deletes fronl nlenlory
the contents
of variable.
DelVar variable
PROGRRH:
DELMRTR
: DelUar.
[R]I
GraphStyle(
I
GraphStyle( designates the style of the graph to be drawn.
fanction#
is the number of the Y= function name in the
current graphing mode. graphstyle is a number from 1 to 7
that corresponds
to the graph style, as shown below.
1
2
3
4
=
=
=
=
".
"i
![
[k
(line)
(thick)
(shade
(shade
above)
below)
5 = '_.)(path)
6 = .'.'.'(animate)
7 = ". (dot)
GraphStyle{fanction#,graphstyle)
For example, GraphStyle(1,5) in Func mode sets the graph
style for Y1 to '_.)(path; 5).
Not all graph styles are available in all graphing modes. For
a detailed description of each graph style, see the Graph
Styles table in Chapter 3,
Programming
16-15
PRGM
I/0 (Input/Output)
PRGM I/0 Menu
To display
press
_
CTL
I10
i:
the
[]
Instructions
PRGM I/0 (progranl
fronl
within
menu,
editor
only.
EXEC
Enters
Input
a value
or uses
Prompts
3: Disp
Displays
text, value, or the home screen.
Displays
the current
graph.
Displays
the current
table.
Displays
text at a specified
position.
Cheeks the keyboard
for a keystroke.
Clears the display.
Clears the current
table.
Gets a wtriable
froln another
TI-83.
Gets a varialfle
from CBL 2/CBL or CBR.
Sends a variable
to CBL 2JCBL or CBR.
5: DispTable
6:Output(
7: getKey
8:C1 rHome
9: ClrTable
O: GetCalc(
A: Get(
B: Send(
for enhT
the cursor.
2: Prompt
4: DispGraph
These instructions
control
program
during execution.
and displayTo return
press
Displaying a
Graph with Input
input/output)
tile prograln
answers
input
They
during
to the program
values.
to and output fronl a
allow you to enter values
program
editor
of variable
execution.
without
selecting
an item,
@.
Input without
a variable
displays
the
current
graph.
You
can move the free-moving
cursor,
which updates
X and Y
(and R and 0 for PolarGC format).
The pause indicator
is
on. Press [gNYgmto resulne
prograln
execution.
Input
Program
PROGRRM: GIHPUT
: FnOff
:ZOeoimal
I:Input
: Dise
Output
Pr, gmG IHPUTI
X, V
I1=_:,6
[.
?=:!..5
PrgmG IHPUT
2.6
1.5
Done
16-16
Programming
Storing
Variable
with
a
Value
Input
Input with
variable
displays
a ? (question
nlark)
prompt
dm'ing execution,
variable
may be a real number,
complex
number,
list, matrix,
string, or Y= function.
Dm'ing program
execution,
enter a wdue, which can be an expression,
and
then press [_T_].
The value is evaluated
and stored to
variable,
and the program
resumes
execution.
Input
[variable]
You can display- text or the contents
of Strn (a string
variable)
of up to 16 ehm'acters
as a prompt.
During
program
execution,
enter a value after the prompt
and then
press [_T_]. The value is stored to variable,
and the
progranl
resunlos
execution.
Input ["text",variable]
Input [Strn,variable]
Program
PROGRRM:
HINPUT
output
Pr.gFiH INPUT
?2
-'InPut
"YI=",YI
?{1,2,3}
-'InPut
DRTR
:OisP
:OisP
"DRTR=",
Vt ="2X+2"
VI(R)
YI(LI)
-"Oi_P
'_t (LORTR)
DRTR={4,
5, 6}
6
{4 6 8}
{10 12 14}
Oone
Note: When a program prompts for input of lists and Yn functions
during execution, you must include the braces ( { } ) around the list
elements and quotation marks ( " ) around the expressions.
Programming
16-17
During
Prompt
program
execution,
Prompt
displays
each
variable,
one at a time, followed
by =?. At each prompt,
enter a
value or expression
for each variable,
and then pl_ss
[ggT_. The values are stored,
and the prograln
resulnes
execution.
Prompt
variableA
[,variableB,...,variable
n]
Program
PROGRAM:WINDOW
:PronPt XMin
:Pror_Pt
XMax
:ProMPt Ymin
output
:PromPt
V_ax=?3
XMin=?-le
X_ax=?lO
_Min=?-3
PrgMWINOOW
YMax
Done
Note: Y= functions are not valid with Prompt.
Displaying the
Home Screen
Disp (display)
without
a value displays
the home screen.
To _ew the home screen
during program
execution,
follow
the
Disp instruction
with
a Pause
instruction.
Disp
Displaying
Values and
Messages
Disp with
one or more
values
displays
Disp [valueA,valueB,valueC,...,value
is a variable,
the value
of each.
n]
•
If value
•
If value is an expression,
it is evaluated
displayed
on tile right side of the next
•
If value is text within quotation
marks, it is displayed
the left side of the current
display- line. -) is not valid
text.
Program
:OisP "THE
PROGRRM:R
R IS
,x/2
RNSWE
If Pause is encountered
temporarily
so you can
execution,
press [_T_].
the current
value
is displayed.
and the result
line.
is
on
as
Output
PPgNA
THE ANSWER
IS
1.578796327
Done
after Disp, the program
halts
examine
the screen, To resume
Note: If a matrix or list is too large to display in its entirety, ellipses (...)
are displayed in the last column, but the matrix or list cannot be
scrolled. To scroll, use Pause w/ue (page I6-I2).
16-18
Programming
DispGraph
DispGraph
(display-
graph)
displays
the current
graph.
Pause is encountered
after DispGraph,
the program
temporarily
so you can examine
the screen. Press
resume
execution,
If
halts
_
to
DispTable
DispTable (display
table) displays
program
halts temporarily
so you
Press _
to resume
execution,
Output(
Output( displays text or value on the current home screen
beginning at row (1 through 8) and column (1 through 16),
ove_vriting any existing characters.
Tip:
tile current table, The
can examine
the screen.
You may want to precede Output( with ClrHome
(page 16-20).
Expressions
are evaluated and values are displayed
according to the current mode settings. Matrices are
displayed in entw format and wrap to the next line. -> is
not valid as text.
Output(fvw,column,"text")
Output(row,column,v_ue)
Program
• I
PROGRRM.OJTPUT
:3+5+B
:CIrHoMe
:OutPut(5,4,"RHS
WER:"
:Out.eut.(5,12,B)
For Output( on a Horiz split screen, the nlaxinlunl
row is 4.
value for
Programming
16-19
getKey returns a number corresponding
to the last key
pressed, according to the key code diagraln below. If no
key- has been pressed, getKey t_turns O. Use getKey inside
loops to transfer control, for example, when creating video
getKey
gaines.
Program
PROGRRM:GETKEV
:While 1
:getKeu+K
:While K=O
:getKe_eK
:End
:OisP K
:I¢ K=105
Output
PPg_GETKEV
Note: _,
[_,
[_,
and
were pressed during
program execution.
:Stop
:End
Note: You can press [_
program (page 16-5).
TI-83 Key Code
Diagram
at any time during execution to break the
C15D12_22!
IZD C_
IZ]
Ei_
--E521-
ClrHome (clear home screen)
during program execution.
ClrHome,
CIrTable
1
Done
clears the home screen
ClrTable (clear table) clears the values in the table during
program execution.
16-20
Programming
GetCalc(
GetCalc(
gets the contents
of variable
on another
TI-83
and
stores it to variable
on the receiving
TI-83. variable
can be
a real or complex
number,
list element,
list name, matrix
element,
matrix name, string, Y= variable,
graph database,
or picture.
GetCalc(variable)
Note: GetCalc(
Get(, Send(
does not work between TI-82s and TF83s.
Get( gets data fronl the Calculator-Based
Laboratory
TM
(CBL 2 TM, CBL TM) System or Calculator-Based
Ranger TM
(CBR TM) and stores
it to variable
on the receiving
TI-83.
variable
can be a real number,
list element,
list name,
nmtrix element,
nmtrix name, string, Y= variable,
graph
database,
or picture.
Get(variable)
Note: If you transfer a program that references the Get( command to
the TF83 from a TI-82, the TF83 will interpret it as the Get( described
above. Use GetCalc( to get data from another TI-83.
Send( sends the contents
of variable
to the CBL 2/CBL or
CBR. You cannot use it to send to another
TI-83. variable
can be a real
nmnber,
list element,
list name,
matrix
element,
matrix name, string, Y= variable,
graph
or picture,
variable
can be a list of elements.
database,
Send(variable)
PROGRRM:GETSOUND
:Send({3,.000_5,
99,1,0,0,0,0,1})
:Get(L1)
:Get(Lz)
Note: This program
and time in seconds
CBL 2/CBL.
gets sound data
from
Note: You can access Get(, Send(, and GetCalc( from the
CATALOG to execute them from the home screen (Chapter 15).
Programming
16-21
Calling
Other Programs
Calling a
Program from
Another Program
as Subroutines
On the TI-83, any stored program can be called fronl
another program as a subroutine, Enter the name of the
program to use as a subroutine
on a line by itself,
You can enter a program name on a conunand line in either
of two ways,
• Press NggM][] to display the PRGM EXEC menu and
select the name of the program (page 16-7). prgmname is
pasted to the cm_'ent cm_sor location on a conullalld line.
• Select prgm from the PRGM CTL menu, and then enter
the program name (page 16-15),
prgmnome
When prgmname is encountered
during execution, the next
command that the program executes is the first command
in the second program. It returns to the subsequent
conunand in the first program when it encounters
either
Return or the implied Return at the end of the second
program.
Pro_lram
PROGRAM: VOLCYL
:Input
"D=",D
: InPut.
"H=",H
:PPgrIRRERCIR
:RmH÷V
:DisP V
Subroutine
Output
H=5
62. 83185307
Done
I t
PROGRRM:RRERCIR:Return:n.RZ÷A:D/2÷R
I
Notes
Calling
about
Programs
Variables
are global.
label used with Goto and kbl is local to the program
where
it is located,
label in one program
is not recognized
by
another
program.
You cannot use 6oto to branch
to a label
in another
program.
Return exits a subroutine
and returns
to the calling
program,
even if it is encountered
within nested loops.
16-22
Programming
7
Contents
Applications
Comparing
Test Results Using Box Plots ................
Graphing Pieeewise
Functions
...........................
Graphing Inequalities
....................................
Sohdng a System of Nonlinear
Equations
................
Using a Program to Create the Sierpinski
Triangle .......
Graphing Cobweb Attractors
............................
Using a Program to Guess the Coefficients
...............
Graphing the Unit Circle and Trigonometric
(;ma_es ......
Finding the Area between
Curves ........................
Using Parametric
Equations:
Ferris Wheel Problem ......
Demonstrating
the Fundamental
Theorem
of ('aleulus...
('omputing
Areas of Regular N-Sided Polygons
..........
Computing
and Graphing Mortgage
Payments
...........
TEXAS
17-2
17-4
17-5
17-6
17-7
17-8
17-9
17-10
17-11
17-12
17-14
17-16
17-18
TI-83
INSTRUMENTS
J
STATPLOT
TBLSET
FORMAT
CALC
TABLE
Applications
17-1
Comparing
Problem
Test Results
An experiment
Using Box Plots
found
a significant
difference
between
boys
and gifts pertaining
to their ability to identify objects
held
in their left hands,
which are controlled
by the right side of
their brains, versus their right hands, which are controlled
by the left side of their brains, The TI Graphics
team
conducted
a similm" test for adult men and women.
The test involved
30 slnall objects, which pm'ticipants
were
not allowed
to see. First, they held 15 of the objects one by
one in their left hands and guessed
what they were. Then
they held the other 15 objects
one by one in their right hands
and guessed
what they were. Use box plots to compare
_isually the eotTect-guess
data from this table.
Correct
Women
Le_
Women
8
9
12
11
10
8
12
7
9
11
Procedure
Guesses
Men
Men
Right
Left
Right
4
1
8
12
11
!1
13
!2
!1
12
7
8
7
5
7
8
11
4
!0
14
13
5
12
6
12
12
7
11
12
8
12
11
9
9
1, Press _
5 to select 5:SetUpEditor, Enter list names
WLEFT, WRGHT, MLEFT, and MRGHT, separated
by
conlnlas,
Press [_.
The stat list editor now contains
only these four lists.
2. Press
[_Y]
1 to select
1:Edit.
3. ]_nter into WLEFT the number
of correct
guesses
each
woman made using her left hand (Women
Left). Press []
to move to WRGHT and enter the number
of correct
guesses
Right).
each
woman
made
using
her right hand
4. Likewise,
enter each lnan's correct
guesses
(Men Left) and MRGHT (Men Right).
(Women
in MLEFT
5. Press [_
[STAT
PLOT],
Select 1:Plot1. Turn on plot 1;
define it as a modified
box plot 4>- that uses WLEFT.
Move the eta'sot to the top line and select Plot2. Turn on
plot 2; define it as a modified
box plot that uses WRGHT,
17-2
Applications
6.Press
@.Turnoffallfunctions,
7.Press
_.
SetXscl=landYscl=0.
Press
_
9to
select
9:ZoomStat.
Thisadjusts
theviewing
windowand
displays
theboxplotsforthewomen's
results.
8. Press
_.
kd=9.5
Use
[]
and
[]
to
exalnine
minX, Ol, Med, O3,
right hand? With which hand
accurate
guessers,
according
maxX
and
for each plot. Notice the outlier to the women's
hand data. What is the median
ff)r the left hand?
were the women
to the box plots?
rightFor the
more
9. Examine
the men's results.
Redefine
plot 1 to use
MLEFT, redefine
plot 2 to use MRGHT. Press _.
_"
d=7.5
Men's right-hand data
" "
Press [] and [] to examine minX, Q1, Med, Q3, and maxX
for each plot. What difference
do you see between the
plots?
10.Compare
the left-hand
results.
Redefine
plot 1 to use
WLEFT, redefine
plot 2 to use MLEFT, and then press
to examine
minX, Q1, Med, Q3, and maxX for each
plot. Who were the better left-hand
guesse_\% men or
women?
11. Company the right-hand
results. Define plot 1 t_) use
WRGHT, define plot 2 to use MRGHT, zu_d then press
to examine
minX, OI, Med, O3, and maxX for each
plot. Who were the better right-herod
guesse_?
In the original experiment
boys did not guess as well
with right hands, while girls guessed
equally well with
either hand. This is not what our box plots show for
adults. Do you think that this is because
adults have
learned
to adapt or because
our sample was not large
enough?
Applications
17-3
Graphing
Piecewise
Problem
The
Functions
fine for speeding
on a road
with
a speed
limit
of 45
kilometers
per hour (kph) is 50; plus 5 for each kph from
46 to 55 kph; plus 10 for each kph froln 56 to 65 kph; plus
20 for each kph from 66 kph and above. Graph the
piecewise
function
that describes
the cost of the ticket.
The
Procedure
fine (Y) as a function
of kilometers
per horn" (X) is:
Y=0
0<X_<45
Y= 50 + 5 (X- 45)
Y= 50 + 5 *10 +10 (X - 55)
Y= 50 + 5. 10 + 10. 10 + 20 (X-
45 < X_< 55
55<X_<65
65 < X
1,
Press
Noel.
Select
65)
Func and the default
settings.
2. Press @. Tm'n off all functions
and stat plots. Enter
Y= function
to describe
the fine. Use the TEST menu
operations
to define the pieeewise
graph style for Y1 to ". (dot).
PloLt
F'lol:2
function.
the
Set the
PI<,I:_:
'..Y1 B(50+5(X-45)
)
(45<X) (X_<55)+(10
0+10(X-55)
) (5.J< X
)(X_<65)+(200+20(
X-65)
,,yz=
,,V_=
) (65< X)I
Press _
and set Xmin=-2, Xscl=10, Ymin=-5, and
Yscl=10. Ignore Xmax and Ymax; they are set by AX and
AY in step 4.
Press [_
[QUIT] to return to the holne screen.
Store 1 to
AX, and then store 5 to AY, AX and AY m'e on the
VARS Window X/Y secondary
menu. AX and AY specify
the horizontal
and vertical
distance
between
the centers
of adjacent
nice values
Press _
the ticket
17-4
Applications
pixels, Integer
for tracing,
values
to plot the function.
exceed
250?
for AX and AY produce
At what
speed
does
Graphing
Problem
Inequalities
Graph the inequality 0.4X;_ - 3X + 5 < 0.2X + 4. Use the
TEST menu operations to explore the values of X where the
inequMity is true and where it is false,
Procedure
Press [M0_]. Select Dot, Simul, and the default settings.
Setting Dot mode changes 'all graph style icons to
'. (dot) in the Y= editor.
Press @. Turn off all functions and stat plots. Enter the
left side of the inequality as Y4 and the right side as Y5.
'..9 _B. 4X^3-3X+5
I"-Y _B. 2X+411
...Yti=
[..Y?=
Enter the statement of the inequality as Y6. This
function evaluates to 1 if true or 0 if false.
'..Y_B. 4X"3-3X+5
'..Y_B; 2X+4
'-.Y_B_<Y_II
.5??=
4.
Press _
window.
6 to graph the inequality
in the standard
5, Press _
[] [] to move to Y6, Then press [] and []
to trace the inequality, observing the value of Y,
--'
;'
=
[
11=.ti_8;;9;_87 I?=i.
Press @. Turn off Y4,Y5,and Y6.Enter equations to
graph only the inequality.
'..'.?_=, 4X"3-3X+5
".Y_=. _.X+4
'..9_=_,_<9_
..YnBYt*9_
Press _.
Notice that the values of Y7 and Y8 are
zero where the inequality- is false.
?ll=¥fi_?_;
ll:':t._Bg._6;_
!Y:0
:I=':L4Bg._fi,_
t=0
Applications
17-5
Solving a System
of Nonlinear
Problem
a graph,
Using
solve
Equations
the equation
X :_- 2X = 2cos(X).
Stated
another
way-, solve the system
of two equations
and two
unknowns:
Y = X:_-2X and Y = 2cos(X),
Use ZOOM factors
to control the decimal
places
displayed
on the graph.
Procedure
Press [_,
Select the default lnode
Turn off 'all functions
and stat plots.
settings.
Press @.
Enter the functions.
\V_BX_-2X
",'t
oB2cos
Press _
that two
functions
(X) I
4 to select 4:ZDecimal,
The display
shows
solutions
may exist (points
where the two
appear to intersect).
r
3,
Press _
[] 4 to select 4:SetFactors
fi'om the ZOOM
MEMORY menu. Set XFact=lO and YFact=lO.
4. Press _
2 to select 2:Zoom In. Use [_, [], [], and []
to move the free-moving
cm_or onto the apparent
intersection
of the functions
on the right side of the
display. As you move the cursor,
notice that the X and Y
values
have
5, Press [_
intersection,
one decimal
the X and Y values
6, Press [_
cursor
onto
the number
place.
to ZOOln in. Move the cursor
over the
As you move the cursor,
notice that now
have
two
decimal
places.
to zoom in again. Move the free-lnoving
a point exactly- on the intersection,
Notice
of decimal
places.
7. Press K_ [CALC] 6 to select 6:intersect.
Press _
select the first cmwe and [_
to select the second
cm_'e. To guess, move the trace cursor
near the
intersection,
Press [_.
What are the coordinates
the intersection
point?
8, Press _
4 to select
original graph,
4:ZDecimal
to redisplay
the
9. Press _.
Select 2:Zoom In and repeat
steps 4
through
8 to explore
the apparent
function
intersection
on the left side of the display.
17-6
Applications
to
of
Using a Program
to Create the Sierpinski
Triangle
Setting up the
Program
This program creates a drawing of a falnous ffactal, the
Sietpinski Triangle, and stores the drawing to a picture. To
begin, press #ggM] [] [] 1. Name the prograln SlERPINS,
and then press [gg7_l. The program editor is displayed.
Program
PROGRAM:SIERPI NS
:FnOff
:ClrDraw
: Pl otsOff
:AxesOff
::0->Ymi
0->Xmi nn::l->Ymaxl->
Xmax
}
Set _qewing
window.
: rand->X: rand->Y
: Fo r ( K, 1,3 00 0 )
: rand->N
-1-- Beginning
of Fo
r
group.
:Then
:. 5X->X
::If.SY->Y
N<1/3
:End
:If
I/3<N
:Then
If/Then group
}
and N<2/3
7
:. 5(, 5+X)->X
:. 5( I+Y)->Y
:End
If/Then group.
:Then
:. 5 ( l+X )->X
::If. 5Y->Y
2/3<N
:End
: Pt
On( X, Y )
: End
: StorePi
If/Then group,
}
Draw
point.
End of For group.
c 6
Store
picture.
After you execute the prograln above, you can recall and
display the picture with the instruction RecallPic 6.
Applications
17-7
Graphing
Cobweb
Problem
Using
Attractors
Web format,
and repelling
Procedure
you
behavior
can identify
points
in sequence
graphing,
with
Press [MO0_. Select Seq and the default
Press _
[FORMAT]. Select Web format
fonnat settings,
attracting
nlode settings.
and tile default
Press @, Clear all functions
and tul_ off all stat plots.
Enter the sequence
that corresponds
to the expression
Y = K X(1-X),
u(n)=Ku(n- 1)(1 - u(n- 1))
u(nMin)=.01
3,
Press
store
[g_ [QUIT] to return
2.9 to K.
4, Press _,
nMin=0
nMax=lO
PlotStart=l
to tim holne
Set the window
Xmin=0
Xmax=l
Xscl=l
screen,
and then
variables,
Ymin=-.26
Ymax=l.1
Yscl=l
PlotStep=l
Press
trace
_
to display- the graph, and then press [] to
the cobweb.
This is a cobweb
with one attractor,
lu=Hu,:_-:i.XI-u(_-I))
Change
K to 3.44 and trace
with two attractors.
the graph
to show
a cobweb
7, Change
K to 3.54 and trace
with four attractors,
the graph
to show
a cobweb
6,
U=I_u{_-lXl-uCo-1))
17-8
Applications
..- I
Using a Program
to Guess the Coefficients
Setting Up the
Program
This program graphs the function A sin(BX) with random
integer coefficients between 1 and 10. Try to guess the
coefficients and graph your guess at C sin(DX). The
program continues until your guess is correct.
Program
PROGRAM:GUESS
:PlotsOff
:Func
:FnOff
:Radian
:ClrHome
:"Asin(BX)"_Yl
:"Csin(DX)"_Y2
Define
:GraphStyle(l,l)
:GraphStyle(2,5)
:FnOff
2
Set
line and path
styles.
:randlnt(l,lO)_A
:randlnt(l,lO)_B
:O_C:O_D
:-2_Xmin
:2_Xmax
:_/2_Xscl
:-lO_Ymin
:lO_Ymax
:l_Yscl
-
:DispGraph
:Pause
:FnOn 2
:Lbl Z
=
:Prompt
Initialize
graph
coefficients.
I
Set viewing
window.
I
I
C,D
:DispGraph
:Pause
:If
C=A
:Text(l,l,"C
:If
C_A
:Text(l,l,"C
:If
D=B
:Text(l,50,"D
:If
D_B
:Text(l,50,"D
equations,
-
Display
graph,
Prompt
for guess,
Display
graph,
Display results,
IS OK")
IS WRONG")
IS OK")
IS WRONG")
:DispGraph
:Pause
:If
C=A and D=B
-
:Stop
:Goto
--
Display
graph.
Quit if guesses
are
correct,
Z
Applications
17-9
Graphing
the Unit Circle
and Trigonometric
Curves
[ _sing parametric graphing mode, graph the unit circle and
tile sine curve to show the relationship between them.
Problem
Any function that can be plotted in Func mode can be
plotted in Par mode by defining the X component as T and
the Y component as F(T).
Procedure
1. Press [MffffE].
Select Par, Simul, and the default
2. Press _.
Tmin=0
Tmax=2_
Tstep=.1
Set the viewing window.
Xmin=-2
Xmax=7.4
Xscl=_/2
settings.
Ymin=-3
Ymax=3
Yscl=l
3, Press @, Turn off all functions and stat plots. Enter the
expressions to define the unit circle centered on (0,0).
Not:J,
PI0L2
P10t)
",XIT_cos (T)
Y1T lisin(T)
\XzT fiT
YzT lisin(T)
4. Enter the expressions
PlotJ.
Plot_
to define the sine curve.
PloI:3
",X1T lic.os(T)
YIT lisin(T)
"..X
zTliT
Y.-Tlisin(T)
5. Press _.
As the graph is plotting, you may press
[ggT_ to pause and [ggT_ again to resulne graphing as
you watch the sine function "unwrap" from the unit
circle.
:{IT=C.,:,;(T)
==
Y1T=_irff.T)
=
2/
Note: You can generalize the unwrapping. Replace sin(T) in Y2Twith
anyother trig function to unwrapthatfunction.
17-10
Applications
Finding the Area between
Problem
Find the area of the region bounded
fix)
g(x)
x
Procedure
Curves
1.
Press
by
= 300x/(x 2 + 625)
= 3cos(. ix)
= 75
[MffffE].Select
2. Press
_.
Xmin=0
Xmax=100
Xscl=10
the default
Set the viewing
Ymin=-5
Ymax=10
Yscl=l
Xres=l
3. Press @. Turn off all functions
upper and lower functions.
Y1=a00x/(x2+625)
Y2=3COS(.1X)
lnode
settings.
window.
and stat plots. Enter the
4. Press [g_] [CALC]5 to select 5:Intersect. The graph is
displayed. Select a first cutwe, second cut,'e, and guess
for the intersection
toward the left side of the display.
The solution is displayed, and the value of X at the
intersection,
which is the lower limit of the integral, is
stored in Ans and X.
Press _
[QUIT] to go to the home screen. Press
[_ [DRAW]7 and use Shade( to see the area graphically.
Shade(Y2,Y1,Ans,75)
6, Press [2_]
expression
region,
to return to tile honle screen. Enter tile
to evaluate the integral for the shaded
[QUIT]
fnlnt(Y1-Y2,X,Ans,75)
The area is 325.839962.
Applications
17-11
Using Parametric
Problem
Equations:
[ _sing two
Ferris Wheel Problem
pai_\q of parametric
two objects
plane.
in motion
equations,
are closest
to each
determine
other
when
in the Salne
A ferris wheel has a diameter
(d) of 20 meters
and is
rotating
counterclockwise
at a rate (s) of one revolution
ever T 12 seconds.
The paralnetric
equations
below
describe
the location
of a fen'is wheel passenger
at time T,
where (x is the angle of rotation,
(0,0) is the bottom
center
of the fen'is wheel, and (10,10) is the passenger's
location
at the rightmost
point, when T=0.
