TEXAS INSTRUMENTS TI 84 PLUS User Manual

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TI-84 Plus

TI-84 Plus Silver Edition

Guidebook

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iii

Chapter 1:

Chapter 1:Chapter 1: Operating the TI-84 Plus Silver Edition

Operating the TI-84 Plus Silver Edition

Operating the TI-84 Plus Silver EditionOperating the TI-84 Plus Silver Edition

Documentation Conventions

Documentation ConventionsDocumentation Conventions

In the body of this guidebook, TI-84 Plus refers to the TI-84 Plus Silver Edition. Sometimes, as in Chapter 19, the full name TI-84 Plus Silver Edition is used to distinguish it from the TI-84 Plus.

All the instructions and examples in this guidebook also work for the TI-84 Plus. All the functions of the TI-84 Plus Silver Edition and the TI-84 Plus are the same. The two graphing calculators differ only in available RAM memory, interchangeable faceplates, and Flash application ROM memory.

TI-84 Plus Keyboard

TI-84 Plus KeyboardTI-84 Plus Keyboard

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

Keyboard Zones

Keyboard ZonesKeyboard Zones

Graphing — Graphing keys access the interactive graphing features. Editing — Editing keys allow you to edit expressions and values. Advanced — Advanced function keys display menus that access the advanced

functions.

Chapter 1: Operating the TI-84 Plus Silver Edition 1

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

calculator.

TI-84 Plus

TI-84 Plus TI-84 Plus

raphing Keys

Editing Keys

Advanced Function Keys

Scientific Calculator Keys

Chapter 1: Operating the TI-84 Plus Silver Edition 2

Using the Color

Using the Color....Coded Keyboard

Using the ColorUsing the Color

Coded Keyboard

Coded KeyboardCoded Keyboard

The keys on the TI-84 Plus are color-coded to help you easily locate the key you need. The light colored keys are the number keys. The light gray keys along the right side of the

keyboard are the common math functions. The light gray keys across the top set up and display graphs. The Œ key with the purple lettering provides access to applications such as the Inequality Graphing application.

The primary function of each key is printed on the keys. For example, when you press , the

Using the

Using the y and

Using the Using the

MATH menu is displayed.

and ƒ Keys

and and

Key s

Key s Key s

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

TEST menu is displayed. This guidebook describes this keystroke combination

as y:. The alpha function of each key is printed in green above the key. When you press the

green ƒ key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press ƒ and then , the letter

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

Chapter 1: Operating the TI-84 Plus Silver Edition 3

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

ƒ key

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

Turning On and T urning Off the TI-84 Plus

Turning On and T urning Off the TI-84 PlusTurning On and T urning Off the TI-84 Plus

Turning On the Graphing Calculator

Turning On the Graphing CalculatorTurning On the Graphing Calculator

To turn on the TI-84 Plus, press É.

• If you previously had turned off the graphing calcula to r by pr essing yM, the TI-84 Plus displays the home screen as it was when you last used it and clears any error.

Chapter 1: Operating the TI-84 Plus Silver Edition 4

• If Automatic Power Down™ (APD™) had previously turned off the graphing calculator, the TI-84 Plus wi ll return exactly as you left it, including the display, cursor, and any error.

• If the TI-84 Plus is turned off and connected to another graphing calculator or personal computer, any communication activity will “wake up” the TI-84 Plus.

To prolong the life of the batteries, APD turns off the TI-84 Plus automatically after about five minutes without any activity .

Turning Off the Graphing Calculator

Turning Off the Graphing CalculatorTurning Off the Graphing Calculator

To turn off the TI-84 Plus manually, press y M.

• All settings and memory contents are retained by Constant Memory™.

• Any error condition is cleared.

Batteries

BatteriesBatteries

The TI-84 Plus uses five batteries: four AAA alkaline batteries and one SR44SW or 303 silver oxide backup battery. The silver oxide battery provides auxiliary power to retain memory while you replace the AAA batteries. To replace batteries without losing any information stored in memory, follow the steps in Appendix C.

Chapter 1: Operating the TI-84 Plus Silver Edition 5

Setting the Display Contrast

Setting the Display ContrastSetting the Display Contrast

Adjusting the Display Contrast

Adjusting the Display ContrastAdjusting the Display Contrast

You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark.

Note: The TI-84 Plus has 40 contrast settings, so each number 0 through 9 represents

four settings. The TI-84 Plus retains the contrast setting in memory when it is turned off. To adjust the contrast, follow these steps.

1. Press and release the y key.

2. Press and hold † or }, which are below and above the contrast symbol (blue, halfshaded circle).

• † lightens the screen.

• } darkens the screen.

Note: If you adjust the contrast setting to 0, the display may become completely blan k. To

restore the screen, press and release y, and then press and hold } until the display reappears.

Chapter 1: Operating the TI-84 Plus Silver Edition 6

When to Replace Batteries

When to Replace BatteriesWhen to Replace Batteries

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

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

Generally , the graphing calculator will continue to operate for one or two weeks after the low-battery message is first displayed. After this period, the TI-84 Plus will turn off automatically and the unit will not operate. Batteries must be replaced. All memory should be retained.

Note: The operating period following the first low-battery message could be longer than

two weeks if you use the graphing calculator infrequently.

The Display

The DisplayThe Dis play

Types of Displays

Types of DisplaysTypes of Displays

The TI-84 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-84 Plus can display a horizontally or ve rtically sp lit screen to show graphs and text simultaneously.