X(T)
Y(T)
= r cos (x
= r + r sin (x
where
(x = 2xTs
and r = d/2
A person standing
on the ground throws
a ball to the ferds
wheel passenger.
The thrower's
ann is at the sanle height as
the bottoln of the ferds wheel, but 25 meters
(b) to the right
of the fen'is wheel's
lowest point (25,0). The person throws
the ball with velocity (v0) of 22 meters pet" second at an
angle (0) of 66 ° froln the horizontal.
The parametric
equations
below describe
the location
of the ball at tinle T.
X(T)
Y(T)
9,_
Procedure
= b - Tv0 cos0
= Tv0 sin0 - (g/2)
nl/see
T_
where
g =
2
1, Press [MO0_. Select
Simul (sinmltaneous)
nlotion
over tinle.
Press _.
Tmin=0
Tmax=12
Par, Simul, and the default
settings.
mode sinmlates
the two objects
Set the viewing
Xmin=-13
Xmax=34
Tstep=.l
Xscl=lO
in
window.
Ymin=0
Ymax=31
Yscl=lO
Press @. Turn off all functions
and stat plots. Enter tile
expressions
to define tile path of the ferris wheel and tile
)ath of the ball. Set tile graph style for X2T to 4j (path).
i PloL:L Plot_: Plot_:
",X1T B1Ocos(xT/6)
YITBlO+lOsin(_T
t6)
*)XzT B25-22Toos(6
5° )
ViT B22Tsin(66
° )
-(9.8/2)TZ
Tip: Try setting the graph styles to ",.'_XlT and 0 X2T, which simulates
chair on the ferris wheel and the bal! flying through the air when you
press _.
17-12
Applications
a
4. Press [_
to graph the equations.
they are plotted. Notice that the ball
wheel passenger appear to be closest
cross in the top-right quadrant of the
5, Press [_.
concentrate
Tmin=l
Tmax=3
Tstep=.03
Watch closely as
and the ferris
where the paths
ferris wheel,
Change the _iewing window to
on this portion of the graph.
Xmin=0
Ymin=10
Xmax=23.5
Ymax=25.5
Xscl=10
Yscl=10
6. Press _.
After the graph is plotted, press [] to
nlove neat" tile point on the ferris wheel where the paths
cross, Notice the values of X, Y, and T,
IIT=t0_.O_;(1T_
YtT=IO÷10;;_
7, Press [] to nlove to the path of the ball. Notice the
values of X and Y (T is unchanged). Notice where the
cursor is located. This is the position of the ball when
the fetTis wheel passenger passes the inter\section. Did
the ball or the passenger reach the intersection
first?
You can use _
to, in effect, take snapshots in tilne
and explore the relative behavior of two objects in
motion,
Applications
17-13
Demonstrating
Problem 1
the Fundamental
of Calculus
Using the functions fnlnt( and nDeriv( fronl the MATH menu
to graph functions defined by integrals and derivatives
demonstrates
graphically that:
fx
F(x)=
Procedure
Theorem
1
1
1/tdt=ln(x),x>0
Dx
Ifx 1/t dt 1= 1/x
1.
Press
and that
1
1_.
Select
2. Press
_.
Xmin=.01
Xmax=10
Xscl=l
tile default
Set the viewing
Ymin=-l.5
Ymax=2.5
Yscl=l
settings.
window.
Xres=3
Press @, Turn off 'allfunctions and stat plots. Enter tile
numerical integral of 1/T from 1 to X and the function
ln(X). Set the graph style for Y1 to "..(line) and Y2 to
.4:,(path).
Plot:l.
Pl¢,t2
",Yt Bi'n InL(
1,X)
_¢2Bln(g)
4.
P1ot_
l/T,
T,
Press _.
Press [], [], [], and [] to eolnpare
values of Y1 and Y2,
the
5. Press @. Turn off Y1 and Y2, and then enter the
numerical derivative of the integral of 1/X and the
function 1/X. Set the graph style for Y3 to ', (line) and Y4
to _. (thick),
Ploti
p1,,:,l:2 Plot_:
:,Y:,
_oior_1_T,
T,
_Y2'=In(g)
_BnOeri_,(Y1
_,YuBI/X
, X,
Press _.
Again, use the cursor keys to compare
values of the two graphed functions, Y3 and Y4.
17-14
Applications
the
Problem 2
Explore
the functions
X
Y:f-2
Procedure 2
defined
by
X
t2dt'
f0
X
t2dt'
and
f2
t2dt
Press @, Turn off all functions
to define these three functions
the function
in Ys.
and stat plots.
sinmltaneously.
Use a list
Store
_'_=nDerib=(Yt"°Yz=lr_(x)l'x)Pl°t:L
Plol:Z
F'loL_. _ _
,,Y_B?nlnL(T
z,
'_Y_=I/X
i-::,o,2>,x)
2,
Press _
$ to select
3, Press _.
only shifted
Press
@,
T, (
$:ZStandard.
Notice that the functions
vertically
by a constant.
Enter
the numerical
\Y_=nDeriv(Y1,
X)
"*Y_=I/X
"..Y_B_nIn÷.(TZ,
appear
derivative
identical,
of Y5 in Y6,
X,
T, (
-2,0,2>,X)
\YeBnOer
iv(Y_,
X,
x)
Press _.
Notice that although the three graphs
defined by Y5 are different,
derivative,
they
share
tile
same
N="t.9£_Bi!_?i¢).6_,fiBt?9
Applications
17-15
Computing
Problem
Areas
Use
of Regular
the equation
N-Sided
solver
to store
regulm" N-sided polygon,
and then
given the other variables.
Explore
case is the area of a circle, _r 2.
Polygons
a fornmla
Consider
the fonnula
A = NB 2 sin(_/N)
m'ea of a regulm' polygon
with N sides
B distance
from the center to a vertex.
N = 4 sides
Procedure
ff)r the m'ea of a
solve for each vm'iable,
the fact that the limiting
cos(_/N)
for the
of equal length and
N = 8 sides
N = 12 sides
1, Press [_
0 to select 0:Solver froln the MATH menu,
Either the equation
editor or the interactive
solver
editor is displayed.
If the interactive
solver editor is
displayed,
press [] to display the equation
editor,
2, Enter the fonnula
then press [_.
as 0=A-NB2sin(_
The interactive
/ N)cos(_ / N), and
solver editor is
displayed.
R_NBZsin(_/N).,,=O
bound={
3, Enter
-1 E99,
1...
N=4 and B=6 to find the area
a distance
(B) from
center
to vertex
(A) of a square
with
of 6 centimeters,
4, Press [] [] to nlove the cursor
onto A, and then press
@
[SOLVE], The solution
for A is displayed
on the
interactive
solver editor.
:l-NBZsin(_/N)...=el
: 2.00o000000
I
B=6
bound={
-1 E99,
1...
le_t-rt=e
5. Now solve for B for a given area with vm'ious number
of
sides. Enter A=200 and N=6. To find the distance
B,
lnove the cursor onto B, and then press @
[SOLVE].
6, Enter N=8, To find the distance
B, nlove the cursor
onto
B, and then press @
[SOLVE]. Find B for N=9, and
then for N=10.
17-16
Applications
FindtheareagivenB=6,
10000. Compare
with
radius
your
6), which
and N=10, 100, 150, 1000, and
results
with =62 (the area of a circle
is approximately
113.097.
7. Enter B=6. To find the area A, move
and then press @
[SOLVE]. Find
N=100, then N=160, then N=1000, and
Notice that as N gets large, the area
the cursor
onto A,
A for N=10, then
finally N=10000.
A approaches
_B 2.
Now graph the equation to see visually how the area
changes as the number of sides gets lm'ge.
8, Press NgffE].Select the default lnode settings,
9. Press _.
Xmin=O
Xmax=200
Xscl=lO
Set the viewing window.
Ymin=O
Ymax=150
YscI=IO
Xres=l
10.Press @. Turn off all functions and stat plots. Enter the
equation for the m'ea. I Jse X in place of N Set the graph
styles as shown.
Plot].
F'10t2
F'10t._
xViBXBZsin<_/X)c
os(_/X)
-W._BnB z
,.'-,as=
xY.1=
,,V_:=
,&'6=
11. Press _.
After the graph is plotted, press I O0[gNgggl
to trace to X=100. Press 150 [ggTgm.Press 188 [ggTg_.
Notice that _LsX increases, the value of Y converges to
=62, which is approximately
113.097. Y2=_B2 (the area of
the circle) is a horizontal asymptote to Y1. The area of
an N-sided regular polygon, with r as the distance fl'om
the center to a vertex, approaches
the area of a circle
with radius r (_r 2) as N gets large.
;' 1:1-,'B;a_;ir=
r..'n"r' N),2.o _;( Tr_'g :E
'¢_::Tr£:::
8:tBB
8:tEE
_Y=lt3.0762B,
_Y:ti3.0973_
Applications
•
17-17
Computing
Problem
and Graphing
You at_ a loan
Mortgage
officer
Payments
at a mortgage
conlpany,
and you
recently
closed on a 30-yem' holne lnortgage
at 8 percent
interest
with monthly
payments
of 800, The new home
owners
want to know how nmch will be applied to the
interest
and how nmch will be applied to the principal
when they make the 240th payment
20 years from now.
Procedure
1, Press [_
and set the fixed-decimal
lnode to 2 decimal
places. Set the other mode settings to the defaults.
2. Press [_ [FINANCE]
these values.
1 to display" the TVM Solver. Enter
N=360.00
I_=8.00
PV=0.00
PMT=800.00
FV=0.00
P/V=I2.00
C/V=12,00
PMT:[_=[II_
BEGIN
Note: Enter a positive number (800) to show PMT as a cash
inflow. Payment values will be displayed as positive numbers on
the graph. Enter 0 for FV, since the future value of a loan is 0 once
it is paid in ful!. Enter PMT: END, since payment is due at the end
of a period.
3, Move the cursor onto the PV= prompt, and then press
@
[80LYE], The present value, or lnortgage amount,
of the house is displayed at the PV= prompt,
N=360.00
I%=8.00
PV=-IO9026,B0
PMT=B00.00
FV=0.00
P/V=12.00
C/Y=12.00
PMT:LqIL_ BEGIN
17-18
Applications
Nowcompare
thegraphoftheamount
ofinterest
withthe
graphoftheamount
ofprincipal
foreachpayment.
4, Press
[NffffE].Set Par and Simul.
5, Press
these
@, Turn
equations
off all functions
and stat plots. Enter
and set the graph styles as shown.
Plot1 Plol:_ Plot_:
",XIT BT
Vi T BFPr'n(T, T)
_XzT BT
'Y'zT B_- Int.< T, T)
".X_T BT
V:_T BVIT +VZT
Note: ZPrn( and ZInt( are located on the FINANCE
6, Press _.
Tmin=l
Tmax=360
Tstep=12
Set these window
Xmin:0
Xmax=360
Xscl=10
CALC menu,
variables.
Ymin=0
Ymax=1000
Yscl=100
Tip: To increase the graph speed, change Tstep to 24.
7. Press _.
After the graph is drawn, press 240
to move the trace cursor
to T=240, which is equivalent
to 20 years of payments.
IIT=T
?tT='_F'r_rKT__
The graph shows that ff)r the 240th payment
(X=240),
358.03 of the 800 pay3nent is applied
to principal
(Y:368.03).
Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800.
Applications
17-19
8. Press
[] tomovethecursorontothefunction
for
interest
defined
byX2T
andY2T.
Enter240.
The graph shows that for the 240th payment (X=240),
441.97 of the 800 payment is interest (Y=441 .gT).
9. Press
home
_
[QUIT]
[_
screen.
Check
[FINANCE]
the figures
9 to paste 9:bal( to the
from the graph.
_ai(239)
-66295.33
_nsm(.08/12)
-441,97
At which monthly
payment
will the principal
surp_kss the interest
allocation?
17-20
Applications
allocation
18
Contents
Menrn2gq/ement
Checking A_ailable MemolTy .............................
Deleting Items from MemmTy ............................
Clearing Entries and List Elements
......................
Resetting the TI-83 ......................................
TEXAS INSTRUMENTS
I8-2
I8-3
18-4
18-5
TF83
RRM_
Delete...
3:Clear
Entries
4: CIRRI ILists
5: Reset...
J
STAT
PLOT
TBLSET
FORMAT
CALC
TABLE
Memory
Management
18-1
Checking
Available
MEMORY Menu
Memory
To display
the
MEMORY menu,
press
[_
[MEM].
MEMORY
i:
Check
RAM...
Reports
memory
availability/usage,
Displays
DELETE FROM menu,
Clem's ENTRY (l_kst-entry storage).
2: Delete...
3: Clear
Entries
4: ClrAllLists
Clears all lists in memo_T.
Displays RESET menu (all/defaults).
5: Reset..,
Displaying the
Check RAM
Screen
Check RAM displays
the Check RAM screen. The top line
t_ports
the total amount
of available
nlenlol_y-. The
remaining
lines report the amount
of lnelnot7
each
variable
type is using. You can check this screen to see
whether
you need to delete variables
from memo_T to
nmke room for new data, such as programs.
To check
1. Press
RAM usage,
follow
[2_] [MEM] to display
these
the
steps.
MEMORY menu.
RRM...
_:Clear Entries
_:ClrRllLists
5:Reset...
2. Select I :Check RAM to display
the Check RAM screen.
The TI-S3 expresses
memory
quantities
in bytes.
MEM FREE 27285
Real
15
ComPlex
8
List
8
Matrix
8
Y-Vats
248
Prgm
14
4Pio
8
GOB
String
Note:
The J_in the left column
of
the bottom row indicates that you
can scroll or page down to view
more variable types.
0
0
Note: Real, List, Y-Vars, and Prgm variable types never reset to
zero, even after memory is cleared.
To leave the Check RAM screen,
press either [_
@.
Both options
display- the home screen.
18-2
Memmw
Management
[QUIT] or
Deleting
Items from
Deleting an Item
Memory
To increase
any- variable
Y= variable,
follow these
available nlenlol_ by deleting the contents of
(real or colnplex nulnber, list, matrix,
prograln, picture, graph database, or string),
steps.
1. Press [2_] [MEN]to display the MEMORY lnenu.
2. Select 2:Delete to display- the DELETE FROM secondalTynleno.
3. Select the type of data you want to delete, or select 1:All
for a list of all variables of 'all types. A screen is
displayed listing each variable of the type you selected
and the number of bytes each variable is using.
For exalnple,
is displayed.
if you select 4:List, the DELETE:List screen
DELETE: Li_t
_LI
DATA
63
39
4. Press [] and [] to nlove tile selection cursor (_) next to
the item you want to delete, and then press _.
The
variable is deleted fronl nlenlot_y-. You Call delete
individual vm'iables one by one froln this screen.
To leave ally DELETE: screen without deleting anything,
press [_ [QUIT],which displays the home screen.
Note: You cannot delete some system variables, such as the lastanswer variable Ans and the statistical variable RegEQ
Memory
Management
18-3
Clearing
Clear Entries
Entries
and List Elements
Clear Entries clears
storage
area
follow these
1, Press
[_
of the ENTRY (last entry)
the contents
(Chapter
steps.
1). To cleat" the
[MEM] to display
the
2, Select 3:Clear Entries to paste
home screen.
3. Press
[_
IcleaP
to clear
the
Entt'ie_one
area,
MEMORY menu.
the instruction
ENTRY storage
to the
area.
I
Clear Entries, press
To cancel
ENTRY storage
@,
Note: If you select 3:Clear Entries from within a program, the Clear
Entries instruction is pasted to the program editor, and the Entry
(last entry) is cteared when the program is executed.
CIrAIILists
CIrAIILists
sets to 0 tile
To clear
all elements
1, Press
[_
_
from
all lists,
[MEM] to display
2, Select 4:ClrAIIkists
screen.
3. Press
dimension
the
to paste
of each
follow
list in lllelllOl_yL
these
steps,
MEMORY menu,
the instruction
to set to 0 the dimension
to the home
of each
list in
nlenlory.
IC1rA11Lists
To cancel
CIrAIILists,
lionel
press @.
CIrAIILists does not delete list nanles fronl nlenlol_y-, fronl
the LiST NAMES menu, or froln the stat list editor.
Note: If you select 4:CIrAIIkists
from within a program, the
CIrAIILists instruction is pasted to the program editor. The lists are
cleared when the program is executed.
18-4
MemolT
Management
Resetting
the TI-83
RESET
Secondary Menu
The
Resetting All
Memory
Resetting
all nlenloFy Oil the TI-83 restores
nlenlory
to the
factor7 settings,
It deletes
all nonsystem
variables
and all
programs.
It resets all system
variables
to the default
settings.
seconda[7
RESET
lnenu
gives
you the option
of
resetting
all memory
(including
default
settings)
or
_setting
the default
settings
while prese_Mng
other data
stored in lnelno_T, such as programs
and Y= functions.
Tip: Before you reset all memory, consider restoring sufficient
available memory by deleting only selected data (page I8-3).
To reset
all nlenlory
1. Press
[2_] [MEM] to display
2. Select
5:Reset
_...
on the TI-83,
to display
the
follow
these
steps.
MEMORY menu.
the RESET
secondary
menu.
Mer_or-u...
2:: Defau
3, Select
tertimT
lts...
1 :All Memory to display
the
RESET MEMORY
nlenu.
Resetting
memoru
erases
all data
and Programs,
4. Read the message
below
tile
RESET MEMORY menu.
•
To cancel memoL_- reset and retm'n to tile home
screen, select 1:No.
•
To erase fronl lnelnol T all data and progralns,
2:Reset. All factory defaults
are restored.
Mere cleared
is displayed
on the home screen.
I
Mem
select
cleared
Note:When you clearmemory, thecontrast
sometimeschanges.If
thescreenisfadedorblank,adjustthecontrast
(ChapterI).
Memory
Management
18-5
Resetting
Defaults
When
you reset
restored
are not
defaults
on the TI-83,
to the factory
changed.
settings.
Stored
These are some examples
of TI-83
restored
by resetting
the defaults.
defaults
are
and programs
that
are
Mode settings
such as Normal (notation);
Func
(graphing);
Real (numbers);
and Full (screen)
•
Y= functions
•
Window variable
values such
Xscl=l; YscI=I; and Xres=l
•
Stat plots
•
Format
settings
such as eoordOn
(graphing
on); AxesOn; and ExprOn (expression
on)
•
rand
seed
off
value
all TI-83
1. Press
[g_] [MEM] to display
factory
5:Reset
Consider
Xmax=lO;
coordinates
to 0
To reset
4.
as Xmin=-lO;
off
defaults,
to display
3. Select 2:Defaults
tertimT
menu.
to display
the
reset
follow
these
steps.
MEMORY menu.
the RESET
secondary
menu.
the RESET
DEFAULTS
of resetting
defaults.
the consequences
•
To cancel
1:No.
•
To restore
factory
default
settings,
select 2:Reset.
Default settings
are restored.
Defaults set is
displayed
on the home screen.
Defaults
Memmw
data
•
2. Select
18-6
all defaults
Management
and return
set
to the home
screen,
select
19
Contents
ci° municati°n
Getting Started: Sending Variables
.......................
TI-83 kINK ...............................................
19-2
19-3
Selecting Items to Send ..................................
Receiving Items ..........................................
Transmitting
Items .......................................
Transmitting
Lists to a TI-82 .............................
Transmitting
from a TI-82 to a TI-8:I .....................
19-4
19-5
19-6
19-8
19-9
Backing Up MemmTy".....................................
TEXAS INSTRUMENTS
19-10
1"1=83
RECEIVE
to TI82...
J
STAT
PLOT
TBLSET
FORMAT
CALC
T._,B L E
Communication
Link
19-1
Getting
Getting
Started:
Started
Sending
is a fast-paced
Variables
introduction.
Read the chapter
for details.
Create and store a wu'iable and a matrix, and then transfer then] to another
TI-83.
On the home screen of the sending unit,
press 5 [] 5 [email protected]
O. Press [gfff_ to
store 5.5 to Q.
Press[_[[][_[[l
1[]2[_[11[_[[
] 3 _ 412_ [1 ] [2_ [1 ] _
[NN_ 1.
Press [_
to store the lnatrix to [A].
3.
Connect the calculators with the link
cable. Push both ends in firmly.
4.
On the receiving unit, press [_ [LINK] [] tO
display tile RECEIVE menu. Press 1 to
select 1:Receive. The message Waiting... is
displayed and the busy indicator is on.
SEHD [_
IERec.e ive
5, On the sending unit, press [2_]
display the SENDmenu.
[LINK]
to
Z,_AI RECEIVE
6, Press 2 to select 2:All-. The All- SELECT
screen is displayed.
3:Prgm...
4:List...
5:List.s to TI82...
6:GOB...
7gPic...
Press [] until the selection cursor ( _ ) is
next to [A] MATRX.Press [ggTEg].
8. Press [] until the selection cursor is next
to Q REAL. Press [_.
A square dot next
to [A] and O indicates that each is selected
to send.
TRRNSMIT
k_
LIST
.L_
LIST
[R]
MRTRX
Window
WINOW
RclWindouZSTO
TblSet
TABLE
_Q
RERL
9.
SELECT
7,
On the sending unit, press [] to display the
TRANSMIT menu.
IdII._IIIiIIi
[llTransr_it
10. On the sending unit, press 1 to select
1:Transmit and begin transmission.
The
receiving unit displays the message
Receiving....When the items are
transmitted, both units display the name
and type of each transmitted
variable.
19-2
Conununication
Link
Receiving,..
[ R]
MRTRX
'Q
REDRLne
TI-83 LINK
TI-83 Link
Capabilities
The
TI-83
has a port to connect
and conlnlunicate
Linking Two
TI-83s
You can transfer
all variables
and programs
to another
TI-83 or backup
the entire nlenlol'y
of a TI-83. The
softwm'e
that enables
this communication
is built into
TI-83. To transmit
from one TI-83
steps on pages
19-6 and 19-7.
Linking a TI-82
and a TI-83
You can transfer
programs.
L1 through
fronl
a TI-82
that
enables
to another,
to a TI-83
Also, you cal_ tral_sfer
L6.
The softwaxe
from
Two
with
perform
follow
all variables
a TI-83
and
lisL_
is built int_) the
t_) a TI-83,
follow
•
The only data type you can transmit
from a TI-83 to a
TI-82 is list data stored
in L1 through
L6, Use the kINK
SEND menu item 5:Lists to TI82 (page 19-8).
2. Insert
the other
calculator's
end of the cable
into
from
the
You cannot
TI-83,
either
backup
the
•
1. Insert
a memory
TM
TM
the
to a TI-82
this conunm_ication
TI-83. To tral_nlit
data from a TI-82
steps on pages 19-6 at_d 19-7.
Connecting
Calculators
the Cable
with
another TI-83, a TI-82, the Calculator-Based
Lal)oratory
(CBL 2 TM, CBL TM) System,
the Calculator-Ba_ed
Ranger
(CBWM), or a personal
conlputer.
The unit4o-unit
link
cable is included
with the TI-83. This chapter
describes
how to comnmnicate
with another
calculator.
a TI-82
the port very
end of the cal>le into
to a
firmly.
the other
port.
Linking to a CBR
or the CBL 2/CBL
System
CBR and the CBL 2/CBL System are optional
that connect
to a TI-83 with the unit-to-unit
With a CBR or a CBL 2/CBL and a TI-83,
and analyze
real-world
data.
you can
Linking to a PC
or Macintosh
TI-GRAPH LINK TM is an optional
to enable conmmnication
with
that links
conlputer.
accessorya personal
Communication
accessories
link cal fie,
collect
Link
a TI-S3
19-3
Selecting
Items to Send
LINK SEND Menu
To display
LINK SEND menu,
the
press
[_
[LINK].
SEND RECEIVE
i : A11 +..,
2 : A11 -..,
3 : P rgm...
4:
5:
6:
7:
8:
9:
0:
A:
B:
Displays
Displays
Displays
Li st...
Lists
to T182...
GDB...
Pi c...
Matrix...
Real ...
Compl ex..,
Y Vars...
String.,.
C: Back Up.,,
M1 items
'all items
selected.
deseleeted.
all progranls
names.
'all list names,
Displays
Displays
list names L1 through
Displays
'all graph databases.
Displays
M1 picture
data types,
Displays
'all matrix
data types.
M1 real vmiables,
Displays
Displays
'all complex
variables.
M1 Y= variables.
Displays
Displays
all string variables.
Selects
all for backup
to TI-83.
Ls.
When you select an item on the LINK SEND menu, the
corresponding
SELECT screen is displayed.
Note: Each SELECT screen, except All+ SELECT, is displayed
initially with no data selected.
Selecting Items
to Send
To select items to send on the sending
steps.
unit, follow these
1. Press [2_] [LINK]to display" the LINK SEND menu.
2. Select the menu item that describes the data type to
send. The corresponding
SELECT screen is displayed.
3. Press [] and [] to nlove the selection
item you want to select or deselect.
4. Press _
nalnes
are
to select or deselect
with a ..
cursor
(_) to an
the iteln. Selected
nlarked
_
TRRNSMIT
EQU
• Y_
EQU
Xl T
EQU
Vi T
EQU
u
EQU
FWindow
WINDW
RclWindowZSTO
5, Repeat steps 3 and 4 to select or deselect additional
19-4
Conununication
Link
items.
Receiving
LINK RECEIVE
Menu
Receiving Unit
Items
To display
LINK RECEIVE menu,
the
SEND RECEIVE
1 : Re e e i v e
Sets
unit to receive
press
data
_
[LINK] C_.
transmission.
VClmnyou select 1:Receive from the LINK RECEIVE menu on
the receiving unit, the message Waiting... and the busy
indicator are displayed. The receiving unit is ready to
t_eeive transmitted
items. To exit the receive mode
without receiving items, press [0N], and then select 1 :Quit
from the Error in Xmit menu.
To transmit,
follow
the steps
on page
19-6.
When transmission
is complete,
the unit exits the receive
mode. You can select 1 :Receive
again to receive
mot_
items. The receiving
unit then displays
a list of items
received.
Press [_
[QUIT] to exit the receive
mode.
DuplicateName
Menu
During transmission,
if a variable name is duplicated, the
Dup[icateName menu is displayed on the receixqng unit.
Dupl i cateName
i : Rename
2: Overwrite
Prompts to rename
Ove_wvrites data in
Skips transmission
Stops transmission
3: Omit
4: Quit
receiving variable.
receiving variable.
of sending variable.
at duplicate variable.
When you select 1:Rename,the Name=prompt is displayed,
and alpha-lock is on. Enter a new variable name, and then
press [_.
Transinission resuines.
When you select 2:Overwrite, the sending unit's data
ovet_vrites the existing data stored on the receiving unit.
Transmission resumes.
When you select 3:Omit, the sending
unit does not
data in the duplicated
variable
name. Transmission
resumes
with the next item.
When
you select
receiving
Insufficient
Memory in
Receiving Unit
unit
4:Quit, transmission
exits
receive
stops,
send
the
and the
mode.
During transmission,
if the receiving unit does not have
sufficient lnelnol T to receive an item, the Memory Full lnenu
is displayed on the receiving unit.
•
To skip this item for the current transmission,
select
1 :Omit. Transmission resumes with the next item.
•
To cancel the transmission
select 2:Quit.
and exit receive mode,
Communication
Link
19-5
Transmitting
Items
Transmitting
Items
To transmit selected items after you have selected items to
send on the sending unit (page 19-4) and set the receiving
unit to receive (page 19-5), follow these steps.
unit to display- the TRANSMIT
1. Press [] on tile sending
nlenu,
I T%Ts
I
2. Confirm that Waiting,.. is displayed on the receiving
unit, which indicates it is set to receive (page 19-5).
3. Press [g_-gm to select 1:Transmit. The name and type of
each item are displayed line by line on the sending unit
as the item is queued for transmission,
and then on tile
receiving unit as each item is accepted.
*'79
9t
EQoUoneEQU
I
*V_
VIRotei_,,i
ng...
EQ_oneEQU
I
After all selected items have been transmitted,
the lnessage
Done is displayed on both calculators. Press [] and [] to
scroll through the names.
Stopping a
Transmission
To stop a link transmission,
press []_]. The Error in Xmit
menu is displayed on both units. To leave the error menu,
select 1 :Quit.
Error Conditions
A transnlission
error
occurs
after
one or two seconds
•
A cable
is not
attached
to the sending
•
A cable
is not
attached
to the receiving
if:
unit.
unit.
Note: If the cane is attached, push it in firmly and try again.
•
The receiving
•
You
•
You attempt
a data transfer
from a TI-83 to a TI-82 with
data other than lists L1 through
L6 or without
using
menu item 5:Lists to TI82.
attempt
unit is not
a backup
Although a transmission
conditions nlay prevent
19-6
Conununication
set to receive
between
transmission.
a TI-82
and a TI-Sa.
error does not occur, these two
successful transmission.
•
You ttT to use Get( with a calculator
CBL 2/CBL or CBR.
•
You tit to use GetCalc( with a TI-82 instead
Link
instead
of a
of a TI-83,
Transmitting
Items to an
Additional TI-83
After sending
transmission
sending
reselect
or receiving
to additional
data, you can repeat
the same
TI-83 units--from
either the
unit or the receiving
unit--without
data to send. The current
items
having to
remain
selected.
Note: You cannot repeat transmission if you selected All+ or All-.
To transmit
to an additional
1, Set the TI-83
TI-83,
to receive
(page
follow
these
steps.
19-5),
2, Do not select or deselect
any new items to send. If you
select or deselect
an item, all selections
or deselections
from the previous
transmission
are cleared.
3, Disconnect
the link cable
to the additional
TI-83,
4.
Set the additional
TI-83
from
one TI-S3
to receive
5, Press [7_ [LINK] on the sending
LINK SEND menu.
(page
TI-83
and connect
19-5),
to display
the
6, Select the menu item that you used for the l_kst
transmission.
The data from your last transmission
still selected.
7, Press
8,
[] to display
Confirm
(page
9, Press
that
the
LINK TRANSMIT
the receiving
unit
it
is
menu,
is set to receive
19-5).
[EfiY_ to select
1 :Transmit
and begin
Communication
translnitting.
Link
19-7
Transmitting
Lists to a TI-82
Transmitting
Lists to a TI-82
The
only data
is list data
To transmit
lists
type
stored
you can transmit
in L1 through
to a TI-82
the list data
L1, L2, L3, L4, LS, or L6, follow
1, Set the TI-82
to receive
fronl
a TI-83
to a TI-82
L6.
(page
that
is stored
these
steps.
to TI-83
19-5).
2, Press [_
[LINK] 5 on the sending
TI-83 to select
5:Lists to TI82. The SELECT screen is displayed.
3, Select
4. Press
each
[] to display
5, Confirm that
(page 19-5).
6, Press
list to transmit.
[_
the
LINK TRANSMIT
the receiving
to select
unit
menu,
is set to receive
1 :Transmit and begin
transmitting.
Note: If dimension > 99 for a T1-83 list that is selected to send, the
receiving TI-82 will truncate the list at the ninety-ninth element during
transmission.
19-8
Coinnmnication
Link
Transmitting
from
a TI-82 to a TI-83
Resolved
Differences
between the TI-82
and TI-83
but differences
between
tile two products
may affect some
transmitted
data, This table shows differences
for which
GenerMly,
you can transmit
items
to a TI-83
fronl
the software
built into the TI-83 automatically
when a TI-83 receives
TI-82 data,
TI-82
TI-83
nMin
PlotStart
nStart
Un
Vn
nMin
u
v
UnStart
VnStart
TblMin
u(nMin)
v(nMin)
TblStart
a TI-82,
adjusts
For example,
if you transmit
from a TI-82 to a TI-83 a
program
that contains
nStart on a command
line and then
display" the p_ogram
on the receiving
TI-83, you will see
that nMin has automatically
conlnland
line,
Unresolved
Differences
between the TI-82
and TI-83
The
s(dtware
differences
described
built
into
replaced
nStart
the TI-S3 cannot
on the
resolve
some
between
the TI-82 and TI-83, which are
below. You nmst edit the data on the TI-83
you transmit
to account
for these
will misinterpret
the data.
differences,
The TI-83 reinterprets
TI-82 prefix functions
()pen parentheses,
which may add extraneous
to transmitted
expressions.
after
or the TI-83
to include
parentheses
For example,
if you transmit
sin X+5 from a TI-82 to a
TI-83, the TI-83 reinteq_rets
it as sin(×÷5. Without
a closing
parenthesis
after ×, the TI-83 interprets
this as sin(×÷5), not
the stun of 5 and sin(X).
If a TI-82 instruction
that
the TI-83
cannot
translate
is
transmitted,
the ERR:INVALID menu is displayed
when the
TI-83 attempts
to execute
the instruction.
For example,
on
the TI-82, the chm'acter
group Un-1 is pasted
to the cursor
location
when you press _
[un- 1]. The TI-83 cannot
directly
translate
Un-1 to the TI-83 syntax
u(n-1), so the
ERR:INVALID
menu
is displayed.
Note: T1-83 implied multiplication rules differ from those of the T1-82.
For example, the TI-83 evaluates 1/2X as (1/2)*X, while the TI-82
evaluates 1/2X as 1/(2"X) (Chapter 2).
Communication
Link
19-9
Backing
Up Memory
Memory Backup
To copy the exact contents of lnelnol_y- in the sending TI-83
to the lnelnory of the receiving TI-83, put the other unit in
t_ceive mode. Then, on the receiving unit, select C:Back Up
fronl the LINK SEND menu.
Warning:
receiving
receiving
C:Back Up ove_wvrites
the lnelnol_y- in the
unit; all information
in the lnelnory
of the
unit is lost.
Note: If you do not want to do a backup, select 2:Quit to return to
the LINK SEND menu.
•
Select 1:Transmit to begin transmission.
BItTt-ansr_
2: Quit
Receiving Unit
i t
As a safety check to prevent accidental loss of nlenlory,
the message WARNING - Backup is displayed when the
t_cei_lng unit receives notice of a backup.
•
•
To continue with the backup process,
The backup transmission
begins.
To prevent the backup, select 2:Quit.
Note:If a transmissionerroris returnedduring
unit is reset.
Memory Backup
Complete
(domnmnication
a backup,
the receiving
When the backup is complete, both the sending calculator
and receiving calculator display a confirlnation
screen.
IMEMOR'? BACKUDPonel
19-10
select 1:Continue.
Link
A
Contents
Tablesand Reference
Information
Table
of Functions
and Instructions
.....................
TI-83 Menu Map .........................................
Variables
................................................
Statistics
Formulas
......................................
Financial Formulas
......................................
Tables
and
Reference
A-2
A-39
A-49
A-50
A-54
Information
A-1
Table
of Functions
and Instructions
Functions return a value, list, or matrix. You can use functions in an expression.
Instructions initiate an action. Some functions and instructions have arguments.
Optional arguments and accompanying conunas are enclosed in brackets ( [ ] ).
For details about an item, including argument descriptions and restrictions, turn
to the page listed on the right side of the table.
From the CATALOG, you can paste any function or instruction to the home
screen or to a conunand line in the program editor. However, some functions
and instructions
are not wflid on the home screen. The items in this table
appear in the same order as they- appear in the CATALOG.
f indicates keystrokes that are valid in the program editor only. Some keystrokes
display menus that are available only in the program editor. Others paste mode,
fommt, or table-set instructions only- when you are in the program editor.
Function or Instruction/
Arguments
abs(value)
abs(complex
'value)
Returns the nmgnitude of a
complex nmnber or list.
ANOVA(listl,list2
[,list3,...,list20])
Ans
and
CPX
5:abs(
[_ [TEST]
LOGIC
1 :and
Returns 1 if both valueA and
valueB are € 0. valueA and
valueB ean be real numbers,
expressions, or lists.
Returns the polar angle of a
[_
complex number or list of
CPX
complex numbers.
4:angle(
Performs a one-way analysis of [gg_]
variance for comparing the
TESTS
means of two to 20
F:ANOVA(
populations.
Returns the last answer.
[_
[ANS]
angle{value)
Tables
Key or Keys/
Menu or Screen/Item
Returns the absolute value of a [_
real number, expression, list,
NUM
or matrix.
1 :abs(
valueA and valueB
A-2
Result
Reference
Information
2-13
10-10
2-19
2-26
2-19
13-25
1-18
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
Retm'ns a mahlx, width is
matrixB
appended to matrixA
as new colunms.
MATH
7:augment(
10-14
augment(listA,listB)
Returns a list, which is listB
concatenated
to tile end of
listA.
_
[LIST]
OPS
9:augment(
11-15
AxesOff
Turns off the graph axes.
; [2_
AxesOn
Turns on tile graph axes.
; [2_ [FORMAT]
AxesOn
3-14
a+bl
Sets tile mode to reetangular
complex number mode (a+bi).
i I_
a+bi
bal(npmt[,roundvalue])
Computes
the balance at npmt
for an amortization
schedule
using stored values for PV, I%,
and PMT and rounds the
computation
to roundvalue.
[_
[FINANCE]
CALC
9:bal(
binomcdf(numtrials,p[,x])
Computes
a cumulative
probability
at x for the discrete
binomial distribution
,slth tile
specified numtrials
and
probabilityp
of success
on
each trial.
[_
[D}STR]
DISTR
A:binomcdf(
binompdf(numtriols,p[,x])
Computes
a probability
tile discrete binomial
at x for
[_
[DtSTR]
DISTR
distribution
_ith tile specified
nuratrials
and probabilityp
of
success on each trial.
0:binompdf(
Computes
tile g 2 distribution
probability
between
lower'bound
and upped)ound
for the specified
degrees of
freedom dJ2
_
[DISTR]
DISTR
7:x2cdf(
augment(matrixA,matrixB)
[FORMAT]
AxesOff
x2cdf(low6_pbound,
upperbound,dy')
Tables
and
Reference
3-14
1-12
14-9
13-33
13-33
13-31
Information
A-3
Function or Instruction/
Arguments
z2pdf(x,dj ")
Key or Keys/
Menu or Screen/Item
Result
Computes the probabi]ity
density function (pdf) for tile
X2 distribution
at a specified
x
value for the specified
degrees
of freedom
df
[_
z2-Test(observedmatrix,
expeetedmatrix
[,drawflag])
Performs
a ehi-square
test.
drmqflag=l
draws results;
drmqflag=O
calculates
results.
i [_
TESTS
C:x2-Test(
Circle(X,Y, radius)
Draws a circle with
(X,Y) and radius.
[_
Clear Entries
center
Clears the contents of the Last
EntKy storage area.
ClrAIILists
Sets to 0 the dimension
lists in memoKy'.
ClrDraw
Clears all drawn elements
a graph or dra_lng.
from
ClrHome
Clears
Clrkist listnamel
[,listuame2,
...,
listname
n]
Sets to 0 the dimension
or more listnames.
ClrTable
Clears
table.
conj(value)
Returns tile complex
of a complex number
complex numbers.
Connected
Sets connected
plotting mode;
resets all Y= editor graph-style
settings to "...
A-4
Tables
and
Reference
the home
of all
all values
Information
screen,
of one
from the
conjugate
or list of
[DISTR]
DISTR
6:z2pdf(
13-31
13-22
[DRAW]
DRAW
9:Circle(
8-11
[_dl [MEM]
MEMORY
3:Clear Entries
18-4
[_
[MEM]
MEMORY
4:ClrAIIkists
18-4
[_
[DRAW]
DRAW
1 :ClrDraw
8-4
i [0ggM]
IIO
8:Clrl-tome
16-20
[gg_]
EDIT
4:ClrList
12-20
i [gggM]
I/O
9:ClrTable
16-20
[_TH]
CPX
1 :conj(
2-18
i
Connected
1-11
Function or Instruction/
Arguments
CoordOff
Key or Keys/
Menu or Screen/Item
Result
TLims oft" cursor coordinate
value display.
i- _
CoordOn
Turns on cursor
value display.
1 [2_
cos(value)
Returns cosine of a
real nunlber,
expression,
list.
[FORMAT]
CoordOff
coordinate
CoordOn
or
arccosine
of areal
expression,
or list.
2-3
Returns
number,
cosh(value)
Returns hyperbolic
cosine of a
real number,
expression,
or
list.
Kffd] [CATALOG]
cosh(
cosh-l(value)
Returns hyperbolic
arccosine
of a real number,
expression,
or list.
Kffd] [CATALOG]
cosh-l(
CubicReg [Xlistname,
Ylistname_fr_qlist,
regequ]
Fits a cubic regression
model
to Xlistname
and Ylistname
with frequencyfrvqlist,
and
stores tile regression
equation
to vegequ.
NTAf]
CALC
6:CubicReg
cumSum(list)
Returns a list of the cumulative
stuns of tile elements
in list,
starting _lth the first element.
[_
[LIST]
OPS
6:cumSum(
cumSum(matrix)
Returns a matrix
cunmlative
sums
MATH
of tile
of matrix
Kffd] [cos -1]
2-3
15-10
15-10
12-26
elements.
returned
Each element inthe
nmtrlx is a cunmlative
SUnl
of a matrix
cohlnln fi'om
to[) to bottom.
0:cumSum(
dbd(datel,date2)
Calculates
the number of days
between date1 ram date2 using
the actual-day-count
method.
Kffa] [F,NANCE]
CALC
D:dbd(
value_Dec
Displays a real or complex
number, expression,
list, or
matrix in decimal format.
MATH
2:_Dec
and
3-14
[g6N]
cos-l(volue)
Tables
3-14
[FORMAT]
Reference
11-12
10-15
Information
14-13
2-5
A-5
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
Degree
Sets degree angle mode.
i
DelVar variable
Deletes from nlemolTy" the
contents
of .variable.
i
DependAsk
Sets table to ask for
dependent-variable
values.
-1-[_
DependAuto
Sets table to generate
dependentwariable
values
automatically.
-;- [_
Degree
det(matrix)
Returns
matrix.
determinant
DiagnosticOn
Sets
dim(listname)
Returns tile dilnenslon
listname.
of
dim(matri:vname)
Returns tile dimension
matri:_'name
as a list.
of
Depend: Auto
7-3
Assigns anew dimension
(length) to a new or existing
listname.
Assigns new dimensions
to a
new or existing matri:vname.
Disp
Displays
and Reference
10-12
_
[CATALOG]
DiagnosticOff
12-23
mode; r, r2, [_
[CATALOG]
and R2 m'e displayed as
DiagnosticOn
regression model results.
Disp [valueA,valueB,
valueC,...,value
n]
7-3
[TBLSET]
diagnostics-on
{rows,columns}->
dim(matri:vname)
Tables
Depend: Ask
MATH
l:det(
Sets dia_lostlcs-offmode;
r, r2,
and R 2 are not displayed as
regression model results.
length->dim(listname)
16-15
[TBLSET]
of
DiagnosticOff
A-6
CTL
G:DelVar
1-11
Displays
the home
each value,
Information
screen.
12-23
[_
[LIST]
OPS
3:dim(
11-11
MATH
3:dim(
10-12
_
[LIST]
OPS
3:dim(
11-11
MATH
3:dim(
10-13
i
IIO
3:Disp
16-18
I/O
3:Disp
16-18
i
Function or Instruction/
Arguments
Result
DispGraph
Displays tile graph.
DispTable
Displays
value_DMS
Displays
Key or Keys/
Menu or Screen/Item
; I_
I/O
tile table.
value
4:DispGraph
16-19
IIO
5:DispTable
16-19
-;-
il1 [)MS fornlat.
[_
[ANGLE]
ANGLE
4:_DMS
Dot
Sets (lot plotting
mode; resets
all.Y= editor graph-style
to ...
DrawF expression
Draws expression
X) on the graph.
i [_
settings
(in terms
of
Dot
[DRAW]
DRAW
6:OrawF
Draws the immerse of
expression
by plotting X values
on the y-axis and Y values on
the x-axis.
[_
[DRAW]
DRAW
8:Drawlnv
:DS<(variable,value)
:commandA
:commands
Decrements
variable by 1;
skips cornmandA
if variable
value.
i
e^(power)
Returns
e^(list)
Returns a list of e raised
list of powers.
Exponent:
valueEexponez_t
Returns value
exponez_t.
Exponent:
listEe_onent
Retm'ns list elements
to the exponent.
Exponent:
rnatrixEexponecnt
Returns matrix
elements
10 to the exponea_t.
_Eff(nominal
rate,
compounding
periods)
Computes
rate.
8-9
8-9
<
to power.
1-11
[_
Drawlnv expression
e raised
2-24
CTL
B:DS<(
_
[ex]
_
[ex]
[_
[EE]
[_
tEE]
[_
tEE]
16-14
2-4
times
to a
2-4
10 to the
1-7
the effective
times 10
1-7
times
1-7
interest
[_
[FINANCE]
CALC
C:_Eff(
14-12
Else
See If:Then:Else
Tables
and
Reference
Information
A-7
Function or Instruction/
Arguments
End
Key or Keys/
Menu or Screen/Item
Result
Identifies
end of For(,
If-Then-Else,
Repeat, or While
loop.
Eng
Sets engineering
display
-;CTL
7:End
mode.
Eng
Equ)String(Y=
va_;Stru)
1-10
Converts
tile contents
of a Y=
vat to a string and stores it in
Stru.
[_
[CATALOG]
Equ)String(
expr(string)
Com_erts
expression
[_
ExpReg [Xlistname,
}qistuame,flreqlist,regequ]
Fits an exponential
regression
model to Xlistuame
and
lqistuame
with frequency
freqlist, and stores the
regression
equation to regequ.
ExprOff
Turns off the expression
display during TRACE.
-;- [_
ExprOn
Turns on the expression
display during TRACE.
-;- [_
Fcdf(lowerbound,
upperbound,
numerator
df,
denominator
dr)
Computes
the F distribution
probability
between
lowerbound
and upperbound
for the specified
numerator
(degrees of freedom) and
denominator
djr
_M]
Fill(value,raatri:_name)
Stores value
mat.ri:vname.
to each
Fill(volue,listuame)
Stores value
listuame.
to each
Fix #
Sets fixed-decimal
of decimal places.
Float
A-8
SD'_ng
and
Reference
Information
decimal
15-7
all
and executes
Sets floating
Tables
to
[CATALOG]
expr(
it.
15-7
CALC
0:ExpReg
12-26
[FORMAT]
ExprOff
3-14
[FORMAT]
ExprOn
3-14
[DISTR]
DISTR
9:Fcdf(
df
element
element
mode for #
mode.
16-12
i
13-32
in
MATH
4:Fill(
10-13
in _
[LIST]
OPS
4:Fill(
11-11
i
0123456789
(select
one)
1-10
Float
1-10
i
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
fMax(expression,variable,
lower',upper'[,tolerance])
Retm'ns the value of variable
where the local maximum
of
expression
occm's, between
lower" and upper', with
specified
toleronee.
fMin(expression,variable,
lower',upper'[,toleranee])
Returns tile value of variable
where the local mininmn] of
expression
occm's, between
lower" trod upper', with
specified
toleronee.
fnlnt(expression,variable,
lower',upper'[,tolerance
Returns the function
integral of [_
expression
with respect to
MATH
variable, between/ower,
and
9:fntnt(
upper', with specified
toleronce.
FnOff [function#,
function#,...,function
FnOn [function#,
.function#,..._function
D
n]
Deselects
specified
all Y= functions
Y= functions.
n]
Selects all Y= fimctions
specified Y= functions.
MATH
7:fMax(
2-6
MATH
6:fMin(
2-6
Y-VANS On/Off
2:FnOff
3-8
Y-VANS On/Off
1 :FnOn
3-8
or
:For(variable,begin,er_d
[,incremer_t])
:commands
:End
:commands
Executes
commands
through
End, incrementing
variable
fi'om begin by increment
until
variable>end.
i [gggM]
CTL
4:For(
fPart(value)
Returns the fractional
part or
pm'ts of a real or complex
number, expression,
list, or
matrix.
[_
NUM
4:fPart(
Computes
tile g distribution
probability
between
lower'bound
and upperbound
for tile specified
numerator
(degrees of freedom)
and
dermminator
df
[_
Fpdf(x,numerotardf,
denominator
dy)
2-7
or
16-10
Tables
and
2-14
10-11
[DtSTR]
DISTR
8:Fpdf(
df
Reference
13-32
Information
A-9
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
value_Frac
Displays a real o1"eon]plex
nmnber, expression,
list, or
matrix as a fraction simplified
to its simplest terms.
[_
MATH
1 :_Frac
Full
Sets full screen
i [_
Full
Func
Sets function
mode.
graphing
mode.
2-5
Func
gcd(valueA,
valueB)
geometcdf_,x)
geometpdf(p,x)
Get(variable)
GetCalc(variable)
Returns the greatest
common
divisor of volueA and valueB,
which can be realnmnbers
or
lists.
[_
NUM
9:gcd(
(;omputes
a emnulative
probability
at x, the number of
the trial on which the first
suceess oeeurs, for tile diserete
geometric distribution
with tile
specified
probability
of success
p.
[_
Computes a probability at x, the
number of the trial on which the
[_
[DISTR]
DISTR
first success occurs, for the
discrete geometric distribution
wlth the specified probability of
success p.
D:geometpdf(
Gets data from the CBL 2/CBL
System or CBR and stores it in
variable.
-;-
Gets contents of variable
on
another TI-83 and stores it to
i
variable
1-12
i
1-11
2-15
[DISTR]
DISTR
E:geometcdf(
13-34
13-34
I/O
A:Get(
16-21
I/O
on the receix_ N TI-83.
0:GetCalc(
16-21
getKey
Returns tile key code for the
current keystroke,
or 0, if no
key is pressed.
i [0_
IIO
7:getKey
16-20
Goto label
Transfers
i
control
to label.
CTL
O:Goto
A-IO
Tables
and
Reference
Information
16-13
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
GraphStyle(function#,
grophstyle#)
Sets a grophstyle
function#.
GridOff
Turns
off grid format,
i- _
GridOn
Turns on grid format.
-;- _
G-T
Sets graph-table vertical
split-screen
mode.
i
Horiz
Sets horizontal
split-sereen
mode.
for
-;CTL
H:GraphStyle(
16-15
[FORMAT]
6ridOff
Horizontal
y
identity(dimension)
Draws
a horizontal
line at y.
Returns the identity matrix of
dimension
rows x dimension
eolumns.
= O (false),
skips
3-14
[FORMAT]
GridOn
3-14
G-T
1-12
i I_bg]
Horiz
1-12
[_
[DRAW]
DRAW
3:Horizontal
MATH
S:identity(
:If condition
:commandA
:commands
If condition
commandA.
i [g_
CTL
1:If
:If condition
:Then
:commands
:End
:commands
Executes
commands
from
Then to End if condition
= 1
(true).
i [0ggM]
CTL
2:Then
:If condition
:Then
:commands
:Else
:commands
:End
:commands
Executes
commands
from
Then to Else if condition
= 1
(true); from Else to End if
condition
= O (false).
i [0ggM]
CTL
3:Else
imag(value)
Returns the imaginmTy
(nonreal)
part of a complex
number or list of complex
numbers.
8-6
10-13
16-9
16-9
16-10
Tables
and
Reference
CPX
3:imag(
2-18
hfformation
A-11
Function or Instruction/
Arguments
IndpntAsk
Key or Keys/
Menu or Screen/Item
Result
Sets table to ask for
independent-variable
-;-[_
[TBLSET]
Indpnt: Ask
values.
IndpntAuto
Sets table to generate
independent-variable
values
automatically.
-1-[2_
[TBLSET]
Indpnt: Auto
Input
Displays
graph.
-1IIO
1:Input
Input [.variable]
Prompts
for value
Input
variable.
["text",variable]
Input [Strn,variable]
to store
7-3
to
I/0
1:Input
16-17
I/O
1:Input
16-17
-;-
inString(s#qng,subs#qng
[,start])
Returns tile (-haraeter position
in string of tile first eharaeter
of substring
beginning
at start.
[_
[CATALOG]
inString(
int(value)
Returns the lm'gest integer
real or complex ntmlber,
expression, list, or matrkx.
[_TH]
NUM
5:int(
_<a
Conlputes
tile sum, rounded
roundvalue,
of the interest
amount between pmtl
and
pint2 for an amortization
schedule.
invNorm(area[,p,_;])
Computes
emnulative
to
tile inverse
normal distribution
funetion for a given area under
the normal distribution
curve
specified
by/_ and a.
iPart(value)
A-12
Tables
Returns tile integer part of a
real or eomplex number,
expression,
list, or matrix.
and
Reference
Inforination
16-16
i
Displays Strn and stores
entered value to variable.
Elnt(pmtl,pmt2
[,roundvalue])
7-3
15-7
2-14
10-11
[_
[FINANCE]
CALC
A:Zlnt(
14-9
_
[DtSTR]
DISTR
3:invNorm(
13-30
NUM
3:iPart(
2-14
10-11
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
irr(OFO,OFList[,OFF_q])
Returns the interest rate at
which the net present vahle of
file cash flows is equal to zero.
[_
[FINANCE]
CALC
8:irr(
:lS>(variable,value)
:commandA
:commands
Increments
variable
by 1; skips commandA
variable>volue.
i
Llistname
Identifies
characters
list name.
LabelOff
Turns off axes
14-8
LabelOn
if
the next one to five
as a user-created
labels.