Home Screen

Home ScreenHome Screen

The home screen is the primary screen of the TI-84 Plus. On this screen, enter instructions to execute and expression s to evaluate. The answers are displayed on the same screen.

Chapter 1: Operating the TI-84 Plus Silver Edition 7

Displaying Entries and Answers

Displaying Entries and AnswersDisplaying Entries and Answers

When text is displayed, the TI-84 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display . If an expression on the home screen, the Y= edito r (Chapter 3), or th e 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 (Ch apter 3), a long expression scrolls to the right and left.

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

Entry Answer

The mode settings control the way the TI-84 Plus interprets expressions and displays answers.

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 display the answer.

Entry Answer

Returning to the Home Screen

Returning to the Home ScreenReturning to the Home Screen

To return to the home screen from any other screen, press y5.

Chapter 1: Operating the TI-84 Plus Silver Edition 8

Busy Indicator

Busy IndicatorBusy Indicator

When the TI-84 Plus 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.

Display Cursors

Display CursorsDisplay Cursors

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

Cursor Appearance Effect of Next Keystroke

Entry Solid rectangle

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

Insert Underline

Second Reverse arrow

Alpha Reverse A

Full Checkerboard rectangle#No entry; the maximum characters are entered at

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

A character is inserted in front of the cursor location

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

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

a prompt or memory is full

A (A). If you

press y during an insertion, the underlined cursor becomes an underlined # (#). Graphs and editors sometimes display additional cursors, which are described in other

chapters.

Chapter 1: Operating the TI-84 Plus Silver Edition 9

Interchangeable Faceplates

Interchangeable FaceplatesInterchangeable Faceplates

The TI-84 Plus Silver Edition has interchangeable faceplates that let you customize the appearance of your unit. To purchase additional faceplates, refer to the TI Online Store at education.ti.com.

Removing a Faceplate

Removing a FaceplateRemoving a Faceplate

1. Lift the tab at the bottom edge of the faceplate away from the TI-84 Plus Silver Edition case.

2. Carefully lift the faceplate away from the unit until it releases. Be careful not to damage the faceplate or the keyboard.

Chapter 1: Operating the TI-84 Plus Silver Edition 10

Installing New Faceplates

Installing New FaceplatesInstalling New Faceplates

1. Align the top of the faceplate in the corresponding grooves of the TI-84 Plus Silver Edition case.

2. Gently click the faceplate into place. Do not force.

3. Make sure you gently press each of the grooves to ensure the faceplate is installed properly. See the diagram for proper groove placement.

Using the Clock

Using the ClockUsing the Clock

Use the Clock to set the time and date, select the clock display format, and turn the clock on and off. The clock is turned on by default and is accessed from the mode screen.

Chapter 1: Operating the TI-84 Plus Silver Edition 11

Displaying the Clock Settings

Displaying the Clock SettingsDisplaying the Clock Settings

1. Press z

2. Press the † to move the cursor to

SET CLOCK.

3. Press Í.

Changing the Clock settings

Changing the Clock settingsChanging the Clock settings

1. Press the ~ or | to highlight the date format you want, example: M/D/Y. Press Í.

2. Press † to highlight

YEAR. Press ‘ and type

the year, exam ple: 2004.

3. Press † to highlight

MONTH. Press ‘ and

type the number of the month (a number from 1–

12).

4. Press † to highlight

DAY. Press ‘ and type

the date.

5. Press † to highlight

TIME. Press ~ or | to

highlight the time format you want. Press Í.

6. Press † to highlight

HOUR. Press ‘ and type

the hour. A number from 1–12 or 0–23.

Chapter 1: Operating the TI-84 Plus Silver Edition 12

7. Press † to highlight

MINUTE. Press ‘ and

type the minutes. A number from 0–59.

8. Press † to highlight

AM/PM. Press ~ or | to

highlight the format. Press Í.

9. To Save changes, press † to select

SAVE. Press

Í.

Error Messages

Error MessagesError Messages

If you type the wrong date for the month, for example: June 31, June does not have 31 days, you will receive an error message with two choices:

• To Quit the Clock application and return to the Home screen, select

1: Quit. Press Í.

— or —

• To return to the clock application and correct the error, select

Turning the Clock On

Turning the Clock OnTurning the Clock On

2: Goto. Press Í.

There are two options to turn the clock on. One option is through the

MODE screen, the

other is through the Catalog.

Chapter 1: Operating the TI-84 Plus Silver Edition 13

Using the Mode Screen to turn the clock on

1. If the Clock is turned off, Press † to highlight

TURN CLOCK ON.

2. Press Í Í.

Using the Catalog to turn the clock on

1. If the Clock is turned off, Press y N

2. Press † or } to scroll the selection cursor points to

CATALOG until the

ClockOn.

3. Press Í Í.

Turning the Clock Off

Turning the Clock OffTurning the Clock Off

1. Press y N.

2. Press † or } to scroll the selection cursor points to

CATALOG until the

ClockOff.

3. Press Í.

ClockOff will turn off the Clock display.

Chapter 1: Operating the TI-84 Plus Silver Edition 14

Entering Expressions and Instructions

Entering Expressions and InstructionsEntering Expressions and Instructions

What Is an Expression?

What Is an Expression?What Is an Expression?

An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-84 Plus, you enter an expression in the same order as you would write it on paper. For

example, pR You can use an expression on the home screen to calculate an answer. In most places

where a value is required, you can use an expression to enter a value.