CTL
A:IS>(
16-13
[_
[UST]
OPS
B:L
11-16
-1-[_
[FORMAT]
LabelOff
Turns ol1 axes labels,
i- [_
[FORMAT]
LabelOn
Lbl label
3-14
3-14
Creates a label of one or two
characters.
i
Icm(valueA,valueB)
Returns the least conunon
inultiple of volueA and valueB,
which can be real nulnbers
or
lists.
[_
NUM
8:lcm(
length(string)
Returns the number
chm'aeters
in st_ng,
[_
[CATALOG]
length(
Line(X1,Y1Jd2,Y2)
[)raws a line from
(X2,Y2).
(X1,Y1)
to
[_
[DRAW]
D RAW
2:Line(
S-5
Line(X1,Y1,X2,Y2,0)
Erases a line from
(X2,Y2).
(X1,Y1)
to
[_
[DRAW]
D RAW
2:Line(
8-5
Tables
and
of
Reference
CTL
9:Lbl
16-13
2-15
Information
15-8
A-13
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
LinReg(a+bx) [Xlistname,
Iqistname,freqlist,
regequ]
Fits a linear regression inodel
to Xlistname
and Iqistname
with frequencyfrvqlist,
and
stores the regression
equation
to regequ.
kinReg(ax+b)
[Xlistname,
Iqistname_freqlist,
regequ]
Fits a linear regression
model
to Xlistname
and Iqistname
with frequency.fr_qlist,
and
stores the regression
equation
to regequ.
[g_g]
CALC
4:kinReg(ax+b)
LinRegTTest [Xlistname,
Iqistname,freqlist,
olternative,regequ]
Performs
a linear regression
and a t-test, alternative=-1
is
<; alternative=O
is €;
alternative=l
is >.
i [g_g]
TESTS
E:LinRegTTest
AList(list)
Returns a list containing
the
differences between
consecutive
elements in list.
_
Fills matrixname
colunm by
cohmm with the elements from
each specified listuame.
[_
In(value)
Returns the natural logarithm
of a real or complex number,
expression,
or list.
@
knReg [Xlistname,
Ylistname,fr_qlist,
regequ]
Fits a logarithmic
regression
model to Xlistuame
and
}qistuame
with frequency
freqlist, and stores the
regression
equation to regequ.
[g_T]
CALC
9:LnReg
log(value)
Returns
[[OG]
List_ matr(listnamel,...,
listname n,matri:_'name)
complex
logarithm
nilnlber,
or list.
A-14
Tables
and
Reference
Information
of a real or
expression,
CALC
8:LinReg(a+bx)
12-26
12-25
13-24
[LIST]
OPS
7:AList(
11-12
[LIST]
OPS
0:List _ matr(
10-14
11-15
2-4
12-26
2-4
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Logistic [Xlistname,
YTist.name,fr_ql.ist,
regequ]
Fits a logistie regression mode]
to Xlistname
and YTistname
with frequeneyfr_qlist,
and
stores the regression
equation
to regequ.
[gTAT]
CALC
B:kogistic
Matr_ list(matrix,
listnameA,...,listname
Fills each listname
with
elements
from eaeh column
matrix.
[_
[LIST]
OPS
A:MatO list(
n)
MatrMist(mat.rix,
column#,listname)
Fills a listuame
from a specified
matrix.
rnax(valueA,valueB)
Returns the larger
and valueB.
in
_lth elements
eoluran#
in
12-27
[_
10-14
11-16
[LIST]
OPS
A:MatO list(
10-14
11-16
of valueA
NUM
7:rnax(
2-15
max(list)
Returns largest real or
complex element in list.
[2_] [LIST]
MATH
2:max(
rnax(listA,listB)
Retm'ns a real or eomplex list of
the larger of each pair of
elements in listA and listB.
[2_] [LIST]
MATH
2:max(
max(value,
Retm'ns a real or complex list of
the larger of value or each list
element.
[_
[LIST]
MATH
2:max(
11-16
rnean(list[,frvqlist])
Returns the mean
frequeney frvqlist.
[_
[LIST]
MATH
3:mean(
11-16
median(list[,fr_qlist])
Returns the median
frequeney frvqlist.
[_
[LIST]
MATH
4:median(
11-16
Med-Med [Xlistname,
Ylistname_fr_qlist,
regequ]
Fits a median-median
model to
Xlistname
and Ia'ist'name _lth
frequeneyfrvqlist,
and stores
the regression
equation to
regequ.
Menu("title","textl"',labell
[,...,"textT',labelT])
Generates
a menu of up to
seven items during program
exeeution.
11-16
11-16
list)
Tables
and
of list with
of list with
Reference
CALC
3:Ned-Ned
12-25
i [_
CTL
C:Menu(
16-14
hfformation
A-15
Function or Instruction/
Arguments
min(valueA,valueB)
Key or Keys/
Menu or Screen/Item
Result
Returns
valueB.
smaller
of valueA
and
NUM
6:min(
min(list)
Returns smallest
complex element
real or
in list.
_
2-15
[LIST]
MATH
l:min(
11-16
min(listA,listB)
Returns real or complex
list of
tile smaller of each pair of
elements
in listA and listB.
[_
[LIST]
MATH
1 :min(
11-16
min(value,list)
Returns a real or complex list
of the smaller of value or each
list element.
_
[LIST]
MATH
1 :min(
11-16
Returns the number of
combinations
of valueA
valueB at a time.
[_
PRB
3:nOr
2-21
Returns a list of the
combinations
of value taken
each element in list at a time.
PRB
3:nCr
2-21
Returns a list of the
combinations
of each element
in list taken value at a time.
PRB
3:nCr
2-21
nCr valueB
valueA
value
nCr list
list nCr value
listA
nCr listB
nDeriv(expression,variable,
value[,e])
*Nom(ef_t_ct'ive
compounding
rate,
pe/riods)
Normal
taken
Returns a list of the
combinations
of each element
in listA taken each element in
listB at a time.
[_TH]
PRB
3:nOr
Returns approximate
numerical
derivative
of
expression
with respect
variable at value, with
specified
e.
[_
MATH
8:nDeriv(
Computes
rate.
Sets normal
the nominal
display
to
2-21
2-7
interest
mode.
[2_] [FINANCE]
CALC
B:*Nom(
Normal
A-16
Tables
and
Reference
Information
14-12
i
1-1O
Function or Instruction/
Arguments
normalcdf(low_rbound,
upperbound
[, _,(_])
Key or Keys/
Menu or Screen/Item
Result
(;omputes
tile normal
distribution
probability
between low_rbound
and
upperbound
for the specified
and _.
[_
[DISTR]
D IST R
2:normalcdf(
p
13-27
normalpdf(x[,p,(_])
(;omputes
tile probability
[_
[DtSTR]
density function for the nornlal
DISTR
distribution
at a specified x
1 :normalpdf(
value for tile specified/_ and c_.
not(value)
Returns 0 if value is :/: 0. value
can be a real number,
expression,
or list.
[_
[TEST]
LOG IC
4:not(
2-26
Returns tile number of
permutations
of volueA
valueB at a time.
taken
[_TH]
PRB
2:nPr
2-21
nPr list
Returns a list of tile
permutations
of value taken
each element in list at a time.
[_TH]
PRB
2:nPr
2-21
list nPr value
Returns a list of tile
permutations
of each element
in list taken value at a time.
[_TH]
PRB
2:nPr
2-21
Returns a list of tile
permutations
of each element
in listA taken each element in
listB at a time.
[_TH]
PRB
2:nPr
npv(interest
rate,CFO,
CFList[,CFFreq])
Computes
the sum of the
present values for cash inflows
and outflows.
[2_] [FINANCE]
CALC
7:npv(
valueA
Returns 1 if valueA or volueB
is € 0. volueA and valueB can
be realnumbers,
expressions,
or lists.
[2_] [TEST]
LOGIC
2:or
valueA
value
listA
nPr valueB
nPr listB
or volueB
Tables
and
Reference
13-29
2-21
14-8
2-26
hfformation
A-17
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Output(vow,coluran,"text")
Displays
specified
text beginning
at
row and column.
i [P_M]
I/O
6:Output(
16-19
Output(row,column,value)
Displays
specified
value begiJming at
row and column.
i [gggN]
I/O
6:Output(
16-19
Param
Sets parametric
mode.
Pause
Suspends
program
until you press _.
Pause ['value]
Displays value; suspends
program execution
until you
press [_.
i
Plot#(type,Xlistuame,
YTistname,mark}
Defines Plot# (1, 2, or 3) of
type Scatter
05"xyLine for
Xlistuame
and Iqistuame
using mark.
1 [2_]
Plot#(type,Xlistuame,
,frvqlist)
Defines Plot# (1, 2, 05"3) of
type Histogram 05"Boxplot for
Xlistuame
_lth frequency
fr_qlist.
; [2_] [STAT PLOT]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
12-37
Plot#(type,_istuame,
.fr_qlist,mark)
Defines Plot# (1, 2, or 3) of
type ModBoxplot for
Xlistname
_lth frequency
frvqlist using mark.
-;-[_
[STAT
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
Plot#(type,datalistname,
data axis,mark)
Defines Plot# (1, 2, 05"3) of
-;-[_
[STAT PLOT]
type NormProbPIot for
PLOTS
datalistuame
on data axis
1:Plot1(
using mark. data axis can be X
2:Plot2(
or Y.
3:Plot3(
12-37
PlotsOff
[1,2,3]
Deseleets all star plots or one
or more specified stat [)lots (1,
2, 05"3).
_
[STAT
PLOT]
STAT PLOTS
4:PlotsOff
12-35
PlotsOn [1,2,3]
Selects all stat plots o1" one or
more specified
stat plots (1, 2,
or 3).
[_
[STAT PLOT]
STAT PLOTS
5:PlotsOn
12-35
A-18
Tables
and
Reference
Information
graphing
i
Par
execution
1-11
i [gggN]
CTL
8:Pause
CTL
8:Pause
[STAT
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
16-12
16-12
PLOT]
12-37
PLOT]
12-37
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Pmt_Bgn
Specifies an mmuity due,
where payments
occur at the
beginning
of each payment
period.
F2Ta] [FINANCE]
Pmt_End
Specifies an ordinary annuity,
where payments
occur at the
end of each payment period.
F2na][FINANCE]
CALC
E:Pmt_End
poissoncdf(,u,x)
(;omputes
a cumulative
probability
at x for the discrete
Poisson distribution
with
specified
mean ,u.
[_
Computes a probabilii7 at x for
the discrete Poisson distribution
F2na][DtSTR]
DISTR
with the specified
B:poissonpdf(
poissonpdf(_,x)
Polar
eomplex
Sets polar
'value i.Polar
CALC
F:Pmt_Bgn
14-13
nlean _.
graphing
Displays eomplex
polar format.
PolarGC
Sets polar graphing
coordinates
fornmt.
prgmname
Executes
DISTR
C:poissoncdf(
13-34
Pol
1-11
CPX
7:_Polar
2-19
'value in
; r2_ [FORMAT]
PolarGC
3-13
the program
name.
EPrn(pmtl,pmt2
[,roundvolue])
Computes
the sum, rounded
roundvalue,
of the prineipal
amount between pmtl
and
pint2 for an amortization
schedule.
prod(list[,sta,r¢,e/nd])
Returns product
of list
elements
between start
end.
n]
Prompts for value for
variableA,
then variableB,
so on.
Tables
13-33
i
mode.
i
CTRL
D:prgm
Prompt variableA
[,variableB,...,vaviable
14-13
[DtSTR]
and
to
16-15
[_
[FINANCE]
CALC
0:EPrn(
14-9
and
and
Reference
[_
[LIST]
MATH
6:prod(
11-18
i [0ggM]
I/O
2:Prompt
16-18
hfformation
A-19
Function or Instruction/
Arguments
Result
1-PropZlnt(x,n
[,confidence
level])
Computes
a one-proportion
z eonfidence
interval.
i
2-PropZlnt(xl,nl
[,confidence
Computes
a two-proportion
z eonfidence
interval.
i
1-PropZTest(pO,x,n
[,alternative,drawflag])
Computes
a one-proportion
z test. olternative=-I
is <;
alternative=O
is _;
alternative=l
is >. d'rmqflog=l
draws results; drawflog=O
calculates
results.
i
2-PropZTest(xl
,nl ,x2,n2
[,alternative,drawflog])
Computes
a two-proportion
z test. olternative=-I
is <;
alternative=O
is €;
alternative=l
is >. drmqflog=l
draws results; drawflog=O
calculates
results.
i [g_g]
TESTS
6:2-PropZTest(
Pt-Change(x,y)
Reverses
[_
[DRAW]
POINTS
Pt-Off(x,y[,mark])
Erases
mark.
a point
at (x,y) using
Pt-On(x,y[,mark])
Draws
mark.
a point
at (x,y) using
PwrReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a power regression
model
to Xlistname
and Ylistname
with frequencyfr_qlist,
and
stores the regression
equation
to regequ.
,x2,n2
level])
Key or Keys/
Menu or Screen/Item
a point
at (x,y).
TESTS
A:l-PropZlnt(
13-20
TESTS
B:2-PropZlnt(
13-21
TESTS
5:1 -PropZTest(
13-14
13-15
3:Pt-Change(
2:Pt-Off(
Tables
and
Reference
Information
8-15
[_
[DRAW]
POINTS
l:Pt-On(
A-20
8-15
[_
[DRAW]
POINTS
8-14
[g_
CALC
A:PwrReg
12-27
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
Pxl-Change(row,column)
Reverses pixel at
(_w,column);
0 <_row <_62
and 0 _<column <_94.
[_
[DRAW]
POINTS
6:Pxl-Change(
S-16
Pxl-Off(row,column)
Erases pixel at (_vw,eolumn);
0 <- row <_62 and
0 <_column <_94.
[_
[DRAW]
POINTS
5:PxI-Off(
8-16
Pxl-On(row,column)
Draws pixel at (row,column);
0 <- row <- 62 and
0 <_column <_94.
[_
[DRAW]
POINTS
4:PxI-On(
8-16
pxI-Test(row,column)
Returns 1 if pixel (row,
column)
is on, 0 if it is oft';
0 <_row <_62 and
0 <_column <_94.
[_
[DRAW]
POINTS
7:pxI-Test(
P)Rx(r,0)
Returns X, given polar
coordinates
r and O or a list of
polar coordinates.
[_
[ANGLE]
ANGLE
7:P_.Rx(
2-24
P)Ry(r,O)
Returns Y, given polar
eoordflmtes
r and O or a list of
polar coordinates.
[_
[ANGLE]
ANGLE
8:P_.Ry(
2-24
QuadReg [Xlistname,
Ylistname,fr_qlist,
regequ]
Fits a quadratic
regression
model to Xlistname
and
Iqist,name
with frequency
frvqlist, and stores the
regression
equation to regequ.
[g_
CALC
5:OuadReg
OuartReg
[Xlistname,
Iqistname,frvqlist,
regequ]
Fits a quartie regression
model
to Xlistname
and Iqistname
with frequeneyfrvqlist,
and
stores the regression equation
to regequ.
[gTfT]
CALC
7:QuartReg
Radian
Sets radian angle mode.
i 1_
Radian
rand [(numtrials)]
Returns a ral]dom nt:[mber
between
0 and 1 for a
speeified
number of trials
numtrials.
randBin(numtrials,prob
[,numsimulations])
Generates
and displays a
random real number from a
specified
Binonfial distribution.
Tables
and
Reference
8-16
12-25
12-26
1-11
[_
PRB
1 :rand
2-20
PRB
7:randBin(
2-22
hfformation
A-21
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
randlnt( lower, upper
[,numtrials])
Generates
all(] displays a
randoln integer withil] a range
specified
by lower and upper
integer bounds for a specified
number of trials numtrials.
[_tH]
PRB
S:randlnt(
randM(rows,columns)
Returns a random matrix of
rows (1-99) x columns (1-99).
[_
MATH
6:randM(
randNorm(p,c_[,numtrials])
Generates and displays a
random real number from
specified
specified
specified
numtriols.
2-22
10-13
PRB
a
Normal distribution
by p and _ for a
number of trials
6:randNorm(
2-22
re^Oi
Sets tile mode to polar
complex number mode
Real
Sets inode to display complex
results only when you enter
complex numbers.
i [M0_]
Real
real(value)
Returns the real part of a
complex number or list of
complex numbers.
[_
CPX
2:real(
2-18
[_
[DRAW]
STO
4:RecallGDB
8-20
[_
[DRAW]
STO
2:RecallPic
S-1S
CPX
6:_Rect
2-19
RecaIIGDB
RecallPic
complex
n
(re^Oi).
Restores
all settings stored
tile graph database variable
GDBn.
n
in
Displays tile graph 31l(1 adds
tile picture stored in Picn.
'value _Rect
Displays complex
'value or list
in rectangular
format.
RectGC
Sets rectangular graphing
coordinates
format.
ref(matrix)
A-22
i
Tables
Returns tile row-echelon
of a matrix.
and
Reference
Inforination
re^Oi
1-12
1-12
1 _
[FORMAT]
RectGC
3-13
forln
MATH
A:ref(
10-15
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
:Repeat condition
:commands
Executes
condition
eommands
is true.
until
i [_
CTL
:End
:commands
i [0ggM]
CTL
E:Return
16-15
Returns
round(value[,#deeimals])
Returns a number, expression,
list, or matrix rounded
to
#decimols
(<_9).
[_
NUM
2:round(
*row(value,matrix,row)
Returns a matrix
matrix
nmltiplied
stored in row.
MATH
E:*row{
10-16
MATH
D: row+(
10-16
*row+(value,matrix,
rowA,rowB)
program.
16-11
Return
row+(matrix,rowA,rowB)
to tile calling
6:Repeat
_lth row of
by volue and
Returns a matrix _lth rowA of
matrix
added to rowB and
stored in rowB.
Returns a matrix _lth rowA of
matrix
nmltiplied
by volue,
added to rowB, and stored in
rowB.
rowSwap(matrix,rowA,
rowB)
Returns
matrix
a matrix
swapped
rref(matrix)
Returns
echelon
the reduced
rowform of a matrix.
R_Pr(x,y)
R_PO(x,y)
_lth
_lth
rowA of
rowB.
MATH
F:*row+(
1O- 16
MATH
C:rowSwap(
10-16
MATH
B:rref(
10-15
Returns R, given reetanguhu"
coordinates x and y or a list of
rectangular
coordinates.
[2_
Returns 0, given rectangular
coordinates x and y or a list of
rectangular
coordinates.
[_
Tables
and
Reference
2-13
[ANGLE]
ANGLE
5:R_Pr(
2-24
[ANGLE]
ANGLE
6:R_PO(
2-24
hfformation
A-23
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
2-SampFTest
[listnameZ,
listname2_fr_qlistl,
fr_qlist2,alternative,
drowflag]
(Data list input)
Performs a two-san]pie Ftest.
alternative=-1
is <;
alternative=O
is _;
alternative=
l is >. drawflag= l
draws results; drawflag=O
calculates
results.
i
2-8ampFTest
Sxl,nl,
Sx2,n2[,alternative,
drowflag]
(Summary stats input)
Performs
a two-sample
F test.
alternative=-1
is <;
alternative=O
is _;
alternative=l
is >. drawflag=l
draws results; drawflog=O
calculates
results.
i
2-SampTInt [listnamel,
listname2,
frvqlistl
_frvqlist2,
canfidezwe
level,pooled]
(Data list input)
Computes
a two-sample
t
confidence
intm_'al, pooled=l
pools variances;
pooled=O does
not pool variances.
i
2-SampTInt 21,Sx1,n1,
22,Sx2,n2
[,confidence
level,pooled]
(Sununary
stats input)
Computes
a two-sample
t
confidence
intm_,al, pooled=l
pools variances;
pooled=O does
not pool variances.
i
2-SampTTest
[listnamel,
listname2_frvqlistl
,
frvqlist2,alternative,
pooled,draw
flag]
(Data list input)
Computes
a two-sample
t test.
alternative=-1
is <;
alternative=O
is _;
alternative=
l is >. pooled= l
pools variances;
pooled=O does
not pool vm'iances,
drawflog=l
draws results; drawflog=O
calculates
results.
i
A-24
Tables
and
Reference
TESTS
D:2-SampFTest
13-23
TESTS
D:2-SampFTest
13-23
TESTS
0:2-SampTInt
13-19
Information
TESTS
0:2-SampTInt
13-19
TESTS
4:2-SampTTest
13-13
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
_r_tq
2-Sam pTTest 5l,Sxl,nl,
22 ,Sx2 ,n2[ ,o lternative
pooled,draw.flag]
(Smmnary stats input)
Computes
a two-sample
t test.
alternative=-1
is <;
alternative=O
is _;
alternative=
l is >. pooled= l
pools variances;
pooled=O does
not pool variances,
drawflog=l
draws results; drawflog=O
calculates
results.
2-SampZInt(_l,a,
[,listnamel
,listname2
frvqlistl
_frvqlist2,
canfidence
level])
(Data list input)
Computes
confidence
2-SampZlnt(_l,_,
_1,nl ,_2,n2
[,confidence
level])
(Smmnary stats input)
Computes a two-sample z
confidence intm_al.
2-SampZTest(_l,_
[,listnamel
,listname2
.frvqlistl ,frvqlist2,
alternative,drowflag])
(Data list input)
Computes
a two-sample
z test.
alternative=-1
is <;
alternative=O
is _ ;
alternative=l
is >. drawflag=l
draws results; drawflag=O
calculates
results.
2-SampZTest(61
,_,
_1 ,nl ,_2,n2
[,alternative,drawflog])
(Summary stats input)
Computes
a two-sample
z test.
alternative=-1
is <;
alternative=O
is ;_;
alternative=
l is >. draw.flag= l
draws results; drawflog=O
calculates
results.
i [gt_]
TESTS
3:2-SampZTest(
Sci
Sets scientific
mode.
i [MODEl
Sci
Select(Xlistname,
Iqistname)
a two-sample
intm_al.
TESTS
4:2-SampTTest
13-13
z
TESTS
9:2-SampZlnt(
13-18
TESTS
9:2-SampZlnt(
13-18
notation
display
Seleets one o1" more speeific
data points from a scatter plot
or xyLine plot (only), and then
stores the selected data points
to two new lists, Xlistname
and Ylistname.
Tables
and
Reference
TESTS
3:2-SampZTest(
13-12
13-12
_
1-10
[LIST]
OPS
8:Select(
11-12
hfformation
A-25
Function or Instruction/
Arguments
Send(variable}
Key or Keys/
Menu or Screen/Item
Result
Sends contents
of variable
to
the CBL 2/CBL System or CBR.
-;-
seq(expression,variable,
begin,end[,increment])
Returns list ereated by
evaluating
expression
_lth
regard to 'variable, from begin
to end by incremez_t.
_
Seq
Sets sequence
i
Sequential
Sets mode to graph ftmetions
sequentially.
SetUpEditor
Removes all list names from
the stat list editor, all(] then
restores list names L1 through
L6 to eolumns 1 through 6.
graphing
mode.
I/O
B:Send(
OPS
5:seq(
11-11
Seq
1-11
Sequential
1-12
i
EDIT
5:SetUpEditor
12-21
SetUpEditor
listnamel
[,listname2,...,
listname20]
Removes all list names from
the stat list editor, then sets it
up to display one or more
listnames
in the specified
order, starting _lth eohmm 1.
Shade(lowe:rfune,
upperfunc[,Xleft_rqght,
pattern,patres])
Draws lowerfune
and
upperfune
in terms of X on the
current graph and uses
pattern
and pat'r_s to shade the
area bounded
by lowerfunc,
upperfunc,
Xleft, and X'rqght.
[_
Shadez2(lowerbound,
upperbound,dy')
Draws the density function
the Z2 distribution
specified
degrees of freedom
dfand
shades tile area between
[_
[DISTR]
DRAW
3:Shade)_2(
lowerbound
A-26
Tables
and
Reference
and upper_ound.
Information
16-21
[LIST]
for
by
EDIT
5:SetUpEditor
12-21
[DRAW]
DRAW
7:Shade(
8-10
13-36
Function or Instruction/
Arguments
ShadeF(lowerbound,
upperbound,
numerator
df,
denominator
d,f)
Key or Keys/
Menu or Screen/Item
Result
Draws the density function
for
the F distribution
specified by
numerator
(lf and
denorainator
df and shades the
area between
lower'bound
and
_
[DISTR]
DRAW
4:ShadeF(
upperSound.
13-36
$hadeNorm(lower'bound,
upper'bound[,p,G])
Draws the normal density
function specified
by p and (_
and shades the area between
lower'bound
and upper'bound.
_
[DISTR]
DRAW
1 :ShadeNorm(
Shade_t(lower'bound,
upperbound,dJ')
Draws the density function
for
the Student-t distribution
specified
by degrees of
freedom df, and shades the
area between
lower'bound
and
upperSound.
[_
[DISTR]
DRAW
2:Shade_t(
Simul
Sets mode to graph
simultaneously.
i [_Dg]
S imul
sin(volue)
Returns
number,
tile sine of a real
expression,
or list.
Ig]N]
sin-l(volue)
Returns
number,
tile m-csine
expression,
[_
sinh(volue)
Returns tile hypet%olic
sine of
a real number,
expression,
or
list.
_
[CATALOG]
sinh(
Returns the hyperbolic
arcsine
of a real number,
expression,
or list.
_
[CATALOG]
sinh -1(
sinh-l(value)
Tables
and
functions
of a real
or list.
Reference
13-35
13-36
1-12
2-3
[SIN-1]
2-3
15-10
15-10
hfformation
A-27
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
SinReg [iterations,
Xlistname,I_istname,
period,regequ]
Attempts iterations
times to fit
a sJnusoJdal regression
model to
Xlistname
and Iqistname
using
aperiod
guess, and stores the
regression
equation to regequ.
solve(expression,variable,
guess,{lower',upper_)
Solves expression
for variable,
given an initial guess and lower"
and upper" bounds within
which the solution is sought.
i
SortA(listuame)
Sorts elements
of listname
ascending
order.
_
[LIST]
OPS
1 :SortA(
SortA(keylistuame,
dependlistl
[,dependlist2,
...,dependlist
n])
Sorts
SortD(listuame)
Sorts elements of listname
descending order.
elements
of
in
keylistuame
in ascending
order, then sorts
each dependlist
as a dependent
list.
in
SortD(keylistuarae,
Sorts
de_er_dlistl
dependlist
in descending
order, then sorts
each dependlist
as a dependent
list.
[,deper_dlist2,...,
n])
elements
of
keylistuarae
CALC
C:SinReg
12-27
MATH
0:solve(
2-12
[2_] [LIST]
OPS
l:Sorth(
[_
[LIST]
OPS
2:SortD(
[_
[LIST]
OPS
2:SortD(
stdDev(list[,frvqlist])
Returns the standard deviation
of the elements in list with
frequencyfrvqlist.
[_
[LIST]
MATH
7:stdDev(
Stop
Ends program execution;
returns to home screen.
i [gggM]
CTL
Store: value_variable
Stores value
_
StoreGDB
Stores current graph
datahase GDBn.
F:Stop
A-28
n
Tables
and
Reference
in variable.
Information
in
[_
11-10
12-20
11-10
12-20
11-10
12-20
11-10
12-20
ll-lS
16-15
1-14
[DRAW]
STO
3:StoreGDB
8-19
Function or Instruction/
Arguments
StorePic
n
String_*Equ(string,Y=
Key or Keys/
Menu or Screen/Item
Result
Stores eun'ent pleture
picture Picn.
vat')
in
[_
[DRAW]
STO
l:StorePic
Converts stt'ing iJlto an
equation and stores it in Y:
vat_
_
[CATALOG[
String_Equ(
sub(string,begin,h_.ngth)
Returns a string that is a subset
of another string, from begin
to length.
[gffd][CATALOG]
sub(
sum(list[,stat't,end])
Returns the sum of elements
list from start to end.
[gffd][LIST]
MATH
5:sum(
tan(value)
Returns
nunlber,
or list.
the ttmgent
expression,
8-17
15-8
of
15-9
11-18
of a real
2-3
tan-l(value)
Returns the aretangent
of a
real nunlber,
expression,
or
list.
[gffd][TAN-1]
Tangent(ea_ression,value)
Draws a line tangent to
expression
at X=value.
[gffd][DRAW]
D RAW
5:Tangent(
tanh(value)
Returns hyperbolic
tangent of a
real number, expression,
or list.
[_
[CATALOG]
tanh(
15-10
tanh-l(value)
Returns the hyperbolic
aretangent
of a real number,
expression,
or list.
_
[CATALOG]
tanh-l(
tcdf(lowerbound,
upp_rbound,dJ_
Computes
the Student-t
distribution
probability
between lower_ound
and
upperSound
for the specified
degrees of freedom
4/:
[2_
Text(row,column,textl,
text2,...,text
n)
Writes text on graph
at pixel (row,column),
0 <_row <_57 and
0 <_column <_94.
beginning
where
[_
[DRAW]
DRAW
0:Text(
Tables
Reference
2-3
8-8
15-10
[DISTR]
DISTR
5:tcdf(
13-31
8-12
Then
See If:Then
and
hfformation
A-29
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Time
Sets sequenee graphs
with respect to time.
Tlnterval [listname,
.fr_qlist,eonfidence
(Data list input)
Computes
inte_ral.
a t confidence
Tlnterval ;7,Sx,n
[,confidence
level]
(Summary stats input)
Computes
inte_ral.
a t confidence
tpdf(x,df)
Computes
the probability"
density" function
(pdf) for the
Student-t distribution
at a
specified x value _ith specified
degrees of freedom
ddq
Trace
Displays the graph
TRACE mode.
level]
T-Test pO[,listname,
frvqlist,alternative,
d'r'o_ag]
(Data list input)
Tables
and
Performs
a t test with
frequeneyfrvqlist.
alternative=-1
is < ;
alternative=O
is €: ;
alternative=l
is >. drawflag=l
draws results; drawf!og=O
ealeulates
results.
Reference
Information
-;-[_
[FORMAT]
Time
6-8
i
TESTS
8:Tlnterval
13-17
TESTS
8:Tlnterval
13-17
i
[_
[DISTR]
DISTR
4:tpdf(
13-30
and enters
Performs
a t test with
frequeneyfrvqlist.
alternative=-1
is <;
alternative=O
is €;
alternative=
l is >. drawflag=
draws results; drawfiag=O
calculates
results.
T-Test pO, _,Sx,n
[,olternative,drawflag]
(Summary stats input)
A-30
to plot
3-18
i
TESTS
2:T-Test
l
13-11
i
TESTS
2:T-Test
13-11
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
tvm_FV[(N,I%,PV,PMT,
P/Y,C/Y) ]
Conlptltes
tile ftlture va]ue.
[_
[FINANCE]
CALC
6:tvm_FV
14-7
tvm_I%[(N, PV,PMT,FV,
PlY, C/Y)]
(;omputes
rate.
tile annual
[_
[FINANCE]
CALC
3:tvm_I%
14-7
tvm_N[(I%,PV, PMT,FV,
P/Y,C/Y)]
(;omputes tile number
payment periods.
of
tvm_Pmt[(N,I%,PV,FV,
P/If, C/Y)]
(;omputes
payment.
the amount
tvm_PV[(N,I%,PMT,FV,
P/Y,C/Y) ]
(;omputes
tile present
uvAxes
Sets sequence graphs to [)lot
u(n)on the x-axis and v(n)on
the y-axis.
; [2_]
Sets sequence graphs to [)lot
u(n) on the x-axis and w(n) on
the y-axis.
; [2_]
[Xlistname,
Performs
one-variable
analysis
on tile data in XTistname
_ith
frequeneyfrvqlist,
[gT_]
CALC
l:l-Var
2-Mar Stats [Xlistname,
Ylistnarae,fr_qlist]
Performs two-variable
analysis
on the data in Xlistnarae
and
Iaistname
with frequeney
fr_qlist.
[gT_]
CALC
2:2-Mar Stats
variance(list[,fr_qlist])
Returns the variance
of the
elements
in list wlth frequeney
frvqlist.
[g_] [LIST]
MATH
8:variance(
Vertical
Draws
at x.
[_
[DRAW]
D RAW
4:Vertical
uwAxes
1-Mar Stats
.frwqlist]
vwAxes
Web
x
a vertical
interest
_
[FINANCE]
CALC
5:tvm_N
14-7
of eaeh
[_
[FINANCE]
CALC
2:tvm_Pmt
14-6
value.
[_
[FINANCE]
CALC
4:tvm_PV
14-7
line
[FORMAT]
uv
6-8
[FORMAT]
uw
6-8
Stats
12-25
Sets sequenee graphs to [)lot
v(n) on the x-axis and w(n) on
the y-axis.
i- [2_]
Sets sequence
as webs.
; [2_] [FORMAT]
Web
Tables
graphs to trace
and
Reference
12-25
11-18
S-6
[FORMAT]
vw
6-8
hfformation
6-8
A-31
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
:While condition
:commands
:End
:command
Executes
condition
valueA
Returns 1 if only valueA or
valueB = O. valueA and valueB
can be real numbers,
expressions,
or lists.
_
[TEST]
LOGIC
3:xor
Displays a graph, lets you draw
a box that defines a new-
-;-
xor valueB
ZBox
commands
is true.
_ewing window,
the window.
ZDecimal
while
i
CTL
5:While
2-26
ZOOM
and updates
1:ZBox
3-20
Adjusts tile _dewing window so
that aX=0.1 and AY=0.1, and
displays tile graph screen with
tile origin centered on the
screen.
i
Redefines
tile viewing window
using these dimensions:
AX=I
XscI=10
AY=I
YscI=I 0
i
Zlnterval c_[,listname,
.fr_qlist,confidence
level]
(Data list input)
Computes
intel_al.
a z confidenee
i
Zlnterval c_,;7,n
[,confidence
level]
(Summary stats input)
Computes
intel_al.
a z confidenee
Zoom In
Magnifies tile part of the graph
that surrounds
the eursor
location.
i
Displays a greater portion of
the graph, centered on the
cursor location.
i
Zlnteger
Zoom Out
A-32
Tables
and
Reference
Inforination
16-11
ZOOM
4:ZDecimal
3-21
ZOOM
8:Zlnteger
3-22
TESTS
7:Zlnterval
13-16
i [_
TESTS
7:Zlnterval
13-16
ZOOM
2:Zoom
In
ZOOM
3:Zoom Out
3-21
3-21
Function or Instruction/
Arguments
ZoomFit
ZoomRcl
ZoomStat
Recalculates Ymin and Ymax
to hmlude tile nlininluni
and
nlaxinmm
Y values, between
Xmin and Xmax, of the
selected functions
and replots
tile functions.
i
Graphs tile selected functions
in a user-defined
_dewing
window.
i
Redefines
tile viewing window
so that all statistical
data
i
points
ZoomSto
ZPrevious
ZSquare
ZStandard
Key or Keys/
Menu or Screen/Item
Result
ZOOM
O:ZoomFit
3-22
MEMORY
3:ZoomRcl
ZOOM
are displayed.
Immediately
stores
viewing window.
tile current
i
Adjusts tile X or Y window
settings so that each pixel
represents
m] equal width and
height in the coordinate
system, and updates
the
viewing window.
i
Replots the functions
immediately,
updating
the
window variables
to the
default values.
i
and
Reference
9:ZoomStat
3-22
MEMORY
2:ZoomSto
3-23
i
Replots tile graph using the
window variables
of the graph
that was displayed
before you
executed
the last ZOOM
instruction.
Tables
3-23
MEMORY
1:ZPrevious
3-23
ZOOM
5:ZSquare
3-21
ZOOM
6:ZStandard
3-22
Information
A-33
Function
or Instruction/
Key or Keys/
Menu or Screen/Item
Arguments
Result
Z-Test(pO,_[,listname,
f_qlist,elternative,
drawflag])
(Data list input)
Performs
a z test with
frequencyfreqlist.
alterr_ative=-I
is <;
alterr_ative=O is €;
alterr_ative= l is >. drawflag=
draws results; drawflag=O
calculates
results.
i [_
TESTS
1:Z-Test(
l
13-10
Z-Test(pO,_,_,n
[,olterr_ative,drawflag])
(Smmnary stats input)
Performs a z test.
alterr_ative=-I
is <;
alterr_ative=O is €;
alterr_ative=l
is >. draw.flag=l
draws results; drawflog=O
calculates
results.
i
ZTrig
Replots the functions
immediately,
updating
i
Factorial:
value!
Factorial:
Degrees
Radian:
the
ZOOM
7:ZTrig
faetodal
Returns factorial
elements.
notation:
value °
angle r
13-10
window variables
to preset
values for plotting trig
functions.
Returns
list!
TESTS
1:Z-Test(
3-22
of value.
PRB
4:!
2-21
PRB
4:!
2-21
of list
Interprets
designates
fornlat.
value as degrees;
degrees in [)MS
[_
Interprets
angle as radim]s.
[_
[ANGLE]
ANGLE
1 :°
ANGLE
3: r
Transpose:
A-34
matrix
Tables
T
and
Retrains a matrix in wltich each
element (row, column) is
swapped with tile
corresponding
element
(cohmm, row) of matrix.
Reference
Information
g-23
[ANGLE]
g-24
MATH
2: T
10-12
Function or Instruction/
Arguments
Result
xt_ZrootX_value
Retm'ns
xtlZrootX_list
Returns
listAX_listB
Cube
Returns
value 3
root: 3_(value)
Equal: valueA=valueB
Not equal: valueAcvalueB
Less than:
x_root
Returns xthroot
elements.
listX_value
Cube:
Key or Keys/
Menu or Screen/Item
valueA<valueB
of value.
2-6
MATH
5:x-_
2-6
MATH
5:x-_
2-6
MATH
5:x-_
2-6
of list
list roots
listA
MATH
5:x_
of value.
roots
of listB.
Returns the cube of a real or
complex nmnber, expression,
list, or square matrix.
[_TH]
MATH
3:3
Remms tile cube root of a real or
complex nmnber, expression, or
list.
MATH
4:3_(
Returns l lfvalueA
= valueB.
Returns 0 if valueA _ valueB.
valueA and valueB can be real
or complex numbers,
expressions,
lists, or matriees.
[_
[TEST]
TEST
1 :=
Returns 1 if valueA _ valueB.
Returns 0 if valueA = volueB.
valueA and volueB can be real
or complex nmnbers,
expressions,
lists, or matrices.
[_
[TEST]
TEST
2:€
Returns 1 if volueA
Returns 0 if volueA
valueA and volueB
[2T3] [TEST]
TEST
S:<
o1"eomplex
expressions,
Tables
< volueB.
>_valueB.
can be real
2-6
10-10
2-6
2-25
1O- 11
2-25
10-11
nunlbers,
or lists.
and
2-25
Reference
hfformation
A-35
Function or Instruction/
Arguments
Greater than:
valueA>valueB
Key or Keys/
Menu or Screen/Item
Result
Returns 1 if valueA
Returns 0 if valueA
valueA and valueB
O1" eonlplex
[_
[TEST]
TEST
3:>
llUIslbers_
expressions,
Less than or equal:
volueA<_volueB
> valueB.
<_valueB.
can be real
or lists.
Returns 1 if valueA
Returns 0 if valueA
valueA and volueB
O1"eoIslplex
expressions,
2-25
<_valueB.
> volueB.
can be real
_
[TEST]
TEST
6:_<
nunlbers,
or lists.
2-25
Greater than or equal:
valueA>valueB
Returns 1 if volueA 2 valueB.
Retunls 0 if volueA < valueB.
valueA and volueB can be real
O1"eonlplex nunlbers,
expressions,
or lists.
_
[TEST]
TEST
4:>
Inverse:
Returns
[]
value -1
1 dix_ded by a real or
eonsplex
nunsber
2-25
or
expression.
Inverse:
list -1
Inverse:
matrix
2-3
Returns 1 divided
elements.
-1
Returns
Squm'e: value 2
matrix
by list
[]
inverted.
[]
2-3
Returns value multiplied
by
itsel£ value can be a real or
eonlplex nunlber
expression.
10-10
[]
or
2-3
Square:
list 2
Returns
list elements
squared.
[]
Square:
mat'ri:_ _
Returns
itsel£
matrix
by
[]
Powers:
value^power
Returns value raised to power.
value can be a real 05"eoinplex
number or expression.
[]
Powers:
list^power
Returns
power'.
[]
Powers:
value^list
Returns value
elements.
2-3
A-36
Tables
and
Reference
multiplied
10-10
list elements
Information
raised
to
2-3
2-3
raised
to list
[]
2-3
Function or Instruction/
Arguments
Powers:
mat'rix^pow_"
Negation:
-volue
Key or Keys/
Menu or Screen/Item
Result
Returns matrix
raised to power.
elements
[]
1O- 10
Returns the negative of a real
o1"complex number,
expression,
list, o1"matrix.
[]
2-4
10-9
Power
of ten: lo^(volue)
Returns 10 raised to tile value
power, volue can be a real or
conlplex ntlnlber or
expression.
_
[10x]
Power
of ten: lo^(list)
Returns a list of 10 raised
the list power.
_
[10x]
Square
root: ,[(value)
Returns square root of a real or
complex number, expression,
or list.
_
[_]
Multiplication:
volueA*valueB
Returns
[]
Multiplication:
volue*list
Returns
element.
Multiplication:
list*value
Returns each
times volue.
Multiplication:
listA*listB
Returns listA elements
listB elements.
Multiplieation:
value*matrix
Returns value times
elements.
Multiplication:
matrixA*matrixB
Returns matrixA
matrixB.
Division:
valueA/valueB
Returns
valueB.
Division:
list/value
Division:
Division:
volueA
times
to
2-4
2-4
volueB.
2-3
2-3
volue
times
each list
[]
2-3
valueA
list element
[]
2-3
times
[]
2-3
matrix
[]
10-9
times
[]
10-9
dMded
by
[]
Returns list elements
by value.
dMded
[]
value/list
Returns value
elements.
by list
[]
listA/listB
Returns
by listB
2-3
2-3
dMded
2-3
listA elements
elements.
Tables
and
dMded
Reference
[]
2-3
hfformation
A-37
Function or Instruction/
Arguments
Result
Key or Keys/
Menu or Screen/Item
Addition:
valueA+valueB
Returns
Addition:
list+value
Returns list in which value
added to each list element.
Addition:
listA+listB
Returns listA elements
listB elements.
valueA
plus valueB.
[]
is
plus
2-3
[]
2-3
Addition:
matrixA+matrixB
Returns matrixA
elements
plus matrixB
elements.
[]
Concatenation:
string l +string2
Concatenates
strings.
[]
Subtraction:
valueA -valueB
Subtracts
valueB
Subtraction:
value-list
Subtracts
value.
list elements
Subtraction:
list- value
Subtracts
elements.
value
Subtraction:
listA-listB
Subtracts
listB
listA elements.
Subtraction:
matrixA-matrixB
Subtracts
matrixB
elements
from matrixA
elements.
[]
Minutes notation:
degrees°minutes
seeonds"
[_
'
Interprets
minutes
angle
nleasurement
as minutes.
Seconds notation:
degrees°minutes
seeonds"
'
A-38
Tables
2-3
[]
10-9
two or more
15-6
from val'ueA.
[]
2-3
from
[]
2-3
from list
[]
2-3
elements
Interprets
seconds angle
nleasurenlent
as seconds.
from
[]
2-3
10-9
[ANGLE]
ANGLE
2:'
@
2-23
[.]
2-23
and
Reference
Information
TI-83 Menu Map
The TI-83
Menu
tile keyboard
Map
layout
I
begins
from
at the top-left
left to right.
I
(Func
Plotl
Plot3
",,YI=
",,Y2=
",Y3=
",,Y4=
......
",,Y9=
",,YO=
mode)
Plot2
and follows
and settings
are shown,
I
(Pol mode)
Plotl
Plot2
Plot3
",rl=
",r2=
",r3=
",r4=
",rS=
",r6=
",X6T=
Y6T=
(Seq mode)
Plotl
Plot2
Plot3
nMin=l
",u(n)=
u(nMin)=
",v(n)=
v(nMin)=
",w(n)=
w(nMin)=
[_][STATPLOT]
__1
I
I
I
STAT PLOTS
l:Plotl...Off
_:L LI L2 m
2:Plot2...Off
_:L LI L2 _
3:Plot3...Off
_:L LI L2 m
4:PlotsOff
5:PlotsOn
I
(PRGM editor)
PLOTS
l:Plotl(
2:Plot2(
3:Plot3(
4:PlotsOff
5:PlotsOn
I
I
(PRGM editor)
TYPE
l:Scatter
2:xyLine
3:Histogram
4:ModBoxplot
5:Boxplot
6:NormProbPlot
I
I
(Par mode)
WINDOW
Tmin=O
Tmax=_2
(Pol mode)
WINDOW
Omin=O
Omax=_2
Xscl=1
Ymin= 10
Ymax=10
Yscl=1
Xres=1
Tstep=_/24
Xmin= 10
Xmax=iO
Xscl=1
Ymin= 10
Ymax=iO
Yscl=1
Ostep=_/24
Xmin= 10
Xmax=iO
Xscl=1
Ymin= 10
Ymax=iO
Yscl=1
[TBLSET]
iI
TABLE SETUP
TblStart=O
(PRGM editor)
MARK
Z:D
2:+
3:,
I
(Func mode)
WINDOW
Xmin= i0
Xmax=lO
ATbI=I
Indpnt:Auto
Depend:Auto
of the keyboard
values
I
(Par mode)
Plotl
Plot2
Plot3
",XIT=
YIT=
",X2T=
Y2T=
[STATPLOT]
corner
Default
(Seq mode)
WINDOW
nMin=1
nMax=10
PlotStart=1
PlotStep=1
Xmin= i0
Xmax=lO
Xscl=l
Ymin= i0
Ymax=lO
Yscl=l
_
[TBLSET]
FI
(PRGM editor)
TABLE SETUP
Ask
Ask
Indpnt:Auto
Depend:Auto
Tables
Ask
Ask
and
Reference
Information
A-39
i I
I
ZOOM
1:ZBox
2:Zoom In
3:Zoom Out
4:ZDecimal
5:ZSquare
6:ZStandard
7:ZTrig
8:Zlnteger
9:ZoomStat
O:ZoomFit
I
MEMORY
1:ZPrevious
2:ZoomSto
3:ZoomRcl
4:SetFactors_
MEMORY
(Set Factors,.,)
ZOOM FACTORS
XFact=4
YFact=4
[FORMAT]
I
I
I
(Func/Par/Po] modes)
RectGC PolarGC
CoordOn CoordOff
GridOff
GridOn
AxesOn AxesOff
LabelOff
LabelOn
ExprOn
ExprOff
(Seq mode)
Time Web uv vw uw
RectGC PolarGC
CoordOn CoordOff
GridOff
GridOn
AxesOn AxesOff
LabelOff
LabelOn
ExprOn
ExprOff
[CALC]
I
I
(Func mode)
CALCULATE
1:value
2:zero
3:minimum
4:maximum
5:intersect
6:dy/dx
7:if(x)dx
(Par mode)
CALCULATE
1:value
2:dy/dx
3:dy/dt
4:dx/dt
I
(Pol mode)
CALCULATE
1:value
2:dy/dx
3:dr/dO
H
Normal Sci Eng
Float
0123456789
Radian Degree
Func Par Pol Seq
Connected
Dot
Sequential
Simul
Real a+bt re^Bt
Full
Horiz
G T
A-40
Tables
and
Reference
Information
I
(Seq mode)
CALCULATE
1:value
I
SEND
1:A11+...
2:All-...
3:Prgm...
4:List._
5:Lists
to
6:GDL
7:Pic._
8:Matrix...
9:Real._
I
RECEIVE
1:Receive
T182...
O:Complex._
A:Y Vars...
B:String._
C:Back Up...
i I
EDIT
1:Edit._
2:SortA(
3:SortD(
4:ClrList
5:SetUpEditor
I
I
CALC
1:1Var
Stats
2:2 Var Stats
3:Med Med
4:LinReg(ax+b)
5:QuadReg
6:CubicReg
7:QuartReg
8:LinReg(a+bx)
9:LnReg
O:ExpReg
A:PwrReg
B:Logistic
C:SinReg
TESTS
I:Z Test...
2:T Test...
3:2 SampZTest...
4:2 SampTTest...
5:1 PropZTest...
6:2 PropZTest...
7:Zlnterval...
8:Tlnterval...
9:2 SampZlnt._
0:2 SampTlnt._
A:I PropZlnt._
B:2 PropZlnt._
C:Z 2 Test...
D:2 SampFTest._
E:LinRegTTest...
F:ANOVA(
Tables
and
Reference
Information
A-41
[LIST]
I
1
I
NAMES
l:listname
2:listname
3:listname
1
OPS
l:SortA(
2:SortD(
3:dim(
4:Fill(
5:seq(
6:cumSum(
7:AList(
8:Select(
9:augment(
O:List_matr(
A:Matr_list(
B:L
I I
1
MATH
l:_Frac
2:_Dec
3:3
4:3_r(
5: x_
6:fMin(
7:fMax(
8:nDeriv(
9:fnlnt(
O:Solver._
MATH
1:min(
2:max(
3:mean(
4:median(
5:sum(
6:prod(
7:stdDev(
8:variance(
1
NUM
l:abs(
2:round(
3:iPart(
4:fPart(
5:int(
6:min(
7:max(
8:Icm(
9:gcd(
CPX
1:conj(
2:real(
3:imag(
4:angle(
5:abs(
6:_Rect
7:_Polar
[2nd][TEST]
I
I
TEST
i:=
2:_
3:>
4:>
5:<
LOGIC
l:and
2:or
3:xor
4:not(
6:<
A-42
Tables
and
Reference
Information
1
PRB
1:rand
2:nPr
3:nCr
4:!
5:randlnt(
6:randNorm(
7:randBin(
I I
NAMES
I:[A]
2:[B]
3:[C]
4:[D]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
O:[J]
I
I
r_q [AN_LE]
I
MATH
1:det(
2: I
3:dim(
4:Fill(
5:identity(
6:randM(
7:augment(
8:Matr_list(
9:List_matr(
O:cumSum(
A:ref(
B:rref(
C:rewSwap(
D:row+(
E:*row(
F:*row+(
EDIT
l:name
2:na_
2:na_e
I
6:Repeat
7:End
8:Pause
9:Lbl
O:Goto
A:IS>(
B:DS<(
C:Menu(
D:prgm
EDIT
I:[A]
2:[B]
3:[C]
4:[D]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
O:[J]
I
EXEC
l:nan_
(PRGM editor)
CTL
1:If
2:Then
3:Else
4:For(
5:While
F--
I
1: °
2:'
3: r
4:_DMS
5:R_Pr(
6:R_PO(
7:P_Rx(
8:P_Ry(
I
NEW
1:Create
I
(PRGM editor)
I/0
1:Input
2:Prompt
3:Disp
4:DispGraph
5:DispTable
6:Output(
7:getKey
8:ClrHeme
9:ClrTable
O:GetCalc(
A:Get(
B:Send(
ANGLE
New
I
(PRGM editor)
EXEC
m:name
2:name
E:Return
F:Stop
G:DelVar
H:GraphStyle(
Tables
and
Reference
Information
A-43
I
I
DRAW
l:C]rDraw
2:Line(
3:Horizontal
4:Vertical
5:Tangent(
6:DrawF
7:Shade(
8:Drawlnv
9:Circle(
O:Text(
A:Pen
I
POINTS
1:Pt
On(
2:Pt
Off(
3:Pt
Change(
4:Pxl
On(
5:Pxl
Off(
6:Pxl
Change(
7:pxl
Test(
1
STO
1:StorePic
2:RecallPic
3:StoreGDB
4:RecalIGDB
I
VARS
1:Window._
2:Zoom._
3:GDB...
4:Picture._
5:Statistics...
6:Table...
7:String._
Y VARS
1:Function._
2:Parametric...
3:Polar._
4:On/Off...
VARS
i
I
I
(Window...)
X/Y
l:Xmin
2:Xmax
3:Xscl
4:Ymin
5:Ymax
6:Yscl
7:Xres
8:AX
9:AY
0:XFact
A:YFact
A-44
Tables
I
(Window...)
T/e
1:Tmin
2:Tmax
3:Tstep
4:emin
5:6max
(Window...)
U/V/W
1:u(nMin)
2:v(nMin)
3:w(nMin)
4:nMin
5:nMax
6:6step
6:PlotStart
7:PlotStep
and
Reference
Information
VARS
I
I
I
(Zoom...)
ZX/ZY
(Zoom...)
ZT/Ze
(Zoom...)
ZU
l:ZXmin
2:ZXmax
l:ZTmin
2:ZTmax
l:Zu(nMin)
2:Zv(nMin)
3:ZXscl
4:ZYmin
5:ZYmax
3:ZTstep
4:ZOmin
5:[email protected]
3:Zw(nMin)
4:ZnMin
5:ZnMax
6:ZYscl
7:ZXres
6:[email protected]
6:ZPlotStart
7:ZPlotStep
VARS
I
I
(GDB...)