Entering an Expression

Entering an ExpressionEntering an Expression

To create an expression, you enter numb ers, variables, and functions from the keyboard and menus. An expression is completed when you press Í, regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOS™) rules, and the answer is displayed.

is an expression.

Most TI-84 Plus functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press « and

G. If you enter LOG, the TI-84 Plus interprets the entry as implied multiplication of the

variables

Chapter 1: Operating the TI-84 Plus Silver Edition 15

L, O, and G.

45. Do not enter the letters L, O,

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

3 Ë 76 ¥ £ Ì 7 Ë 9 Ã

y C

5 ¤ ¤ Ã 2 « 45 ¤

Multiple Entries on a Line

Multiple Entries on a LineMultiple Entries on a Line

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

Entering a Number in Scientific Notation

Entering a Number in Scientific NotationEntering a Number in Scientific Notation

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

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

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

2. Press y D. â is pasted to the cursor location.

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

Chapter 1: Operating the TI-84 Plus Silver Edition 16

When you enter a number in scientific notation, the TI-84 Plus does not automatically display answers in scientific or engineering notation. The mode settings and the size of the number determine the display format.

Functions

FunctionsFunctions

A function returns a value. For example,

÷, L, +, ‡(, and log( are the functions in the

example on the previous page. In general, the first letter of each function is lowercase on the TI-84 Plus. Most functions take at least one argument, as indicated by an open parenthesis (

Instructions

InstructionsInstructions

An instruction initiates an action. For example,

( ) following the name. For example, sin( requires one argument, sin(value).

ClrDraw is an instruction that clears any

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

Interrupting a Calculation

Interrupting a CalculationInterrupting a Calculation

Circle( requires three arguments, Circle(X,Y,radius).

( ) at the end of the name. For

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

When you interrupt a calculation, a menu is displayed.

• To return to the home screen, select

• To go to the location of the interruption, select

1:Quit.

2:Goto.

Chapter 1: Operating the TI-84 Plus Silver Edition 17

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

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

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

TI-84 Plus Edit Keys

TI-84 Plus Edit KeysTI-84 Plus Edit Keys

Keystrokes Result

~ or | } or †

y |

y ~

‘

{

y 6

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

more than one line; these keys repeat. On the top line of an expression on the home screen, cursor to the beginning of the expression. On the bottom line of an expression on the ho me s cre en , † moves the cursor to the end of the expression.

Moves the cursor to the beginning of an expression. Moves the cursor to the end of an expression. Evaluates an expression or executes an instruction. On a line with text on the home screen, clears the current line.

On a blank line on the home screen, clears everything on the home screen. In an editor, clears the expression or value where the cursor is located; it does not store a zero.

Deletes a character at the cursor; this key repeats. Changes the cursor to an underline (__); inserts characters in front of the

underline cursor; to end insertion, press

y6 or press |, }, ~, or

} moves the

†.

Chapter 1: Operating the TI-84 Plus Silver Edition 18

Keystrokes Result

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

y 7 Changes the cursor to Ø; sets alpha-lock; subsequent keystrokes (on an

„ Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or an n in

Setting Modes

Setting ModesSetting Modes

Checking Mode Settings

Checking Mode SettingsChecking Mode Settings

Mode settings control how the TI-84 Plus displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI-84 Plus is turned off. All numbers, including elements of matrices and lists, are displayed accord ing to the current mode settings.

Changes the cursor to Þ; the next keystroke performs a 2nd operation (an operation in blue above a key and to the left); to cancel 2nd, press

y again.

(a character in green above a key and to the right) or executes SOLVE (Chapters 10 and 11); to cancel ƒ, press ƒ or press |, },

~, or †.

alpha key) paste alpha characters; to cancel alpha-lock, press you are prompted to enter a name such as for a group or a program, alpha-lock is set automatically.

Seq mode with one keystroke.

ƒ. If

Chapter 1: Operating the TI-84 Plus Silver Edition 19

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

Normal Sci Eng Float 0123456789 Radian Degree Func Par Pol Seq Connected Dot Sequential Simul Real a+bi re^qi Full Horiz G-T Set Clock

Changing Mode Settings

Changing Mode SettingsChanging Mode Settings

Numeric notation Number of decimal places Unit of angle measure Type of graphing Whether to connect graph points Whether to plot simultaneously Real, rectangular complex, or polar complex Full screen, two split-screen modes 01/01/01 12:00 AM

To change mode settings, follow these steps.

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

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

3. Press Í.

Chapter 1: Operating the TI-84 Plus Silver Edition 20

Setting a Mode from a Prog ram

Setting a Mode from a Prog ramSetting a Mode from a Prog ram

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

Func or Float. From a blank program command line, select the mode setti ng

from the mode screen; the instruction is pasted to the cursor location.

Normal, Sci, Eng

Normal, Sci, EngNormal, Sci, Eng

Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format.

Normal notation mode is the usual way we express numbers, with digits to the left and

right of the decimal, as in

Sci (scientific) notation mode expresses numbers in two parts. The significant digits

12345.67.

display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of å, as in

Eng (engineering) notation mode is similar to scientific notation. However, the number

1.234567â4.

can have one, two, or three digits before the de cimal; and the power-o f-10 exponent is a multiple of three, as in

12.34567â3.

Note: If you select Normal notation, but the answer cannot display in 10 digits (or the

absolute value is less than .001), the TI-84 Plus expresses the answer in scientific notation.