GRAPH DATABASE
I:GDB1
2:GDB2
(Picture...)
PICTURE
1:Picl
2:Pic2
9:GDB9
O:GDBO
9:Pic9
O:PicO
VARS
I
(Statistics...)
XY
l:n
2:_
3:Sx
4:_x
I
(Statistics...)
Z
I:Zx
2:Zx 2
3:Zy
4:Zy
5:Zxy
6:Sy
7:_y
8:minX
9:maxX
O:minY
2
I
I
I
(Statistics...)
EQ
(Statistics...)
TEST
(Statistics...)
PTS
I:RegEQ
2:a
3:b
1:p
2:z
3:t
i:xl
2:yi
3:x2
4:c
5:d
4:Z 2
5:F
4:y2
5:x3
6:e
7:r
8:r 2
9:R 2
6:df
7:#
8:#1
9:#2
O:s
6:y3
7:Q1
8:Med
9:Q3
A:maxY
A:_I
B:_2
C:Sxl
D:Sx2
E:Sxp
F:nl
G:n2
H:lower
I:upper
Tables
and
Reference
Information
A-45
VARS
I
I
(Table...)
TABLE
1:TblStart
(String...)
STRING
1:Strl
2:ATbl
2:Str2
3:TbIInput
3:Str3
4:Str4
9:Str9
O:StrO
Y VARS
I
I
I
(Function...)
FUNCTION
I:YI
2:Y2
3:Y3
4:Y4
(Parametric...)
PARAMETRIC
I:XIT
2:YIT
3:X2T
4:Y2T
I
(Polar...)
POLAR
i:ri
2:r2
3:r3
4:r4
5:r5
O:Yo
A-46
B:Y6T
Tables
and
Reference
Information
I
(On/Off._)
ON/OFF
1:FnOn
2:FnOff
[_
[DISTR]
I
I
I
DISTR
1:normalpdf(
2:normalcdf(
3:invNorm(
4:tpdf(
5:tcdf(
6:z2pdf(
7:z2cdf(
8:Fpdf(
9:Fcdf(
O:binompdf(
A:binomcdf(
DRAW
1:ShadeNorm(
2:Shade t(
3:Shadez2(
4:ShadeF(
B:poissonpdf(
C:poissoncdf(
D:geometpdf(
E:geometcdf(
I_
[FINANCE]
I
I
CALC
I:TVM Solver...
2:tvm Pmt
3:tvm I%
4:tvm PV
5:tvm N
6:tvm FV
7:npv(
8:irr(
9:hal(
O:XPrn(
A:glnt(
B:_Nom(
C:_Eff(
D:dbd(
E:Pmt End
F:Pmt Bgn
I
VARS
I:N
2:1%
3:PV
4:PMT
5:FV
6:P/Y
7:C/Y
Tables
and
Reference
Information
A-47
MEMORY
[MEM]
i--J
I
I
MEMORY
l:Check
RAM_
2:Delete._
3:Clear
Entries
4:ClrAllLists
5:Reset...
MEMORY
I
I
(Check
RAM...)
MEM FREE 27225
Real
15
(Delete...)
DELETE FROM...
1:All...
Complex
List
Matrix
Y Vars
2:Real._
3:Complex._
4:List...
5:Matrix...
0
0
0
240
Prgm
Pic
GDB
14
0
0
String
0
6:Y
Vars...
7:Prgm...
8:Pic...
9:GDB...
O:String...
(Reset...)
I
Resetting
erases
all
12_]_ALOG]
I
(All
Memory...)
RESET MEMORY
1:No
2:Reset
(Defaults...)
RESET DEFAULTS
1:No
2:Reset
memory
data
CATALOG
cosh(
cosh-l(
Equ_String(
expr(
and
inString(
programs•
length(
sinh(
sinh-1(
String_Equ(
sub(
tanh(
tanh-1(
A-48
Tables
and
Reference
Information
I
(Reset...)
RESET
1:All
Memory...
2:Defaults._
Variables
User Variables
The
TI-83
Some
uses
variables
the variables
listed
are restricted
below
to specific
in various
data
ways,
types.
The variables
A through
Z and 0 are defined
as real or
complex
numbers.
You may store to them. The TI-83 can
update
X, Y, R, 0, and T dm'ing graphing,
so you may want
to avoid using these varial)les
to store nongraphing
data.
The variables
(list nalnes)
L1 through
LS are restricted
lists; you cannot store another
type of data to them.
The wu'iables
(matrix
names)
to matrices;
you cannot store
The vm'iables
Pie1 through
pictures;
you cannot store
to
[A] through
[J] are restricted
another
type of data to them,
Pie9 and Pic0 are restricted
to
another
type of data to them.
The variables
GDB1 through
GDB9 and GDB0 are restricted
to graph databases;
you cannot
store another
type of data
to them,
The variables
Strl through
Str9 and StrO m'e restricted
to
strings; you cannot store another
type of data to them.
You can store any string of characters,
functions,
instructions,
or vm'iables to the functions
Yn, (1 through
9,
and 0), XnT/YnT (1 through
6), rn (1 through
6), u(n), v(n),
and w(n) directly or through
the Y= editor. The validity
string is determined
when the function
is evaluated.
System
Variables
of the
The variables
below nmst be real numbers.
You may store
to them. Since the TI-83 can update some of them, as the
result of a ZOOM, for example,
you nlay want to avoid
using these variables
to store nongraphing
data.
•
Xmin, Xmax, Xsel, AX, XFact, Tstep, PlotStart, nMin, and
()tiler window
variables,
•
ZXmin, ZXmax, ZXscl, ZTstep, ZPIotStart,
other ZOOM variables.
The variables
cannot store
below are resetwed
to them.
Zu(nMin),
for use by the TI-83.
and
You
n, _, Sx, _x, minX, maxX, Ey, Ey 2, Exy, a, b, e, RegEQ, xl, x2,
yl, z, t, F, Z2, p, xl, Sxl, nl, lower, upper, r2, R 2 aft(] other
statistical
variables,
Tables
and
Reference
hfformation
A-49
Statistics
Formulas
This section contains statistics fornmlas for the Logistic and SinReg
regressions,
ANOVA, 2-SampFTest, and 2-SampTTest.
Logistic
The logistic regression algorithm applies nonlinear
t_cursive least-squares
techniques to optimize the
following cost function:
N
j
:z(-i÷o>,
4
c
which is the sunl of the squares
where:
of the residual
errors,
x = the independent
variable list
y = the dependent variable list
N = the dimension of the lists
This technique attempts to estimate the constants
e t_cursively to make J as small as possible.
SinReg
a, b, and
The sine regression algorithm applies nonlinear recut_ive
least-squares
techniques to optimize the following cost
function:
N
J=
E[a
i=1
siyt(bxi
+ e)+
d-
yi]2
which is the sunl of the squares
where:
of the residual
errors,
x = the independent
variable list
y = the dependent variable list
N = the dimension of the lists
This technique attempts to recursively estimate the
c()nstants a, b, c, and d to make J as small as possible.
A-50
Tables
and
Reference
Inforination
ANOVA(
The ANOVA
F
F statistic
is:
Factor
MS'
Error MS
The
mean
Factor
Error
squares
MS'
MS' =
The sum
are:
(MS) that
Factor
SS
Factor
df
Error
SS
Error
df
of squares
make
(SS) that
up F are:
make
up the mean
squares
I
Factor
SS
= E
ni(xi
- 2) 2
i=1
I
Error
SS
= E
(ni
- 1)Sxi 2
i=l
The
degrees
of freedoln
dfthat
make
up the mean
squares
are:
Factor
df = I - 1 = numerator
df for V
I
Ermrdf
where:
= E
i=l
(hi
- 1) = denolninator
I = number
_:i
Sxi
if)r
= the length
_:
= the mean
and
F
of populations
= the mean of each list
= the standard
deviation
ni
Tables
df
of each
of each
list
list
of all lists
Reference
Information
A-51
Below
2-SampFTest
for the 2-SampFTest.
is the definition
Sxl,
Sx2
= Sample
nl-1
standard
and n2-1
deviations
degrees
having
of freedom
df,
respectively.
F = F-statistic
dr(x,
nl-1 , n2-1 )
[ Sx2 )
= Fpdf(
) with
fl'eedom
p = reportedp
2-SampFTest
p = i f(x,
for the alternative
degrees
of
df, hi-1 , and
n2-1
wdue
hypothesis
(s 1 > (s 2.
hypothesis
(_1< (_2-
hypothesis
(_1 :_ (_2.Limits
nl - 1,n 2 - 1)dx
2-SampFTest for the alternative
F
p = ff(x,n
0
1-1,n
2-1)dx
2-SampFTest for the alternative
nmst satisfy the following:
Lb nd
/92=
f f(x'nl0
where:
l'n2-1)dx=
[Lbnd, Ubnd]
ff(x,n
U_,_
1-1,n
2-1)dx
= lower and upper limits
The F-statistic is used as the bound producing the smallest
integral. The reinaining bound is selected to achieve the
preceding integral's equality relationship.
A-52
Tables
and
Reference
Information
2-SampTTest
The following
is the definition
for the 2-SampTTest,
The
two-sample
t statistic
with degrees
of freedom
dfis:
t=
Xl--X2
s
where tile computation
whether the variances
pooled:
S = ]_/$2b'12q
V nl
d f-
l
nl-lk
of S and df are dependent
are pooled. If the variances
on
are not
SX22
n2
S:t;12
+ ,gXd2 )2
nl }
nz-lk
l (s.s/,,
nz )
otherwise:
(n I -
1)SXl
_:t;p =
2 + (n 2 - 1)SX2 2
df
S = J1 + 1 Sxp
V)'_I n2
df = nl+n2-2
and Sxp is the pooled
Tables
variance.
and
Reference
Information
A-53
Financial
This
Formulas
section
contains
amortization,
Time Value
Money
cash
of
financial
flow,
fommlan
interest-rate
for computing
conve_\sions,
time
and days
value
of money,
between
dates.
i=[e(y×ln(x+l))]_l
where:
PMT
€ 0
y = C/Y + P/Y
x = (.01 ×1%)
= compounding
P/Y
= payment
I% = interest
i = (-FV
+ PV)( 1+ N)
_
PMT
= 0
The
used
to compute
0 = PV + PMT
1% = 100 × C/Y
where:
periods
periods
rate
per
per
year
per year
yem"
1
where:
iteration
+ C/Y
C/Y
x G i [1-(1+i)
i:
NI+FV×(I+i)
N
× [e(Y × ln(x + 1)) _ 1]
x = i
y = P/Y+C/Y
G i = l+i×k
where:
k = 0 for end-of-period
payments
k = 1 for beginning-of-period
N-
where:
[PMTxGi+PVxi)
ln(1 + i)
i € 0
N = -(PV + FV) + PMT
where:
A-54
Tables
and
Reference
i = 0
Information
payments
PMT=-ix[PV_
Gi
PV+FV
(I+i)N-
[
where:
PMT
i € 0
= -(PV
+ FV)
where:
+ N
i = 0
J
where:
+ PMT
where:
PMT x Gi
i
× N)
i = 0
PMT i x G i
where:
FV = -(PV
where:
(l+i)
i € 0
PV = -(FV
FV
]
lJ
(l+i)N×
( PV-_
PMT×Gi.)
i € 0
+ PMT
x N)
i = 0
Tables
and
Reference
Information
A-55
Amortization
If computing
Let hal(O)
Iterate
bal(),
pint2
= npmt
= RND(PV)
fronl
m = 1 to pint2
Lm = RND[RND12(-i
x bal(m - 1))]
hal(m)
= bal(m - 1) -[m+ RND(PMT)
then:
hal()
E Prn(
Z Int(
where:
= hal(pint2)
) = bal(pmt2)
) = (pint2
RND
- bal(pmtl)
- pmtl
= round
+ 1) x RND(PMT)
the display-
decimal
RND12
= round
places
A-56
Tables
and
Reference
Information
to the number
selected
to 12 decimal
Balance,
principal,
and interest
values of PMT, PV, I°/o,and pmtl
- Z Prn(
places
are dependent
and pint2.
on the
)
of
Cash Flow
N
npv() = CF0 + _CFj(1
j=l
where:Sj=
ni
+/)
& _(1 - (1 _/)
rq)
J >-1
j= 0
Net present value is dependent on the values of the initial
cash flow (CFII), subsequent
cash flows (CFj), frequency of
each cash flow (nj), and the specified interest rate (i),
irr()
= 100 × i, where
i satisfies
npv()
=0
Internal rate of return is dependent on the values of the
initial c_h flow (CFo) and subsequent cash flow. (CFj),
i = I% + 100
Interest Rate
Conversions
VEff( ) = 100 × (e cT × Zn(x+ 1) _ 1)
where:
x = ,01 x NOM+ CP
_Nom( ) = 100 × CP × [ei + cP × z,.(x+ 1)_ 1]
where:
x = ,01 × EFT"
EFF = effective rate
CP = compounding
NOM = nominal rote
Tables
and
Reference
periods
Information
A-57
Daysbetween Withthedbd(function,
youcanenterorcompute
adate
Dates
within
the range
Jan.
1, 1950, through
Actual/actual
day-count
number
of days per month
Dec. 31, 2049.
method
(assunles
and actual number
actual
of day-s per
year):
dbd(
(days
Number
between
Number
of Days
dates)
of Days
=
II - Number
I = (Y1-YB)
of Days
I
× 365
+ (number
+ DT1
of days
MB to M1)
(Y1 - YB)
+
4
Number
of Day-s II = (Y2-YB)
x 365
+ (number
+ DT2
of days
MB to 11//2)
(Y2 - YB)
+
4
where:
M1
DT1
= month
of first
= day of first
date
date
Y1 = year of first date
M2 = month of second
DT2
= day of second
Y2 = year
= base
month
DB
= base
day (1)
YB = base
A-58
Tables
and
Reference
Information
date
of second
MB
year
date
date
(January)
(first
year
_ter
leap year)
B
Contents
GeneralInformation
Batte_" Infommtion ......................................
In Case of Difficulty .....................................
Error Conditions .........................................
Accuracy Infomlation ....................................
Support and Sep_iee Information .........................
Warranty Infornlation ....................................
General
Information
B-2
B-4
B-5
B-10
B-12
B-13
B-1
Battery
Information
When to Replace
the Batteries
The
TI-83
uses
five batteries:
and one lithium
auxilimTF power
AAA batteries.
When the battery
the TI-83 displays
_Jour
four
AAA alkaline
batteries
battery-. The lithium battery
pro_qdes
to retain menlot T while you replace
voltage level
this message
the
drops below a usable level,
when you turn on the unit.
batteries
are
low.
Reco_r_end
change
o?
batteries.
Alter
this message
is first
displayed,
you can
expect
the
batteries
to function
for about one or two weeks,
depending
on usage. (This one-week
to two-week
period is
based on tests with alkaline
batteries;
the performance
of
other kinds of batteries
may vm3z.)
The
time
you
the
you
low-battery
message
continues
to be displayed
each
you turn on the unit until you replace
the batteries.
If
do not replace
the batteries
within about two weeks,
calculator
may turn off by itself or fail to turn on until
install new batteries.
Replace
Effects
of
Replacing
Batteries
the
Battery
Precautions
Take these precautions
•
•
•
•
•
General
batte_y-
eve_3z three
or four
years.
Do not remove both types of batteries
(AAA and lithium
auxiliat_F) at the same time. Do not allow the batteries
to
lose power
completely.
If you follow these guidelines
and
the steps for replacing
batteries
on page B-3, you can
replace
either type of batter T without
losing any
information
in memo_7.
•
B-2
the lithimn
when replacing
batteries.
Do not mix new and used batteries. Do not mix brands
(or types within brands) of batteries.
Do not mix rechm'geable and nonrechargeable
batteries.
Install batteries according to polarity (+ and -)
diagrams.
Do not place nonreehargeable
batteries in a battery
recharger.
Properly dispose of used batteries immediately.
Do not
leave them within the reach of children.
Do not incinerate batteries.
hfformation
Replacing
Batteries
the
To replace
the batteries,
follow
these
steps.
1. Turn offthe
calculator.
Replacethe
slide cover over the
keybom'd
to avoid inadvertently
turning
on the
calculator.
Turn the back of the calculator
toward
you.
Hold the cMeulator upright. Place your thumb on the
oval indentation
on the battetsz cover. Push down and
toward you to slide the cover al_out IAinch (6 nlnl).
Lift
off the cover to expose the batte_3z eolnpartment.
Note:
To avoid
loss
of infornmtion
memory,
you nmst
turn off the
remove
the AAA batteries
and
simultaneously.
3. Replace
all four
time. Or, replace
stored
calculator.
the lithium
AAA alkaline
batteries
the lithium batte_Ty-.
in
Do not
battery
at the same
•
To replace the AAA alkaline batteries, remove all
four discharged AAA batteries and install new ones
according to the polm'ity (+ and -) diagrams in the
batte_3z compartment.
• To remove the lithimn batte_Ty-,place your index
finger on the battet3z. Insert the tip of a ball-point pen
(or similar instrument)
under the battery at the small
opening provided in the batte_sz compartment.
Carefully P_TY"
the battetsz upward, holding it with
your thumb and finger. (There is a spring that pushes
against the underside of the battet3z.)
• Install the new batte_sz, + side up, by inserting the
batte_3z and gently- snapping it in with your finger.
Use a CR1616 or CR1620 (or equivalent) lithium
batte_y-.
4. Replace the batte_y- compartment
cover. Turn the
calculator on and adjust the display contrast, if
necessmTy- (step 1; page B-4).
General
Information
B-3
In Case of Difficulty
Handling a
Difficulty
To handle a difficulty,
follow these steps.
1. If you cannot see anything
nlay need to be adjusted.
on the screen,
the contrast
To darken the screen, press and release [2_, and then
press and hold [] until the display- is sufficiently dark.
To lighten the screen, press and release [_], and then
press and hold [] until the display is sufficiently light.
2. If an error menu is displayed, follow the steps in
Chapter 1. Refer to pages B-5 through B-9 for details
about specific errors, if necessatT.
3. If a checkerboard
cursor ( N ) is displayed, then either
you have entered the nlaxinlunl number of characters in
a prompt, or nlenlory is full. If nlenlory is full, press [_
[MEM]2 to select 2:Delete, and then delete some items
fronl
nlenlory
(Chapter 18).
4, If the busy indicator (dotted line) is displayed, a graph
or program has been paused; the TI-83 is waiting for
input, Press [gNT_ to continue or press [_] to break,
5, If the calculator does not seem to work at all, be sure
the batteries are flesh and that they are installed
properly. Refer to battew information
on pages B-2 and
B-3.
B-4
General
Information
Error Conditions
When the TI-83 detects an error, it displays ERR:message and an error menu.
Chapter 1 describes the general steps for eotTeeting errors, This table contains
each etTor type, possible causes, and suggestions for correction,
Error Type
ARCHIVED VAR
ARGUMENT
BAD GUESS
Possible Causes and Suggested Remedies
A function or instruction is archived and therefore cannot
be executed or edited. [ _se the unto'chive command to
mmrehive the variable before using it.
A function or instruction does not have the co_Tect number
of arguments. See Appendix A and the appropriate
chapter.
• In a CALC operation, you specified a Guess that is not
between Left Bound and Right Bound.
• For the solve( function or the equation solver, you
specified a guess that is not between lower and upper.
• Your guess and severM points around it are undefined.
Exa]nine a graph of the function. If the equation has a
solution, change the bounds and/or the initial guess.
BOUND
• In a CALC operation or with Select(, you defined
Left Bound > Right Bound,
• In fMin(, fMax(, solve(, or the equation
entered lower >_upper.
solver, you
BREAK
You pressed the [ON]key to break execution of a prograln,
to halt a DRAW instruction, or to stop evaluation of an
expression.
DATATYPE
You entered
a value or variable
that is the wrong data type.
• For a function (including implied lnultiplication)
or an
instruction, you entered an argument that is an invalid
data type, such _ts a complex number where a real
number is required. See Appendix A and the appropriate
chapter.
• In an editor, you entered a type that is not allowed, such
as a matrix entered as an element in the stat list editor.
See the appropriate chapter.
• You attelnpted to store to an incorrect
a nmtrix, to a list.
data type, such as
DIMMISMATCH
You attempted to perform an operation that references
more than one list or lnatrix, but the dimensions do not
lnateh.
DIVIDE BY 0
• You attempted to dixqde by zero. This error is not
returned during graphing. The TI-83 allows for
undefined values on a graph.
• You attelnpted
a linear regression
with a vertical
General
Infornmtion
line.
B-5
Error Type
Possible
DOMAIN
•
You specified
an argument
to a function
or instruction
outside
the wdid range, This elTor is not returned
during
graphing.
The TI-83 allows for undefined
values on a
graph, See Appendix
A and tile appropriate
chapter.
•
You attempted
a logarithmic
or power regression
with
-X or an exponential
or power
regression
with a -Y.
•
You attempted
pint2
< pint1.
Duplicate
Name
Error in Xmit
Causes
and Suggested
to compute
A variable
you attempted
because
a variable
with
receiving
unit.
Remedies
a
XPrn( or Xlnt( with
to transmit
cannot be translnitted
that name already
exists in the
•
The TI-83 was unable to transmit
an item. Check to see
that the cable is firnfly connected
to both units and that
the receiving
unit is in receive
mode.
•
You pressed
•
You attempted
TI-83.
•
You attempted
to transfer
data
1.6) from a TI-83 to a TI-82.
•
You attempted
a TI-82 without
[_
to break
to perform
during
transmission.
a backup
(()tiler
from
than
a TI-82
to a
kl through
to transfer
kl through
L6 from a TI-83 to
using 5:Lists to TI82 on the LINK SEND
nlenu,
ILLEGAL NEST
You attempted
to use an invalid function
a function,
such as seq( within e_ression
INCREMENT
•
The increment
in seq( is 0 or has the wrong sign. This
error is not returned
during graphing.
The TI-83 allows
for undefined
values on a graph,
•
The increment
•
You attempted
to refel_nce
a variable
or use a function
where it is not valid. For example,
Yn cannot reference
Y, Xmin, AX, or TblStart,
•
You attempted
was transferred
INVALID
in a For( loop
in an argument
for seq(.
is 0,
to reference
a variable
or function
that
from the TI-82 and is not valid for the
TI-S3. For example,
you may have transfen'ed
U n-1 to
the TI-83 from the TI-82 and then tried to reference
it.
•
B-6
General
In Seq mode, you attempted
to graph a phase
without
defining
both equations
of the phase
hfformation
plot
plot.
to
Error Type
Possible Causes and Suggested Remedies
INVALID (cont.)
• In Seq nlode, you attempted to graph a recursive
sequence without having input the correct number
initial conditions.
• In Seq mode, you attempted
than (n-l) or (n-2).
to reference
of
terms other
You attelnpted to designate a graph style that is invalid
within the eutTent graph mode.
You attempted to use Select{ without having selected
(turned on) at least one xyLine or scatter plot.
INVALIDDIM
You specified dimensions for an argument
appropriate
for the operation.
You specified a list dimension as something
an integer between 1 and 999.
that are not
other than
You specified a matrix dimension as something
than an integer between 1 and 99.
You attempted
ITERATIONS
to invert a matrix
other
that is not square.
• The solve( function or the equation solver has exceeded
the nmximum number of permitted iterations. Examine
a graph of the function. If the equation has a solution,
change the bounds, or the initial guess, or both.
• irr( has exceeded the nmxinmm number of permitted
iterations.
• When computing
was exceeded.
1%,the nl_Lxinlunl number
is not defined
of iterations
LABEL
The label in the Goto instruction
instruction in the program.
with a Lbl
MEMORY
Memory is insufficient to perform the instruction or
function. You nmst delete items from memory (Chapter
before executing the instruction or function.
18)
Reeursive problems return this error; for example,
graphing the equation YI=Y1.
Branching out of an If/Then, For(, While, or Repeat loop with
a Goto also can return this error because the End statelnent
that terminates the loop is never reached.
General
Information
B-7
Error Type
MemoryFull
Possible Causes and Suggested Remedies
• You are unable to transmit an item because tile receiving
unit's available lnelnol_y- is insufficient. You lnay skip the
iteln
or
exit receive
triode,
• During a lnelnol_y- backup, the receiving unit's available
nlenlory is insufficient to receive all itelns in the sending
unit's lnelnot_yL A lnessage indicates the number of bytes
the sending unit nmst delete to do the lnetnol_- backup.
Delete items and try again.
MODE
You attempted to store to a window variable in another
graphing mode or to perform an instruction while in the
wrong nlode; for exaInple, Drawlnv in a graphing nlode
other than Func.
..............................
The saiv;{ function
a sign change.
_;i the equation
......
• You atteinpted to compute I%when FV, (N*PMT), and PV
are all _>O, or when FV, (N*PMT), and PV are all _<O.
• You attempted to eonlpute
irr( when neither CFList nor
CFO is > O, or when neither CFList nor CFO is < O.
NONREAL ANS
In Real mode, the result of a calculation yielded a complex
result. This error is not returned during graphing. The TI-83
allows fox"undefined values oil a graph.
OVERFLOW
You attempted to enter, or you have calculated, a number
that is beyond the range of the calculator. This error is not
returned during graphing. Tile TI-83 allows for undefined
wdues on a graph.
RESERVED
You attempted to use a wsteln
See Appendix A.
SINGULAR MAT
• A singular matrix (determinant
argument for %
variable
inappropriately.
= 0) is not valid as the
• The 8inReg instruction or a polynomial regression
generated a singular matrix (determinant
= 0) because
could not find a solution, or a solution does not exist.
This error is not returned during graphing.
allows for undefined values on a graph.
B-8
General
hfformation
Tile TI-83
it
Error Type
Possible Causes and Suggested Remedies
SINGULARITY
expression ill the solve( function or the equation solver
contains a singularity (a point at which the function is not
defined). Examine a graph of the function. If the equation
h_s a solution, change the bounds or the initial guess or
both.
STAT
You attempted
appropriate.
• Statistical
• Ned-Ned
partition.
a stat calculation
analyses
with lists that are not
must have at least two data points.
must have at least three points in each
• When you use a frequency
list, its elements
must be _>0.
• (Xmax - Xmin) / Xscl nmst be <_47 for a histogram.
STAT Pt_OT
Y0u atte;_pted to display a graph when a stat plot that uses
an undefined list is turned on.
SYNTAX
The connnand contains a syntax error. Look for lnisplaced
functions, arguments, parentheses,
or colnnlas. See
Appendix A and the appropriate chapter,
TOL NOT MET
You requested a tolerance
retum an accurate result.
UNDEFINED
You referenced a variable that is not currently defined. For
example, you referenced
a stat variable when there is no
current calculation because a list has been edited, or you
referenced a variable when the variable is not valid for the
current calculation, such as a 'after Med-Med.