Chapter 1: Operating the TI-84 Plus Silver Edition 21

Float, 0123456789

Float, 0123456789Float, 0123456789

Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal. 0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display

to the right of the decimal. Place the cursor on the desired number of decimal digit s, and then press Í.

The decimal setting applies to

Normal, Sci, and Eng notation modes.

The decimal setting applies to these numbers:

• An answer displayed on the home screen

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

•The

Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8)

• Results of CALCULATE operations (Chapters 3, 4, 5, and 6)

• The regression equation stored after the execut ion of a regression model (Chapter 12)

Radian, Degree

Radian, DegreeRadian, Degree

Angle modes control how the TI-84 Plus interprets angle values in trigonometric functions and polar/rectangular conversions.

Radian mode interprets angle values as radians. Answers display in radians. Degree mode interprets angle values as degrees. Answers display in degrees.

Chapter 1: Operating the TI-84 Plus Silver Edition 22

Func, Par, Pol, Seq

Func, Par, Pol, SeqFunc, Par, Pol, Seq

Graphing modes define the graphing par ameters. Chapters 3, 4, 5, and 6 describe these modes in detail.

Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3). Par (parametric) graphing mode plots rela tions, where X and Y are functions of T

(Chapter 4).

Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5). Seq (sequence) graphing mode plots seq uences (Chap ter6 ).

Connected, Dot

Connected, DotConnected, Dot

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

functions.

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

Sequential, Simul

Sequential, SimulSequential, Simul

Sequential graphing-order mode evaluates and plo ts one func tion c omp letely before the

next function is evaluated and plotted.

Simul (simultaneous) graphing-order mode evaluates and plo t s all se lected functions for

a single value of X and then evaluates and plots them for the next value of X.

Chapter 1: Operating the TI-84 Plus Silver Edition 23

Note: Regardless of which graphing mode is selected, the TI-84 Plus will sequentially

graph all stat plots before it graphs any functions.

i, re^

Real, a+b

Real, a+bReal, a+b

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

Real

, re^qi

, re^, re^

input. Two complex modes display complex results.

•

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

•

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

Full, Horiz, G-T

Full, Horiz, G-TFull, Horiz, G-T

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

Each split-screen mode displays two screens simultaneously.

•

Horiz (horizontal) mode displays the current graph on the top half of the screen; it

displays the home screen or an editor on the botto m ha lf (Ch ap te r 9).

•

G-T (graph-table) mode displays the current graph on the left half of the screen; it

displays the table screen on the right half (Chapter 9).

Set Clock

Set ClockSet Clock

Use the clock to set the time, date, and clock display formats.

Chapter 1: Operating the TI-84 Plus Silver Edition 24

Using TI-84 Plus Variable Names

Using TI-84 Plus Variable NamesUsing TI-84 Plus Variable Names

Variables and Defined Items

Variables and Defined ItemsVariables and Defined Items

On the TI-84 Plus you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, gra ph pictures, and strings.

The TI-84 Plus uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names.

Variable Type Names

Real numbers A, B, ... , Z Complex numbers A, B, ... , Z Matrices

Lists L1, L2, L3, L4, L5, L6, and user-defined names Functions Y1, Y2, ... , Y9, Y0 Parametric equations X1T and Y1T, ... , X6T and Y6T Polar functions r1, r2, r3, r4, r5, r6 Sequence functions u, v, w Stat plots Plot1, Plot2, Plot3 Graph databases GDB1, GDB2, ... , GDB9, GDB0

ãAä, ãBä, ãCä, ... , ãJä

Graph pictures Pic1, Pic2, ... , Pic9, Pic0 Strings Str1, Str2, ... , Str9, Str0

Chapter 1: Operating the TI-84 Plus Silver Edition 25

Variable Type Names

Apps Applications AppVars Application variables Groups Grouped variables System variables Xmin, Xmax, and others

Notes about Variables

Notes about VariablesNotes about Variables

• You can create as many list names as memory will allow (Chapter 11).

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

• From the home screen or from a program , you can stor e to mat rice s (Ch a pte r 10), lists (Chapter 11), strings (Chapter 15), system variables such as

TblStart (Chapter 7), and all Y= functions (Chapters 3, 4, 5, and 6).

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

Y= functions (Chapter 3).

Xmax (Chapter 1),

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

• You can use

DRAW STO menu items to store and recall graph databases and

pictures (Chapter 8).

• Although most variables can be archived, system variables including r, t, x, y, and q cannot be archived (Chapter 18)

•

Apps are independent applications.which are stored in Flash ROM. AppVars is a

variable holder used to store variables created by independent applications . You cannot edit or change variables in

AppVars unless you do so through the application

which created them.

Chapter 1: Operating the TI-84 Plus Silver Edition 26

Storing Variable Values

Storing Variable ValuesStoring Variable Values

Storing Values in a Variable

Storing Values in a VariableStoring Values in a Variable

Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evalua ted , th e valu e of the var iab l e at that time is used.

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

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

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

3. Press ƒ and then the letter of the variable to whic h you wan t to stor e the valu e.

4. Press Í. If you entered an expression, it is evaluated. The value is stored to the variable.

Displaying a Variable Value

Displaying a Variable ValueDisplaying a Variable Value

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

Chapter 1: Operating the TI-84 Plus Silver Edition 27

Archiving Variables (Archive, Unarchive)

Archiving Variables (Archive, Unarchive)Archiving Variables (Archive, Unarchive)

You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently . Archived variables are indicated by asterisks (ä) to the left of the variable names. Archived variables cannot be edited or executed. They can only be seen and unarchived. For example, if you archive list L1, you will see that L1 exists in memory but if you select it and paste the name L1 to the home screen, you won’t be able to see its contents or edit it until they are unarchived.