WINDOW RANGE
A probleln exists with the window variables.
• You defined Xmax _<Xmin or Ymax _<Ymin.
• You defined
• You attempted
• You defined
to which the algorithln
cannot
0max _<0min and 0step > 0 (or xqce versa).
to define Tstep=0.
Tmax _<Train and Tstep > 0 (or vice versa).
• Window variables are too SLUM1
or too large to graph
correctly. You may have attempted to zoom in or zoom
out to a point that exceeds tile TI-83's nulnerical range.
ZOOM
• A point or a line, instead
• A ZOOM operation
of a box, is defined
returned
in ZBox.
a math error.
General
Information
B-9
Accuracy
Computational
Accuracy
Information
To maximize
accuracy-,
internally
than it displays.
using up to 14 digits with
the TI-83
carries
more
digits
Values m_ stored
in nlemo_a two-digit
exponent.
•
You can store a value in the window
to 10 digits (12 for Xscl, Yscl, Tstep,
vm'iables
using
and 0step).
•
Displayed
values are rounded
as specified
by the mode
setting with a nlaxinmln
of 10 digits and a two-digit
exponent.
•
ReflEO displays
up to 14 digits in Float mode. [ Mng a
fixed-decilnal
setting other than Float causes
ReflEO
results to be rounded
and stored with the specified
number
of decimal
places.
Graphing
Xmin is the center
Accuracy
of the next-to-the-rightmost
pixel. (The rightmost
reserved
for the busy indicator,)
AX is the distance
between
the centers
of two adjacent
pixels.
•
•
of the leffmost
pixel,
up
Xmax is the center
In Full screen
mode, AX is calculated
zks
(Xmax - Xmin) / 94. In G-T split-screen
mode,
calculated
as (Xmax - Xmin) / 46.
pixel
is
AX is
If you enter a value ff)r AX from the home screen
or a
program
in Full screen mode, Xmax is calculated
as
Xmin + AX * 94. In G-T split-screen
mode, Xmax is
calculated
as Xmin + AX * 46,
Ymin is the center of the next-to-the-bottom
pixel; Ymax is
the center of the top pixel. AY is the distance between the
centers of two adjacent pixels.
•
•
B-IO
General
In Full screen mode, AY is calculated as
(Ymax - Ymin) / 62. In Horiz split-screen nlode, AYis
cMculated as (Ymax - Ymin) / 30. In G-T split-screen
mode, AY is c'Mculated as (Ymax - Ymin) / 50.
If you enter a vMue for AYfronl the home screen or a
program in Full screen mode, Ymax is calculated as
Ymin + AY * 62. In Horiz split-screen nlode, Ymax is
eMculated as Ymin + AY * 30. In G-T split-screen nlode,
Ymax is calculated _ksYmin + AY* 50,
Information
Cursor
coordinates
aredisplayed
aseight-character
numbers
(whichmayinclude
anegative
sign,decimal
point,andexponent)
whenFloatmode
isselected.
XandY
areupdated
withanlaxinmln
accuracy
ofeightdigits.
minimum and maximum
on the CALCULATE
are
menu
calculated
with a tolerance
of 1E-5; _f(x)dx is calculated
at
1E-3. Therefore,
the result displayed
nlay not be accurate
to
'all eight displayed
digits. For most functions,
at least five
accurate
digits exist. For fMin(, fMax(, and fntnt( on the
MATH menu and solve( in the CATALOG, the tolerance
can
be specified.
Function
Limits
Function
sn
Range of Input Values
cos. "
....................
0
sin -1 2a', COS-1 X
...........
-1 < x <_1
.......
...............................
ex
-10100< x -<230.25850929940
1_
-10 i00 < x < 100
sinh x, cosh w
tanh x
Ixl _<230.25850929940
Ixl < 10 i°°
sinh :_ x
Ixl < 5 x 109!_
..............................
cosh-1 .%,
l_<x < 5x 1() 9!_
tanh :_ x ...........................................................
-1 <x< .........................
1
_x
(real
lnode)
_X (complex
Function
Results
0 < x < 10100
mode)
Ixl < 10 t°°
x!
-.5 -< x -< 69, where
x is a multiple
Function
1
1
tan- x
-90
Range of Result
o
o
to 90
or-_/2
)
cos-1x
0° to 180°
t0_/2
of .5
(radians)
or 0 to x (radians)
General
Information
B-11
Support
and Service
Information
Product Support
Customers
For
general
in the U.S., Canada, Puerto Rico, and the Virgin Islands
questions,
contact
questions,
phone:
Customers
Contact
Instrunmnts
1-800-TI-CARES
[email protected]
phone:
e-mail:
For technical
Support:
Texas
Customer
Support:
(1-800-842-2737)
call the Progrannning
Assistance
Group
of Custonler
1-972-917-8324
outside the U.S., Canada, Puerto Rico, and the Virgin Islands
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B-12
General
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with
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or contact
Warranty Information
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product
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B-14
General
Information
Index
+
(addition),
2-3, A-38
z2cdf( (chi-square
cdf), 13-31, A-3
x2pdf( @hi-square
pdf), 13-31, A-4
x2-Test (ehi-square
test), 13-22, A-4
:
(colon), 6, 16-5
+
3
3_(
(concatenation),
15-6, A-38
(cube), 2-6, A-35
(cube root), 2-6, A-35
°
/
=
(degrees
notation),
2-3, A-34
(division),
2-3, A-37
(equal-to relational
test), 2-25,
A-35
!
0
'.
"..
>
>
(factorial),
2-21, A-34
(graph style, animate),
3-9
(graph style, (lot), 3-9
(graph style, line), 3-9
(greater than), 2-25, A-35
(greater than or equal to), 2-25,
A-35
-1
<
<
{}
[]
•
.
(mx.erse),
2-3,o 8-9, 10-10, A-36
(less than), 2-25, A-35
(less than or equal to), 2-25, A-36
(list indicator),
11-4
(matrix indicator),
10-7
(minutes
notation),
2-23, A-38
(multiplication),
2-3, A-37
(negation),
1-23, 2-4, A-37
(not equal to), 2-25, A-35
(parentheses),
1-23
(pi), 2-4
(pixel mark), 8-15, 12-34
(pixel mark), 8-15, 12-34
*
()
[]
+
(pixel mark), 8-15, 12-34
_::> (plot type, box), 12-33
2m= (plot type, histogram),
12-32
_:>'_" (plot type, modified
box), 12-32
__
(plot type, normal probability),
12-33
^
(power), ~-3, A-36, A-37
10"( (power often),
2-#,A-37
×/
(root), 2-6, A-35
2
_(
-->
....
(seconds
(square),
notation),
2-23, A-38
2-3, A-36
(square root),
2-3, A-37
Store, 1-1]-_, A-28
(string indicator),
15-3
(subtraction),
2-3, A-38
-Aa+bl (rectangular
complex
1-12, 2-16, A-3
above graph style(N), 3-9
abs( (absolute value),
10-10,A-2
mode),
2-13, 2-19,
accuracy
information
computational
and graphing, B-10
graphing, 3-17
function limits and results, B-11
addition (+), 2-3, A-38
alpha cursor, 1-5
alpha key, 3
alpha-lock,
1-8
alternative
hypothesis,
amortization
hal( (amortization
A-3
13-7
balanee),
14-9,
calculating
schedules,
1]-t-9
fornmla, A-56
Elnt( (sum of interest),14-9,
A-12
EPrn( (sum of principal),
lJ.t-9, A-19
and (Boolean
operator),
2-26, A-2
angle(, 2-19, A-2
ANGLE menu, 2-23
angle modes, 1-11
animate graph style (_), 3-9
ANOVA( (one-way variance analysis),
13-25, A-2
fornmla, A-51
Ans (last answer),
1-18, A-2
APD TM (Automatic
Power Down__),
applications.
,fee examples,
applications
areeosine
(cos < 0, 2-3
aresine (sin<0,
2-3
aretangent
(tan "10, 2-3
1-2
augment(,
10-1J-t, 11-15,A-3
Automatic
Power Down _xt(AP[Y_), 1-2
automatic
regression
equation, 12-22
automatic
residual
list (RESID), 12-22
axes fommt, sequence graphing,
6-8
axes, displaying
(AxesOn, AxesOff),
3-14, A-3
AxesOff,
AxesOn,
3-14t, A-3
3-14t, A-3
Index-1
-Bbacking
- C (continued)
up calculator
19-10
memmTy, 19-4,
bal( (amortization
balance),
batteries,
1-2, B-2
below- graph style (6), 3-9
14-9, A-3
C
calculating,
14-8
fornmla, A-57
irr( (internal rate of return),
A-13
1-12,
2-16, A-3,
1-12, 2-16, 2-18, A-22
variable
coneatenation
(+), 15-6, A-38
confidenee
intervals,
13-8, 13-16
13-21
-
conj((conjugate),
2-18, A-4
Connected
(plotting mode), 1-11, A-4
contrast
(display),
1-3
convergence,
sequence graphing,
6-12
conversions
13-8
14-8,
Circle( (draw" circle), & l 1, A-4
Clear Entries, 1&4 , A-4
clearing
entries (Clear Entries),
18-4, A-4
all lists (ClrAIIkists),
1&4, A-4
draw3ng (ClrDraw),
8-4, A-4
home screen (ClrHome),
16-20, A-4
list (Clrkist),
12-20, A-4
table (ClrTable),
16-20, A-4
ClrAIIkists
(dear all lists), 1&4, A-4
ClrDraw (clear drawing), &4, A-4
ClrHome (clear home screen),
16-20,
A-4
Clrkist (elear list), 12-20, A-4
ClrTable (elear table), 16-20, A-4
coefficients
of determination
(r 2, R2),
12-23
Index-2
re^01),
(c/Y), 14-4, 14-14
npv( (net present value), 14-8, A-17
CATALOG, 15-2
CBL 2/CBL System, 16-21, 19-3, A-IO
CBR, 16-21, 19-3, A-IO
Check RAM (memol_y screen), 18-2
old-square cdf 0_2cdf0,13-31,
A-3
old-square pdf (z2pdf(), 13-31, A-4
eld-squm'e test (z2-Test),
13-22, A-4
colon separator
(:), 6, 16-5
combinations
(nCr), 2-21, A-16
modes (a+bl,
A-22
numbers,
-
CALCULATE metal, 3-25
Calculate output option, 13-6,
cash flow"
complex
compounding-periods-per-year
binomcdf(,
13-33, A-3
binompdf(,
13-33, A-3
Boolean logie, 2-26
box pixel mark ([]), 8-15, 12-34
Boxplot plot type (_),
12-33
busy indicator,
1-4
-
-
)Dec (to deeimal),
2-5, A-5
_DMS (to degree_minute_
seeonds),
2-24, A-7
_Eff (to effeetwe interest rate),
14-12, A-7
Equ_String( (equation-to-string
conversion),
15-7, A-8
_Frac (to fraction conversion),
2-5,
A-IO
kist_matr( (list-to-matrix
conversion),
10-14,
11-15, A-14
MatrHist((matrix-to-list conversion),
10-14, 11-16, A-15
)Nora (to nominal interest rate
conversion),
14-12, A-16
)Polar (to polar
A-19
eonversion),
2-19,
PH_x(, P)Ry( (polar-to-reetangular
conversion), 2-24, A-21
_Rect (to rectangular
conversion),
2-19, A-22
R_Pr(, R_Pe( (reetangular-to-polm"
conversion),
2-24, A-23
String)Equ(
(string-to-equation
conversion),
15-8, A-29
CoordOff, 3-14, A-5
CoordOn, 3-14, A-5
correlation
eoefficient
(r), 12-23,
to 12-27
12-25
cos((cosine),
2-3, A-5
cos'l((areeosine),
2-3, A-5
cosh(
(hyperbolic
cosine),
15-10, A-5
- D (continued)cosh'l(
(hyperbolic
A-5
- D (continued)
arceosine),
cosine (cos(), 2-3, A-5
cross pixel mark (+), 8-15,
cube (3), 2-6, A-35
cube root (3_(), 2-6, A-35
15-10,
12-34
CubicReg (cubic
A-5
regression),
12-26,
cubic regression
A-5
(CubicReg),
12-26,
eunmlative
sum (cumSumO,
10-15,
11-12, A-5
cumSum( (cumulative
sum), 10-15,
11-12, A-5
cursors, 1-5, 1-8
C/Y (compounding-periods-per-year
variable),
124-Y4,124-124
-
D-
Data input option, 13-6, 13-7
days between
dates (dbd0,
14-13, A-5,
A-58
dbd( (days between
A-58
dates),
14-13, A-5,
_Dec (to decimal conversion),
2-5, A-5
decimal mode (float or fixed), 1-10
decrement
and skip (DS<(), 16-14, A-7
definite integral, 2-7, 3-28, 4-8, 5-6
Degree angle mode, 1-11, 2-23, A-6
degrees
notation
(°), 2-3, A-3J4
DELETE FROM menu, 18-3
delete vm'iable contents
(DelVar),
16-15, A-6
DeWar (delete vm'iable contents),
16-15, A-6
DependAsk, 7-3, 7-5, A-6
DependAuto, 7-3, 7-5, A-6
derivative.
See numerical
derivative
det((determinant),
10-12, A-6
determinant
(det0, 10-12, A-6
DiagnostieOff,
12-23, A-6
DiagnostieOn,
12-23, A-6
diagnostics
display mode(r, r2, R2),
12-23
differentiation,
dimensioning
-
a list or matrix,
10-13, 11-11, A-6
dim((dimension),
10-12,
->dim( (assign dimension),
11-11, A-6
10-12,
11-11, A-6
10-13,
Disp (display), 16-18, A-6
DispGraph
(display graph),
display contrast,
1-3
display cursors, 1-5
16-19,
A-7
DispTable
(display table), 16-19, A- 7
DISTR (distributions
memO, 13-29
DISTR DRAW (distributions
drawing
menu), 13-35
distribution
functions
binomedf(, 13-33, A-3
binompdf(,
13-33, A-3
z2cdf(, 13-31, A-3
z2pdf(, 13-31, A-4
Fcdf(, 13-32, A-8
Fpdf(, 13-32, A- 9
geometcdf(,
13-34, A- I O
geometpdf(,
13-34, A-11
invNorm(, 13-30, A-12
normalcdf(,
13-30, A-1 7
normalpdf(,
13-29, A-17
poissoncdf(, 13-324, A-99
poissonpdf(,
13-33, A-19
tcdf(, 13-31, A-29
tpdf(, 13-30, A-29
distribution
shadh]g instructions
Shadex2(, 13-36, A-26
ShadeF(, 13-36, A-27
ShadeNorm(,
13-35, A-27
Shade_t(, 13-36, A-27
dhqsion (/), 2-3, A-37
[)MS (degrees/minutes/seconds
notation), 2-23, A-38
_DMS (to degreegminutes/seconds),
2-224, A- 7
entity"
dot graph style ('..), 3-9
dot pixel Inark (.), 8-15, 12-324
Dot (plotting
mode), 1-11, A-7
DrawF (draw- a function),
&9, A-7
2-8, 3-28, 4-8, 5-6
Index-3
- D (continued)drawing
- E (continued)
on a graph
circles (Circle(), 8-11
flmetions
and inverses (DrawF,
Drawlnv), 8-9
lines (Horizontal,
Line(, Vertical),
8-6, 8-7
line segments
(Line(), 8-5
pixels (PxI-Change,
Pxl-Off, Pxl-On,
pxI-Test), 8-16
points (Pt-Change, Pt-Off, Pt-On),
8-14
tangents
(Tangent), 8-8
text (Text), 8-12
using Pen, 8-13
Drawlnv (draw" inverse), 8-9, A-7
DRAW menu, 8-3
DRAW instructions,
8-3 - 8-16
[)raw- output option, 13-6 - 13--8
DRAW POINTS menu, 8-14
DRAW STO (draw" store menu), 8-17
dr/d0 operation
on a graph, 5-6
DS<( (decrement
and skip), 16-14, A-7
DuplicateName menu, 19-5
dx/dt operation
on a graph, 3-28, 4-8
dy/dx operation
on a graph, 3-28, 4-8,
5-6
-
E-
e (constant),
2-4
e^((exponential),
2-4, A- 7
E (exponent),
1-7, 1-10, A-7
edit keys table, 1-8
t.Eff( (to effective
A-7
Else, 16-10
End, 16-12,
rate),
14-12,
A-8
Eng (engineering
A-8
entry cm'sor,
interest
notation
mode),
1-10,
1-5
ENTRY (last entry key), 1-16
EOS TM (Equation Operating
System),
1-22
eqn (equation
variable),
2-8, 2-12
equal-to relational
test (=), 2-25, A-35
Equation
Operating
System (EOSTM),
1-22
Equation Solver, 2-8
equations
with nmltiple
Index-4
roots,
2-12
-
Equi_String( (equation-to-string
conversion),
15-7, A-8
errors
diagnosing
and correcting,
1-24
messages,
B-5
example _-applieations
m'ea between
cm_es, 17-11
m'eas of regular
17-16
n-sided
polygons,
box plots, 17-2
cobweb attractors,
17-8
fundamental
theorem
of calculus,
17-14
guess the coefficients,
17-9
inequalities,
17-5
mortgage
payments
17-18
parametric
equations:
ferris wheel
problem,
1 7-12
pieeewise
functions,
1 7-4
Sierpinski
triangle, 1 7- 7
solving a system of nonlinear
equations,
17-6
unit circle and trig curves, 17-10
examples_--Getting
Started
box w_th lid 9 to 16
defining a, 9
defining a table of values, 10
finding calculated
maxinmm,
16
setting the viewlng window, 12
tracing the graph, 13
zooming in on the graph, 15
zooming in on the table, 11
coin flip, 2-2
compound
interest, 14-3
drawing a tangent line, 8-2
financing a era', 14-2
forest and trees, 6-2
generating
a sequence,
11-2
graphing a circle, 3-2
mean height of a population,
13-2
path of a ball, J-t-2
pendulum
lengths and periods,
12-2
polar rose, 5-2
- E (continued)
exalnp]es_--Getting
Started
quadratic formula
(continued)
converting
to a fraction,
g
displaying
eomplex
results, 8
entering a calculation,
6
roots of a, 7-2
sendHlg variables,
19-2
solving a system of linear equations,
10-2
unit circle, 9-2
volume of a cylinder, 16-2
examples_-nliseellaneous
convergence,
6-12
daylight hours in Alaska, 12-28
calculating
outstanding
loan
balances,
l J-t-l O
predator-prey
model, 6-13
exponential
regression
(ExpReg),
12-26, A-8
expr( (string-to-expression
conversion),
15-7, A-8
ExpReg (exponential
regression),
12-26, A-8
expression,
1-6
converting
front string (expr(), 15- 7,
A-8
turning on and off (lllxprOn,
lllxprOff), 3-1].t , A-8
lllxprOff (expression
lllxprOn (expression
off), 3-1].t, A-8
on), 3-1].t, A-8
-
F-
ff(x)dx operation on a graph, 3-28
factorial (!), 2-21, A-3]._
fandly of eut_es, 3-16
Fcdf(, 13-32, A-8
Fill(, 10-13, A-8
FINANCE CALC menu, 14-5
FINANCE VARS menu, 1]-t-1]-t
financial functions
amortization schedules, 10.-9
cash flows, 14-8
days between dates, 14-13
interest rate conversions, 14-12
payment method, 14-13
time value of money (TVM), 14-6
- F (continued)
Fix (fJxed-deeimal
-
mode), 1-10, A-8
fixed-deeimal
mode (Fix), 1-10, A-8
Float (floating-decimal
mode), 1-10,
A-8
floating-decimal
A-8
mode
(Float),
1-10,
fMax( (function
maximum),
2-6, A-9
fMin( (function
ndnimum),
2-6, A-9
fnlnt( (function
integral),
2-7, A-9
FnOff (function off), 3-8, A-9
FnOn (function
on), 3-8, A-9
For(, 16-10, k-9
format settings, 3-13, 6-8
formulas
amortization,
A-56
ANOVA, A-51
cash flow, A-57
days between
dates, A-58
factorial, 2-21
interest rate conversions,
A-57
logistic regression,
A-50
sine regression,
A-50
time value of money, A-5].t
two-sample
T-Test, A-52
two-sample
t test, A-53
fPart( (fractional
part), 2-1& 10-11, A-9
Fpdf(, 13-32, A-9
)Frac (to fraction),
2-5, A-IO
free-moving
cursor, 3-17
frequency,
12-2].t
Full (full-screen
mode), 1-12, A-IO
full-screen
mode (Full), 1-12, A-IO
Func
(function
A-IO
function,
graphing
definition
function graphing,
accuracy,
3-17
mode),
1-11,
of, 1-7
3-1 to 3-28
CALC (calculate
menu), 3-25
defining and displaying,
3-3
defining in the Y= editor, 3-5
defining on the home screen, in a
program,
3-6
deselecting,
3- 7
displaying,
3-3, 3-11, 3-15
evaluating,
3- 6
family of cmxres, 3-16
format settings, 3-13
Index-5
- F (continued)
Ftmction
graphing
-
- G (continued)
(continued)
graph
free-moving
cursor, 3-17
graph styles, 3-9
maximunl
of (fMax0, 2-6, A-9
minimmn of (fMin0, 2-6, A-9
modes, 1-11, 3-4,A-10
moving the cursor to a value, 3-19
overlaying functions
on a graph,
3-16
panning,
3-19
pausing or stopping a graph, 3-15
Quick Zoom, 3-19
selecting, 3-7, 3-8, A- 9
shading, 3-10
Snmrt Graph, 3-15
tracing, 3-18
window variables,
3-11, 3-12
Y= editor, 3-5
_ewing window,
3-11
AX and AY window variables,
3-12
ZOOM menu, 3-20
ZOOM MEMORY menu, 3-23
function integral (fnlnt0, 2-7, A-9
functions
and instructions
table, A-2 to
A-2
future vahle, 14-5, 14-7, l J-t-l J-t
present value, 14-5, 14-7, 1J-t-l}-t
FV (future-value
vm'iable), 1J4-J4, 1J4-1J4
-G
gcd( (greatest
A-IO
common
-
divisor),
2-15,
GDB (graph database),
8-19
geometcdf(,
13-34, A- I O
geometpdf(,
13-34, A- I O
Get( (get data from CBL 2/CBL or
CBR), 16-21, A-IO
GetCalc( (get data from TI-83), 16-21,
A-IO
getKey, 16-20, A-IO
Getting Started, 1 to 18. See also
examples,
Getting Started
Goto, 16-13, A-IO
database
(GDB), 8-19
graphing modes, 1-11
graphing-order
modes, 1-12
GraphStyle(,
16-15, A-11
graph styles, 3-9
graph-table
split-screen
mode
1-12, 9-5, A-11
(G-T),
greater than (>), 2-25, A-35
greater than or equal to (>), 2-25, A-35
greatest common
divisor (gcd0, 2-15,
A-IO
greatest
integer
A-12
(intO, 2-14,
GridOff, 3-14, A-11
GridOn, 3-14, A-11
G-T (graph-table
split-screen
1-12, 9-5, A-11
-
H
10-11,
mode),
-
Histogram plot type (2m_), 12-32
home screen, l-J4
Horiz (horizontal
split-screen
mode),
1-12, 9-4, A-11
hyperbolic
functions,
15-10
Horizontal
(draw- line), &6 - 8-7, A-11
hypothesis tests, 13-10 - 13"-15
i (complex
number constant),
2-17
1%(annual interest rate variable),
14-4,
14-14
identity(, 10-13, A-11
if instructions
If, 16-9, A-11
If-Then, 16-9, A-11
If-Then-Else, 16-10, A-11
imag( (imaginmTy" pm't ), 2-18,
imaginary
part (imagO, 2-18,
implied nmltiplieation,
1-23
A-11
A-11
increment
and skip (IS>(), 16-13, A-13
IndpntAsk, 7-3, A-12
IndpntAuto, 7-3, A-12
independent
variable,
7-3, A-12
inferential
Index-6
-
stat editors,
13-6
- I (continued)
-K-
-
inferential
statistics. See also stat tests;
confidence
intervals
alternative
hypotheses,
bypassing
calculating
13-8
editors, 13-8
test results (Calculate),
13- 7
keyboard
layout, 2, 3
ninth operations,
key-code
2-3
diagrmn,
16-20
-
L-
confidence
interval calculations,
13-8, 13-16 - 13-21
data input or stats input, 13-7
L (user-created
list nmne
11-16, A-13
LabelOff, 3-14, A-13
entering argument
values, 13- 7
graphing test results (Draw), 13-8
input descriptions
table, 13-26
pooled option, 13-8
STAT TESTS menu, 13-9
test and interval output variables,
13-28
LabelOn,
labels
Input, 16-16, 16-17, A-12
insert cursor, 1-5
inString( (in string), 15-7, A-12
instruction,
definition
of, 1-7
int( (greatest
integer), 2-1#, 10-11,
A-12
Elnt( (sum of interest),
1#-9, A-12
integer part (iPart0, 2-1#, 10-11, A-12
integral. See nmnerical
integral
interest rate conversions
eMeulating,
14-12
_Eff( (compute
effective
rate), 14-12,
formula, A-57
_Nom( (compute
rate), 1#-12,
interest
A-7
nondnal
A-16
interest
internal rate of return (irr(), 1#-8, A-13
intersect
operation
on a graph, 3-27
inverse (-1), 2-3, 8-9, 10-10, A-36
inverse eunmlative
normal distribution
(invNorm0,
13-30, A-12
inverse trig functions,
2-3
invNorm( (inverse eunmlative
normal
distribution),
13-30, A-12
iPart( (integer part), 2-14, 10-11, A-12
irr( (internal rate of return), 14-8, A-13
I$>( (increment
and skip), 16-13, A-13
symbol),
3-14, A-13
graph, 3-14, A-13
program,
16-13, A-13
Last Entry, 1-16
Lbl (label), 16-13, A-13
Icm( (least common
multiple),
A-13
least
common
A-13
nmltiple
(Icm(),
2-15,
2-15,
length( of string, 15-8, A-13
less than (<), 2-25, A-35
less than or equal to (<), 2-25, A-36
line graph style C'), 3-9
Line( (draw line), 8-5, A-13
line segments,
drawing, &5
lines, drawing, 8-6, & 7
linking
receMng
items, 19-5
to a CBL 2/CBL System or CBR, 19-3
to a PC or Macintosh,
19-3
to a TI-82, 19-3, 19-8
transndtting
items, 19- 6
two TI-83 units, 19-3
LINK RECEIVE menu, 19-5
LINK SEND menu, 19-4
kinReg(a+bx) (linear
12-26, A-14
LinReg(ax+b)
(linear
12-25, A-14
regression),
regression),
LinRegTTest
(linear regression
13-2#, A-14
AList(, 11-12, A-14
LIST MATH menu, 11-17
t test),
List_matr( (lists-to-matrix
conversion),
10-14, 11-15, A-14
LIST NAMES menu, 11-6
LIST OPS menu, 11-10
Index-7
- L (continued)
-
- M (continued)
lists, 11-1 to 11-18
matriees,
aeeessing
an element, 11-5
attaehing fornmlas,
11-7, 12-14
clearing all elements,
12-12, 12-20
eopying, 11-5
creating, 11-3, 12-12
deleting from memory, 11-5, 18-3
detaching
fommlas,
11-8, 12-16
dimension,
11-4, 11-11
entering list names, 11-6, 12-11
indicator ({ }), 11-4.