Recalling Variable Valu es

Recalling Variable Valu esRecalling Variable Valu es

Using Recall (RCL)

Using Recall (RCL)Using Recall (RCL)

To recall and copy variable contents to the current cu rsor location, fo llow these step s. To leave

RCL, press ‘.

1. Press y K. screen.

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

• Press ƒ and then the letter of the variable.

• Press y 9, and then select the name of the list, or press y [

• Press y >, and then select the name of the matrix.

• Press  to display the

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

Chapter 1: Operating the TI-84 Plus Silver Edition 28

RCL and the edit cursor are displayed on the bottom line of the

Ln].

VARS menu or  ~ to display the VARS Y-VARS

• Press  |, and then select the name of the prog ra m (in the pro g ra m edito r

only).

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

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

Note: You can edit the characters pasted to the expression without affecting the

value in memory.

ENTRY (Last Entry) Storage Area

ENTRY (Last Entry) Storage AreaENTRY (Last Entry) Storage Area

Using ENTRY (Last Entry)

Using ENTRY (Last Entry)Using ENTRY (Last Entry)

When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-84 Plus, ENTRY is retained in memory.

Chapter 1: Operating the TI-84 Plus Silver Edition 29

To recall ENTRY, press y [. The last entry is pasted to the current cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line.

Because the TI-84 Plus updates ENTRY only when you press Í, you can recall the previous entry even if you have begun to enter the next expression.

5 Ã 7

y [

Accessing a Previous Entry

Accessing a Previous EntryAccessing a Previous Entry

The TI-84 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press y[ repeatedly . If a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area.

1 ¿ ƒ A

2 ¿ ƒ B

y [

Chapter 1: Operating the TI-84 Plus Silver Edition 30

If you press y[ after displaying the oldest stored entry , the newest stored entry is displayed again, then the next-newest entry, and so on.

y [

Reexecuting the Previous Entry

Reexecuting the Previous EntryReexecuting the Previous Entry

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

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

0 ¿ ƒ N

N Ã 1 ¿ ƒ N

ƒ ã:äŠƒÄN ¡ Í

Í Í

Multiple Entry Values on a Line

Multiple Entry Values on a LineMultiple Entry Values on a Line

To store to ENTRY two or more expressions or instructions, sep arate each expression or instruction with a colon, then press Í. All expressions and instructions separated by colons are stored in ENTRY.

Chapter 1: Operating the TI-84 Plus Silver Edition 31

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

For the equation A=pr

, use trial and error to find the radius of a circle that cove rs 20 0

square centimeters. Use 8 as your first guess.

8 ¿ ƒ R ƒ ã:ä

y B ƒ

R ¡ Í

y [

y |

7 y 6 Ë 95

Continue until the answer is as accurate as you want.

Clearing ENTRY

Clearing ENTRYClearing ENTRY

Clear Entries (Chapter 18) clears all data that the TI-84 Plus is holding in the ENTRY

storage area.

Using Ans in an Expression

Using Ans in an ExpressionUsing Ans in an Expression

When an expression is evaluated successfully from the home screen or from a program, the TI-84 Plus stores the answer to a storage area called

Ans (last answer). Ans may be

a real or complex number, a list, a matrix, or a string. When you turn off the TI-84 Plus, the value in

Ans is retained in memory.

Chapter 1: Operating the TI-84 Plus Silver Edition 32

Y ou can use the variable Ans to represent the last answer in most places. Press yZ to copy the variable name TI-84 Plus uses the value of

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

Ans in the calculation.

Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.

1 Ë 7 ¯ 4 Ë 2

147 ¥ y Z

Continuing an Expression

Continuing an ExpressionContinuing an Expression

Y ou can use

Ans as the first entry in the next expression without entering the value again

or pressing yZ. On a blank line on the home screen, enter the function. The TI-84 Plus pastes the variable name

5 ¥ 2

Ans to the screen, then the function.

9 Ë 9

Storing Answers

Storing AnswersStoring Answers

To store an answer, store

Chapter 1: Operating the TI-84 Plus Silver Edition 33

Ans to a variable before you evaluate another expression.

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

y B Í

¿ ƒ

TI-84 Plus Menus

TI-84 Plus MenusTI-84 Plus Menus

Using a TI-84 Plus Menu

Using a TI-84 Plus MenuUsing a TI-84 Plus Menu

You can access most TI-84 Plus operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen.

• The menu name on the left side of the top line is highlighted. Up to seven items in

• A number or letter identifies each menu item’s place in the menu . The order is 1

• When the menu continues beyond the displayed items, a down arrow ($) replaces

5 ¡

3 Ë 3

that menu are displayed, beginning with item 1, which also is highlighted.

through 9, then 0, then A, B, C, and so on. The

PRGM EDIT menus only label items 1 through 9 and 0.

the colon next to the last displayed item.

LIST NAMES, PRGM EXEC, and

• When a menu item ends in an ellipsis ( editor when you select it.

Chapter 1: Operating the TI-84 Plus Silver Edition 34

...), the item displays a secondary menu or

• When an asterisk (ä) appears to the left of a menu item, that item is stored in user data archive (Chapter 18).

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

Displaying a Menu

Displaying a MenuDisplaying a Menu

While using your TI-84 Plus, you often will need to access items from its menus.

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

MATH menu is displayed as a full screen.

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

Chapter 1: Operating the TI-84 Plus Silver Edition 35

Moving from One Menu to Another

Moving from One Menu to AnotherMoving from One Menu to Another

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

Scrolling a Menu

Scrolling a MenuScrolling a Menu

To scroll down the menu items, press †. To scroll up the menu items, press }. To page down six menu items at a time, press ƒ†. To p age up six me nu items at a

time, press ƒ}. The green arrows on the graphing calculator, between † and }, are the page-down and page-up symbols.

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

Chapter 1: Operating the TI-84 Plus Silver Edition 36

Selecting an Item from a Menu

Selecting an Item from a MenuSelecting an Item from a Menu

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

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

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

After you select an item from a menu, the TI-84 Plus typically displays the previous screen.

Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9

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

Calculate

‡27.

 † † † Í

27 ¤ Í

Chapter 1: Operating the TI-84 Plus Silver Edition 37

Leaving a Menu without Making a Selection

Leaving a Menu without Making a SelectionLeaving a Menu without Making a Selection

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

• Press y 5 to return to the home screen.

• Press ‘ to return to the previous screen.

• Press a key or key combination for a different menu, such as  or y9.

• Press a key or key combination for a different screen, such as o or y0.

VARS and VARS Y-VARS M enus

VARS and VARS Y-VARS M enusVARS and VARS Y-VARS M enus

VARS Menu

VARS MenuVARS Menu

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

To display the which show the names of the system variables. access more than one secondary menu.

VARS Y-VARS 1: Window... 2: Zoom... ZX/ZY, ZT/Zq, and ZU variables

Chapter 1: Operating the TI-84 Plus Silver Edition 38

VARS menu, press . All VARS menu items display secondary menus,

1:Window, 2:Zoom, and 5:Statistics each

X/Y, T/q, and U/V/W variables

VARS Y-VARS 3: GDB... 4: Picture...

Graph database variables Picture variables

5: Statistics... XY, G, EQ, TEST, and PTS variables 6: Table... 7: String...

Selecting a Variable from the VARS Menu or VARS Y-VARS Menu

Selecting a Variable from the VARS Menu or VARS Y-VARS MenuSelecting a Variable from the VARS Menu or VARS Y-VARS Menu

To display the

V ARS Y-VARS menu, press ~. 1:Function, 2:Parametric, and 3:Polar

TABLE variables String variables

display secondary menus of the Y= function variables.

VARS Y-VARS 1: Function... 2: Parametric... 3: Polar... 4: On/Off...

Note: The sequence variables (u, v, w) are located on the keyboard as the second

Yn functions XnT, YnT functions rn functions

Lets you select/deselect functions

functions of ¬, −, and ®. To select a variable from the

1. Display the

VARS or VARS Y-VARS menu.

• Press  to display the

Chapter 1: Operating the TI-84 Plus Silver Edition 39

VARS or VARS Y-VARS menu, follow these steps.

VARS men u.

• Press  ~ to display the VARS Y-VARS menu.

2. Select the type of variable, such as

VARS Y-VARS menu. A secondary menu is displayed.

2:Zoom from the VARS menu or 3:Polar from the

3. If you selected

1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can p ress

~ or | to display other secondary menus.

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

Equation Operating System (EOS™)

Equation Operating System (EOS™)Equation Operating System (EOS™)

Order of Evaluation

Order of EvaluationOrder of Evaluation

The Equation Operating System (EOS) defines the or de r in which fu nctions in expressions are entered and evaluated on the TI-84 Plus. EOS lets you enter numbers and functions in a simple, straightforward sequence.

EOS evaluates the functions in an expression in this order.

Order Number Function

1 2

3 4 Permutations (nPr) and combinations (nCr)

Functions that precede the argument, such as ‡(, sin(, or log( Functions that are entered after the argument, such as 2, M1, !, ¡, r, and

conversions

Powers and roots, such as 2^5 or 5

‡32

5 Multiplication, implied multiplication, and division 6 Addition and subtraction

Chapter 1: Operating the TI-84 Plus Silver Edition 40

Order Number Function

7 8 Logic operator and

9 Logic operators or and xor

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

Relational functions, such as > or



within parentheses are evaluated first.

Implied Multiplication

Implied MultiplicationImplied Multiplication

The TI-84 Plus recognizes implied multiplication, so you need not press ¯ to express multiplication in all cases. For example, the TI-84 Plus interprets

(2…5)7 as implied multiplication. Note: TI-84 Plus implied multiplication rules, although like the TI-83, differ from those of

the TI-82. For example, the TI-84 Plus evaluates evaluates

Parentheses

ParenthesesParentheses

1à2X as 1à(2…X) (Chapter 2).

1à2X as (1à2)…X, while the TI-82

2p, 4sin(46), 5(1+2), and

All calculations inside a pair of parentheses are completed first. For example, in the expression

4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then

multiplies the answer, 3, by 4.

Chapter 1: Operating the TI-84 Plus Silver Edition 41

You can omit the close parenthesis ( ) ) at the end of an expression. All open parenthetical elements are closed automatically at the e nd of an expressio n. This is also 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 11) or matrix (Chapter 10) and specifies a value for which to solve the Y= function.

Negation

NegationNegation

To enter a negative number, use the negation key. Press Ì and then enter the number. On the TI-84 Plus, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.