naming lists, 11-3
storing and displaJAng, 11-4.
transmitting
to and from TI-82, 19-4
using in expressions,
11-9
using to graph a family of curves,
3-16, 11-5
using to select data points from a
plot, 11-13
using ,_th math functions,
11-9
using _th ninth operations,
2-3
In(, 2-4, A-14
LnReg (logarithmic
regression),
12-26,
A-14
log(, 2-4, A-14
logic (Boolean)
operators,
2-26
Logistic (regression),
12-27, A-15
logistic regression
fornmla, A-50
-
MATH CPX (eomplex
MATH menu, 2-5
M
-
menu),
2-18
MATH NUM (number menu), 2-13
math operations,
keyboard,
2-3
MATH PRB (probability
menu), 2-20
MatrHist( (nmtrix-to-list
conversion),
10-14, 11-16, A-15
matrices,
10-1 to 10-16
accessing
elements,
10-8
copying, 10-8
defined, 10-3
deleting from memory, 10-4
dimensions,
10-3, 10-12, 10-13
displaying
a nmtrix, 10-8
displaying
matrix elements,
10-4
editing matrix elements,
10-6
Index-8
-
(eontinued)
indicator
([ ]), 10-7
inverse (-1), 10-10
math functions,
10-9 to 10-11
matrix math functions
(det(, T, dim(,
Fill(, identity(, randM(, augment(,
MatrHist(, List_matr(, cumSumO,
10-12 to 10-16
reDreneing
in expressions,
10- 7
relational
operations,
10-11
row operations(ref(,
rref(, rowSwap(,
row+(, *row(, *row+(),
10-15
selecting, 10-3
xqewing, 10-5
MATRX EDIT menu, 10-3
MATRX MATH menu, 10-12
MATRX NAMES menu, 10-7
max((maximum),
2-15, 11-17, A-15
maximum
of a funetion (fMax0, 2-6,
A-9
maximum
operation
on a graph, 3-27
mean(, 11-17, A-15
median(, 11-17, A-15
Meal-Meal (median-median),
12-25,
A-15
inenlolTy"
backing up, 19-10
checking
available,
18-2
clearing all list elements from,
elem'tng entries from, 18-4
deleting items from, 18-3
insufficient
during transmission,
19-5
18-4
resetting
defaults, 18-6
resetting
memory, 18-5
MEMORY menu, 18-2
Menu( (define menu),
menus, 4, 1-19
16-14,
A-15
defining (Menu(), 16-14, A-15
nmp, A-39
scrolling, 1-19
min( (minhmm0,
2-15, 11-17, A-16
minimum operation
on a graph, 3-27
minimum of a function (fMin0, 2-6,
minutes notation
('), 2-23, A-38
ModBoxplot
plot type (4>.), 12-32
A-9
- M (continued)
modified
-
box [)lot type (o..),
- N (continued)
12-32
mode settings, 1-9
a+bl (complex
rectangular),
2-16, A-3
re^Of (complex
A-22
polar),
1-12,
1-12, 2-16,
Connected
(ploning),
1-11, A-4
Degree (angle), 1-11, 2-24, A-6
Dot (plotting),
1-11, A-7
Eng (notation), 1-10, A-8
Fix (decimal),
1-10, A-8
Float (decimal),
1-10, A-8
Full (screen),
1-12, A-IO
Func (graphing),
1-11, A-IO
G-T (screen),
1-12, A-11
Horiz (screen),
1-12, A-11
Normal (notation), 1-10, A-16
Par/Param (graphing),
1-11, A-18
Pol/Polar (graphing),
1-11, A-19
Radian (angle), 1-11, 2-24, A-21
Real, 1-12, A-22
Sci (notation), 1-10, A-25
Seq (graphing),
1-11, A-26
Sequential
(graphing
order),
A-26
1-12,
Simul (graphing
order), 1-12, A-27
modified box [)lot type (o..), 12-32
multiple entries on a line, 1-6
multiplication
multiplieative
N
-
N (number
of payment periods
variable),
14-4, 14-14
nCr (number of combinations),
A-16
nDeriv(
(numerical
A-16
negation
(-), 1-23,
_Nom( (to nominal
A-16
derivative),
(normal
distribution
probability),
13-30, A-17
normalpdf( (probability
density
function),
13-29, A-17
NormProbPIot
plot type ([__), 12-33
not( (Boolean operator),
2-26, A-17
not equal to (_), 2-25, A-35
nPr (pernmtations),
2-21, A-17
npv( (net present value), 14-8, A-17
numerical
derivative,
2- 7, 3-28, 4-8,
5-6
numerical
integral,
2- 7, 3-28
-
O-
one-proportion
z confidence
inte_ral
(1-PropZInt),
13-20, A-20
one-proportion
z test (1-PropZTest),
13-14, A-20
one-sample
t confidence
inte_al
(Tlnterval),
13-17, A-30
one-variable
statistics
(1-Var Stats),
12-25, A-31
or (Boolean)
operator,
2-26, A-17
order of evaluating
equations,
1-22
Output(, 9-6, 16-19, A-18
panning,
3-19
Par/Param (pm'ametrie
graphing
mode), 1-9, 1-11, A-18
parametric
equations,
4-5
parametric
graphing
CA/C (calculate
operations
on a
(*), 2-3, A-37
inverse, 2-3
-
normalcdf(
-
2-21,
2-7,
2-4, A-37
interest rate),
nonrecursive
sequences,
6-5
normal distribution
probability
(normalcdf(),
13-30, A-17
Normal notation
mode, 1-10, A-16
normal probability
plot type (__),
12-33
14-12,
graph), 4-8
defi_ling and editing, 4-4
free-moving
cursor, 4- 7
graph format, 4-6
graph styles, 4-4
moving the cursor to a value, 4-8
selecting and deseleeting,
4-5
setting parametric
mode, 4-4
tracing, 4- 7
window variables,
4-5
Y= editor, 4-4
zoom operations,
4-8
parentheses,
1-23
path (_.)) graph style, 3-9
Index-9
- P (continued)
-
- P (continued)
-
Pause, 16-12, A-18
pooled
pausing a graph,
Pen, 8-13
power (^), 2-3, A-36, A-37
power of ten (10^0, 2-& A-37
present vahle, 1].t-5, 1].b7, 14-1].t
pernmtations
phase plots,
3-15
(nPr), 2-21, A-17
6-13
Pi (_), 2-4
Pic (pictures),
8-17,
pictures
(Pic), 8-17,
pixel, 8-16
9-6
14-4,
Pmt_Bgn (payment
beghming
variable),
14-13, A-19
Pmt_End (payment
end variable),
14-13,A-19
poissoncdf(,
13-324, A-19
poissonpdf(,
13-33, A-19
Pol/Polar (polar graphing mode), 1-9,
1-11,A-19
polar equations,
5-4
polar form, complex numbers,
2-17
*Polar (to polar), 2-19, A-19
polar graphing
CALC (calculate
operations
on a
5-3
5-6
graph format, 5-5
graph styles, 5-3
moving the cursor to a value, 5-6
selecting and deselecting,
5-4,
mode (Pol/Polar),
1-9, 1-11, 5-3,
A-19
tracing, 5-6
window variables,
5-]-_
Y= editor, 5-3
ZOOM operations,
5-6
PolarG¢
(polm" graphing coordinates),
3-13, A-19
Index-lO
13-8
PRGM EDIT menu, 16-7
PRGM EXEC menu, 16-7
pixels in Horiz/G-T modes, 8-16,
Plot4 (, 12-34, A-18
Plot2(, 12-34, A-18
Plot3(, 12-34, A-18
PlotsOff, 12-35, A-18
PlotsOn,
12-35, A-18
plotting modes, 1-11
plotting stat data, 12-31
PMT (payment amount variable),
14-14
free-moxqngcursor,
13-6,
prexqous entlT (Last Entry), 1-16
PRGM CTL (program
control menu),
16-8
8-18
8-18
graph), 5-6
defining and displaying,
equations,
5-4
option,
P RGM I/O (Input/Output
menu), 16-16
prgm (program
name), 16-15, A-19
PRGM NEW menu, 16-0.
ZPrn( (sum of principal),
12.t-9, A-19
probability,
2-20
probability
density" function
(normalpdfO,
13-29, A-17
prod((product),
11-18, A-19
programming
copying and renaming,
16-7
creating new-, 16J._
defined, 16J.t
deleting, 16J-_
deleting command
lines, 16-6
editing, 16-6
entering command
lines, 16-5
executing,
16-5
instructions,
16-9 - 16-21
inserting
command
lines, 16-6
(prgm), 16-15,
renaming, 16- 7
name
A-19
stopping, 16-5
subroutines,
16-22
Prompt, 16-18, A-19
1-PropZlnt
(one-proportion
z confidence
interval),
A-20
13-20,
1-PropZTest
(one-proportion
13-1].t, A-20
2-PropZlnt
(two-proportion
z confidence
interval),
A-20
z test),
2-PropZTest
(two-proportion
13-15, A-20
z test),
13-21,
P)'Rx(, P)'Ry( (polar-to-rectangular
conversions),
2-24, A-21
Pt-Change(, 8-15, A-20
Pt-Off(, 8-15, A-20
Pt-On(, 8-10, A-20
- P (continued)
PV (present value
114-114
p-value, 13-28
PwrReg
(power
A-20
-
- R (continued)
variable),
lJ4-J4,
regression),
12-27,
Pxl-Change(,
8-16, A- 21
PxI-Off(, 8-16, A-21
PxI-On(, 8-16, A-21
pxI-Test(, 8-16, A-21
PlY (nunlber-of-payment-periods-peryear variable),
l J4-J4, l J4-1J4
QuadReg (quadratic
regression),
12-25, A-21
QuartReg (quartic regression),
12-26
Quick Zoom, 3-19, A-21
-
R-
r (radian notation),
2-2/4, A-3J4
r (correlation
coefficient),
12-23
r2, R 2 (coefficients
of determination),
12-23
Radian angle mode, 1-11, 2-2J4, A-21
radian notation
(r), 2-24, A-34
rand (random number),
2-20, A-21
randBin( @andom binomial),
2-22,
A-21
randlnt( (random integer), 2-22, A-22
randM( (random
matrix), 10-13, A-22
randNorm(
(random Normal),
2-22,
A-22
random
seed, 2-20,
2-22
RegEQ (regression
equation
12-22, 12-29
regression
model
automatic
regression
12-22
automatic
12-22
vm'iable),
equation,
residual
list feature,
diagnostics
display
models, 12-25
mode,
12-23
relational
operations,
2-25, 10-11
Repeat, 16-11, A-23
RESET menu, 18-5
resetting
defaults, 18-6
memmTy', 5, 18-5
resklual list (RESID), 12-22
Return, 16-15, A-23
root (x?), 2-6, A-35
root of a function, 3-26
round(, 2-13, 10-10, A-23
row+(, 10-16, A-23
*row(, 10-16, A-23
*row+(, 10-16, A-23
rowSwap(,
10-16, A-23
RH=r(, I_P0( (reetangular-to-polm"
conversions),
2-2J4, A-23
rref( (reduced-row-echelon
form),
10-15, A-23
-S
2-SampFTest
13-23,
-
(two-sample
A-2J4
g-Test),
RecallPic, 8-18, A-22
_Rect (to rectangulm'),
2-19, A-22
rectangular
form, complex numbers,
2-17
2-SampTInt
(two-sample
t confidence
illtel_ral), 13-19, A-24
2-SampTTest
(two-sample
t test),
13-13, A-2J4, A-25
2-SampZlnt
(two-sample
z confidence
inte_5,al), 13-18, A-25
2-SampZTest (two-sample
z test),
13-12, A-25
Scatter plot type (L_), 12-31
Sci (scientific
notation mode), 1-10,
A-25
RectGC (rectangular
graphing
coordinates),
3-13, A-22
recursive
sequences,
6-6
ref( (row-echelon
form), 10-15, A-22
scientific notation,
1 -7,1-10
screen modes, 1-12
second cursor (2nd), 1-5
second key (2nd), 3
RCL (recall), 1-15, 11-9
re^Oi (polm" complex
mode),
2-16, A-22
Real mode, 1-12, A-22
1-12,
real( (real part), 2-18, A-22
RecalIGDB, 8-20, A-22
Index-
11
- S (continued)
seconds
DMS notation
-
('),
- S (continued)
program,
3-8
functions
in tile Y= editor,
items
from
stat plots
nlenus,
SetUpEditor, 12-21, A-26
shade above (7) graph style, 3-9
shade below- (6) graph style, 3-10
2-23
Select(, 11-12, A-25
selecting
data points from a plot, 11-13
functions from the home screen
or a
3-7
J4
from tile Y= editor,
3-7
Send( (send to (BL 2/('BL or CBR),
16-21, A-26
sending. See trtmsmitting
Seq (sequence
graphing mode), 1-11,
A-26
seq((sequence),
11-12, A-26
sequence graphing
axes fommt, 6-8
CALC (calculate
memO, 6-10
defining and displaying,
6-3
evaluati]lg,
6-10
free-mo_ng
cursor, 6-9
graph fommt, 6-8
graph styles, 6-J4
moving the cursor to a value, 6-9
nonreeursive
sequences,
6-5
phase plots, 6-13
recursive sequences,
6-6
setting sequence
mode, 6-3
selecting and deseleeting,
TI-83 versus TI-82 table,
tracing, 6-9
web plots, 6-11
window variables,
6- 7
Y= editor, 6-J4
6-4
6-15
Index-12
from a program,
7-3
ShadeF(,
13-36, A-27
ShadeNorm(,
13-35, A-27
Shade_t(,
13-36, A-27
shading graph areas, 3-10, 8-10
Simul (simultaneous
graphing order
mode), 1-12, A-27
sin((sine),
2-3, A-27
sin'1((m-csine),
2-3, A-27
sine (sin(), 2-3, A-27
sine regression
formula, A-50
sinh( (hyperbolic
sine), 15-10, A-27
sinh'l( (hyperbolic
m'csine), 15-10,
A-27
SinReg
(sinusoMal
A-28
3-10
regression),
12-27,
Smart Graph, 3-15
solve(, 2-12, A-28
Solver, 2-8
solving for variables
in tile equation
solver, 2-10, 2-11
SortA( (sort ascending),
11-10, 12-20,
A-28
SortD(
(sort
A-28
descending),
11-10,
12-20,
mode, 9-5
mode, 9-#
setting, 9-3, 9-6
split-screen
values, 8-12, 8-16,
square (2), 2-3, A-36
square root (_(), 2-3, A-37
STAT CALC menu, 12-2J-t
STAT KDIT menu, 12-20
stat list editor
attaching formulas
12-1J.t
modes from a program,
1-9
split-screen
modes, 9-3
split-screen
modes from a program,
9-6
tables
Shade(, 8-9, A-26
Shadexi(,
13-36, A-26
split-screen
modes
G-T (graph-table)
Horiz (horizontal)
ZOOM (zoom menu), 6-10
Sequential
(graphing
order mode),
1-12, A-26
service infornmtion,
B-12
setting
display contrast,
1-3
graph styles, 3-9
graph styles from a program,
modes, 1-9
-
9-6
to list names,
clearing elements
from lists, 12-12
creating list names, 12-12
detaching
fornmlas
from list names,
12-16
displaying,
12-10
edit-elements
context,
12-18
- S (continued)
star list editor
-
- S (continued)
(eonthmed)
statistieal
editing elements of fornmlagenerated
lists, 12-16
editing list elements,
12-13
enter-names
context,
12-19
entering list names, 12-11
formula-generated
list names, 12-15
remoxqng lists, 12-12
restoring list names L1-L& 12-12,
12-21
switching
eontexts,
12-17
x_ew-elements
eontext,
12-18
x_ew-names
eontext,
12-19
STAT PLOTS metal, 12-34
stat tests and confidence
intel_rals
ANOVA( (one-way analysis of
variance),
13-25
x2-Test (ehi-squm'e test), 13-22
LinRegTTest (linear regression
t test), 13-24
1-PropZlnt
(one-proportion
z confidence
interval),
13-20
1-PropZTest (one-proportion
z test),
13-14
2-PropZlnt (two-proportion
z eonfidence
interval),
13-21
2-PropZTest
(two-proportion
z test),
13-15
2-SampFTest
13-23
(two-sample
2-SampTInt (two-sample
t eonfidenee
interval),
2-SampTTest
13-13
F-Test),
13-19
(two-sample
t test),
2-SampZlnt (two-sample
z eonfidenee
interval),
2-SampZTest (two-sample
13-12
13-18
z test),
Tlnterval (one-sample
t eonfidenee
inte_x_al), 13-17
T-Test (one-sample
t test), 13-11
Zlnterval (one-sample
z eonfidenee
inte_x_al), 13-16
Z-Test (one-sample
z test), 13-10
Stats input option, 13-6, 13-7
STAT TESTS menu, 13-9
statistieal
distribution
functions.
See
distribution
functions
plotting,
-
12-31
Boxplot (regular box plot), 12-33
defining, 12-34
from a program,
12-37
Histogram,
12-32
ModBoxplot
(modified box plot),
12-32
NormProbPIot
(normal probability
plot), 12-33
Scatter, 12-31
tracing, 12-36
turning on/off stat plots, 3-7, 12-35
x_e,slng window,
12-36
xyLine, 12-31
statistieal
vm'iables table, 12-29
stdDev( (standard
dexdation), 11-18,
A-28
Stop, 16-15, A-28
Store (-)), 1-14, A-28
StoreGDB, 8-19, A-28
StorePic, 8-17, A-29
storing
graph databases
(GDBs), 8-19
graph pictures,
8-17
vmiable values, 1-14
String_Equ(
(string-to-equation
conversions),
15-8, A-29
strings, 15-3 to 15-9
concatenation
(÷), 15-6, A-38
converting,
15-7, 15-8
defined, 15-3
displaying
contents,
15-5
entering,
functions
15-3
in CATALOG, 15-6
indicator
("), 15-3
length (length(),
15-8, A-13
storing, 15-5
vmiables,
15-4
student-t
distribution
probability
(tcdf0, 13-31, A-29
probability
density function
(tpdf0,
13-30, A-30
sub((substring),
15-9, A-29
subroutines,
16-15, 16-22
subtraction
(-), 2-3, A-38
sum((sumnmtion),
11-18, A-29
system variables, A-49
Index-13
-T-
- T (continued)
TABLE SETUP screen, 7-3
tables, 7-1 to 7-6
description,
7-5
variables, 7-3 to 7-5
time value
tangent (tan(), 2-3, A-29
Tangent( (draw line), 8-8, A-29
tangent lines, drawi_lg, 8-8
tan h( (hyperbolic
tangent),
15-10, A-29
tanh'l(
(hyperbolic
aretangent),
15-10,
A-29
ATbl (table step variable),
7-3
TblStart (table start variable),
7-3
tcdf( (student-t
distribution
probability),
13-31, A-29
teelmieal
support, B-12
TEST (relational
menu), 2-25
TEST LOGIC (Boolean menu), 2-26
Text(
instruction,
8-12, 9-6, A-29
placing on a graph, 8-12
Then, 16-9, A-11
thick (_.) graph style, 3-9
TI-82
link differences,
19-9
transmitting
to/from, 19-2-t, 19-8,
19-9
TI-83
16-20
Link. See linking
menu map, A-39
TI-GRAPH LINK, 19-3
Time axes format, 6-8, A-30
time value of money (TVM)
calculating,
12-t-6
C/Y vm'iable (nmnber
of
compounding
periods
12`1-12`1
formulas, A-54
FV vm'iable (furore
I% variable (annual
12.t-12.t
Index-14
value),
interest
(eontinued)
N vm'iable (number of payment
periods),
14-12-t
PMT vm'iable (payment
amount),
14-14
tan((tangent),
2-3, A-29
tan'l((aretangent),
2-3, A-29
features, 17, 18
keyboard, 2, 3
key code diagram,
of money
-
PV variable (present value), 12`1-12`1
PlY vm'iable (number of payment
periods per yem'), 12`1-12-1
tvm_FV (future value), 12-1-7,A-31
tyro_l% (interest
rate), 14-7, A-31
tvm_N (# payment periods),
12-1-7,
A-31
tvm_Pmt (payment
A-31
amount),
14-6,
tvm_PV (present Vahle), 12`1
- 7, A-31
TVM Solver, 12-1-2-1
vm'iables,
12-1-14
Tlnterval (one-sample
t eonfidenee
interval),
13-17, A-30
tpdf( (student-t
distribution
probability
density funetion),
13-30, A-30
TRACE
eursor, 3-18
entering numbers
during, 3-19,
5-6, 6-9
expression
display, 3-12`1,3-18
Trace instruction
in a program,
A-30
4-8,
3-19,
transmitting
error conditions,
19-6
from a TI-82 to a TI-83, 19-9
items to another unit, 19-6
lists to a TI-82, 19-2-1,19-8
stopping, 19- 6
to an additional
TI-83, 19-7
T (transpose
matrix), 10-12, A-34
transpose
matrix (T), 10-12, A-34
trigonometric
functions,
2-3
T-Test (one-sample
t test), 13-11,
per year),
12`1-12`1
rate),
A-30
- T (continued)
-
complex,
tvm_PV (present value), 114-7, A-31
two-proportion
z confidence
inte_a_al
(2-PropZlnt),
13-21, A-20
two-proportion
z test (2-PropZTest),
13-15, A-20
two-sample
F-Test formula, A-52
two-sample
t test formula, A-53
two-vm'iable
statistics
(2-Var Stats),
12-25, A-31
uv/uvAxes
uw/uwAxes
-
6-3
(axes format),
(axes format),
6-8, A-31
6-8, A-31
-V-
function,
7-5
vm'ianee
of a list (variance(),
A-31
VARS menu
11-18,
GDB, 1-21
Picture, 1-21
Statistics, 1-21
String, 1-21
Table, 1-21
Window, 1-21
Zoom, 1-21
Vertical (draw line), &6, A-31
_dewing window, 3-11
(axes
format),
6-3
6-8
W
1-Var Stats (one-variable
12-25, A-31
statistics),
2-Var Stats (two-variable
12-25, A-31
statistics),
value operation
1-11t
real, 1-13
recalling values, 1-15
solver editor, 2-9
statistical,
12-29
string, 15-].L 15-5
test aim inte_xral output, 13-28
types, 1-13
user and system, 1-13, A J-t9
VARS and Y-VARS menus, 1-21
variance(
(variance
of a list), 11-18,
A-31
vw/uvAxes
v sequence
values,
graph databases,
1-13
graph pictures,
1-13
independent/dependent,
list, 1-13, 11-3
matrix, 1-13, 10-3
points, 8-1J4
stat plots, 3-7, 12-35
tvm_FV (future vane),
lj4 - 7, A-31
tyro_l% (interest
rate), 114-7, A-31
tvm_N (# payment
periods),
114-7, A-31
tvm_Pmt
(payment
amount),
114-6,
A-31
u sequence function,
user variables, A-49
1-13
displaying
and storing
equation solver, 2-10
functions,
3- 7
grid, 3-1J4
labels, 3-1J4
pixels, 8-16
U
-
vmialAes
turlling Ol1and off
axes, 3-1J4
calculator,
1-2
coordinates,
3-14
expressions,
3-1J4
-
- V (continued)
on a graph,
3-25
w sequence
function,
warranty
inforlnation,
6-3
B-13
Web (axes format),
web plots, sequence
While, 16-11,A-32
window variables
6-8, A-31
graphing,
6-11
function graphing, 3-11
parametric
graphing, ]4-5
polar graphNg,
5-]4
sequence graphing,
6- 7
Index-15
-X-
- Z (continued)
-
XFact zoom factor, 3-2J4
x-intercept
of a root, 3-26
ZoomSto (store zoom _lndow),
A-33
xor (Boolean)
exclusive
2-26, A-32
x m root (_), 2-6
ZPrevious (use previous
3-23, A-33
or operator,
Z-Test (one-sample
ZTrig (trigonometric
A-3J4
-y-
3-2J4
function graphing, 3-5
parametric
graphing, J4-J4
polar graphing, 5-3
sequence graphing,
624
Y-VARS menu
Function, 1-21
Parametric, 1-21
Polar, 1-21
On/Off, 1-21
AY window variable,
3-12
-Z-
ZBox, 3-20, A-32
ZDecimal, 3-21, A-32
zero operation
on a graph, 3-26
Zlnteger, 3-22, A-32
Zlnterval (one-sample
z confidence
intm_al),
13-16, A-32
zoom, 3-20 to 3-214
cursor, 3-20
factors, 3-2J4
function graphing, 3-20
parametric
graphing, J4-8
polar graphing, 5-6
sequence graphing,
6-10
ZoomFit (zoom to fit function),
A-33
3-22,
Zoom In (zoom in), 3-21, A-32
ZOOM menu, 3-20
ZOOM MEMORY menu, 3-23
Zoom Out (zoom out), 3-21, A-32
ZoomRcl (recall stored window),
3-23,
A-33
ZoomStat
Index-16
(statistics
zoom),
window),
ZSquare (set square pixels), 3-21, A-33
ZStandard (use standard
window),
3-22, A-33
xyLine ([__) plot type, 12-31
AX window variable, 3-12
YFact zoom factor,
Y= editor
3-23,
3-22, A-33
z test), 13-10, A-3]-_
window), 3-22,
_
T1=83
TEXAS INSTRUMENTS
J
STAT
PLOT
TBLSET
A-LOCK
FORMAT
QUiT
INS
LiNK
LiST
CALC
TEST
A
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E{
DRAW
FINANCE
D
SIN
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COS
I
EE
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{
K
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-1
C
DISTR
F
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-1
TABLE
G
1T
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}
L
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IvI
e x
S
L4
T
L5
U
L6
V
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W
RCL
X
L1
Y
L2
Z
L3
®
ME[V]
f_
i
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ANS
?
OFF
CATALOG _
ENTRY
SOLVE
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