For example, M

, evaluates to a negative number (or 0). Use parenthe se s to squ a re a

negative number.

Note: Use the ¹ key for subtraction and the Ì key for negation. If you press ¹ to enter

a negative number , as in an error occurs. If you press ƒ multiplication (

Chapter 1: Operating the TI-84 Plus Silver Edition 42

A…MB).

9 ¯¹7, or if you press Ì to indicate subtraction, as in 9 Ì 7,

A ÌƒB, it is interpreted as implied

Special Features of the TI-84 Plus

Special Features of the TI-84 PlusSpecial Features of the TI-84 Plus

Flash – Electronic Upgradability

Flash – Electronic UpgradabilityFlash – Electronic Upgradability

The TI-84 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new graphing calculator.

As new functionality becomes available, you can electronically upgrade your TI-84 Plus from the Internet. Future software versions include maintenance upgrades that will be released free of charge, as well as new applications and major software upgrades that will be available for purchase from the TI Web site: education.ti.com

For details, refer to: Chapter 19

1.5 Megabytes (M) of Available Memory

1.5 Megabytes (M) of Available Memory1.5 Megabytes (M) of Available Memory

1.5 M of available memory are built into the TI-84 Plus Silver Edition, and .5 M for the

TI-84 Plus. About 24 kilobytes (K) of RAM (random access mem ory) are available for you to compute and store functions, programs, and data.

About 1.5 M of user data archive allow you to store data, programs, applications, or any other variables to a safe location where they cannot be edited or deleted inadvertently. You can also free up RAM by archiving variables to user data.

For details, refer to: Chapter 18

Chapter 1: Operating the TI-84 Plus Silver Edition 43

Applications

ApplicationsApplications

Applications can be installed to customize the TI-84 Plus to your classroom needs. The big 1.5 M archive space lets you stor e up to 94 applications at one time. Ap plications can also be stored on a computer for later use or linked unit-to-unit. There are 30 App slots for the TI-84 Plus.

For details, refer to: Chapter 18

Archiving

ArchivingArchiving

You can store variables in the TI-84 Plus user data archive, a protected area of memory separate from RAM. The user data archive lets you:

• Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.

• Create additional free RAM by archiving variables.

By archiving variables that do not need to be edited frequently, you can free up RAM for applications that may require additional memory.

For details, refer to: Chapter 18

Other TI-84 Plus Features

Other TI-84 Plus FeaturesOther TI-84 Plus Features

The TI-84 Plus guidebook that is included with your graphing calculator has introduced you to basic TI-84 Plus operations. This guidebook covers the other features and capabilities of the TI-84 Plus in greater detail.

Chapter 1: Operating the TI-84 Plus Silver Edition 44

Graphing

GraphingGraphing

You can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polar functions, and up to three sequences. You can use DRAW instructions to annotate graphs.

The graphing chapters appear in this order: Function, Pa rametric, Polar, Sequence, and DRAW.

For graphing details, refer to: Chapters 3, 4, 5, 6, 8

Sequences

SequencesSequences

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

For details, refer to: Chapter 6

Tables

TablesTables

You can create function evaluation tables to analyze many functions simultaneously. For details, refer to: Chapter 7

Split Screen

Split ScreenSplit Screen

Y ou can split the screen ho rizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously.

Chapter 1: Operating the TI-84 Plus Silver Edition 45

For details, refer to: Chapter 9

Matrices

MatricesMatrices

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

For details, refer to: Chapter 10

Lists

ListsLists

You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic comput atio n. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves.

For details, refer to: Chapter 11

Statistics

StatisticsStatistics

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

For details, refer to: Chapter 12

Chapter 1: Operating the TI-84 Plus Silver Edition 46

Inferential Statistics

Inferential StatisticsInferential Statistics

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

For details, refer to: Chapter 13

Applications

ApplicationsApplications

Press Œ to see the complete list of applications that came with your graphing calculator.

Documentation for TI Flash applications are on the product CD. Visit education.ti.com/calc/guides for additional Flash application guidebooks.

For details, refer to: Chapter 14

CATALOG

CATALOGCATALOG

The CATALOG is a convenient, alphabetical list of all functions and instructions on the TI-84 Plus. You can paste any function or instruction from the CATALOG to the current cursor location.

For details, refer to: Chapter 15

Programming

ProgrammingProgramming

You can enter and store programs that include extensive control and input/output instructions.

Chapter 1: Operating the TI-84 Plus Silver Edition 47

For details, refer to: Chapter 16

Archiving

ArchivingArchiving

Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory.

Archived variables are indicated by asterisks (ä) to the left of the variable names.

For details, refer to: Chapter 16

Communication Link

Communication LinkCommunication Link

The TI-84 Plus has a USB port using a USB unit-to-unit cable to connect and communicate with another TI-84 Plus or TI-84 Plus Silver Edition. The TI-84 Plus also has an I/O port using an I/O unit-to-unit cable to communicate with a TI-84 Plus Silver Edition, a TI-84 Plus, a TI-83 Plus Silver Edition, a TI-83 Plus, a TI-83, a TI-82, a TI-73, CBL 2™, or a CBR™ System.

With TI Connect™ software and a USB computer cable, you can also link the TI-84 Plus to a personal computer.

Chapter 1: Operating the TI-84 Plus Silver Edition 48

As future software upgrades become available on th e TI Web site, you ca n download the software to your PC and then use the TI Connect™ software and a USB computer cable to upgrade your TI-84 Plus.

For details, refer to: Chapter 19

Error Conditions

Error ConditionsError Conditions

Diagnosing an Error

Diagnosing an ErrorDiagnosing an Erro r

The TI-84 Plus detects errors while performing these tasks.

• Evaluating an expression

• Executing an instruction

• Plotting a graph

• Storing a value

When the TI-84 Plus detects an error, it returns an error message as a menu title, such as

ERR:SYNTAX or ERR:DOMAIN. Appendix B describes each error type and possible

reasons for the error.

• If you select

• If you select the error location.

Chapter 1: Operating the TI-84 Plus Silver Edition 49

1:Quit (or press y5 or ‘), then the home screen is displayed. 2:Goto, then the previous screen is displayed with the cursor at or near

Note: If a syntax error occurs in the contents of a Y= function during program execution,

then the

Correcting an Error

Correcting an ErrorCorrecting an Error

Goto option returns to the Y= editor, not to the program.

To correct an error, follow these steps.

1. Note the error type (

2. Select

2:Goto, if it is available. The previous screen is displayed with the cursor at or

ERR:error type).

near the error location.

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

4. Correct the expression.

Chapter 1: Operating the TI-84 Plus Silver Edition 50

Chapter 2:

Chapter 2:Chapter 2:

Math, Angle, and Test Operations

Math, Angle, and Test OperationsMath, Angle, and Test Operations

Getting Started: Coin Flip

Getting Started: Coin FlipGetting Started: Coin Flip

Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of

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

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

7:randBin( (random Binomial). randBin( is pasted

to the home screen. Press of coin flips. Press ¢. Press Ë probability of heads. Press ¢. Press the number of simulations. Press ¤.

2. Press Í to evaluate the expression. A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.

MATH PRB menu. Press 7 to select

10 to enter the number

5 to enter the

40 to enter

Chapter 2: Math, Angle, and Test Operations 51

3. Press ~ or | to view the additional counts in the list. Ellipses ( beyond the screen.

4. Press ¿ y d Í to store the data to the list name another activity, such as plotting a histogram (Chapter 12).

Note: Since randBin( generates random numbers,

your list elements may differ from those in the example.

Keyboard Math Operations

Keyboard Math OperationsKeyboard Math Operations

Using Lists with Math Operations

Using Lists with Math OperationsUsing Lists with Math Operations

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

...) indicate that the list continues

L1. You then can use the data for

Chapter 2: Math, Angle, and Test Operations 52

Addition, Subtraction,

Addition, Subtraction, Multiplication,

Addition, Subtraction, Addition, Subtraction,

Multiplication, Divi sion

Multiplication, Multiplication,

Division

DivisionDivision

Y o u can use + (addition, Ã), N (subtraction, ¹), … (multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, an d matrices. You cannot use à with matrices.

valueA+valueB valueA

…valueB

Trigonometric Functions

Trigonometric FunctionsTrigonometric Functions

valueA valueA

N valueB

à valueB

Y ou ca n use the trigonometric (trig) function s (sine, ˜; cosine, ™; and tangent, š) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example,

sin(30) in Radian mode returns L.9880316241; in Degree

mode it returns .5.

sin(value)cos(value)tan(value)

You can use the inverse trig functions (arcsine, y?; arccosine, y@; and arctangent, yA) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.

(value)cos

sin

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

(value)tan

(value)

Chapter 2: Math, Angle, and Test Operations 53

Power, Square, Square Root

Power, Square, Square RootPower, Square, Square Root

You can use

^ (power, ›),

(square, ¡), and ‡( (square root, yC) with real and

complex numbers, expressions, lists, and matrices. You cannot use ‡

value^power

Inverse

InverseInverse

You can use

(inverse, œ) with real and complex numbers, expressions, lists, and

value

‡(value)

matrices. The multiplicative inverse is equivalent to the reciprocal, 1à

-1

value

log(, 10^(, ln(

log(, 10^(, ln(log(, 10^(, ln(

You can use

log( (logarithm, «), 10^( (power of 10, yG), and ln( (natural log, µ)

with real or complex numbers, expressions, and lists.

log(value) 10^(power)ln(value)

( with matrices.

Chapter 2: Math, Angle, and Test Operations 54

Exponential

ExponentialExponential

e^( (exponential, yJ) returns the constant e raised to a power. You can use e^( with

real or complex numbers, expressions, and lists.

e^(power)

Constant

ConstantConstant

e (constant, y [e]) is stored as a constant on the TI-84 Plus. Press y [e] to copy e to

the cursor location. In calculations, the TI-84 Plus uses 2.7182 81828459 for

Negation

NegationNegation

M (negation, Ì) returns the negative of

value. You can use M with real or complex

numbers, expressions, lists, and matrices.

value

EOS™ rules (Chapter 1) determine when negation is evaluated. For example, LA2 returns a negative number, because squaring is evaluated before negation. Use

parentheses to square a negated number, as in

Chapter 2: Math, Angle, and Test Operations 55

(LA)

Note: On the TI-84 Plus, the negation symbol (M) is shorter and higher than the

subtraction sign (N), which is displayed when you press ¹.

PiPi

p (Pi, y B) is stored as a constant in the TI-84 Plus. In calculations, the TI-84 Plus uses 3.1415926535898 for p.

Chapter 2: Math, Angle, and Test Operations 56

MATH Operations

MATH OperationsMATH Operations

MATH Menu

MATH MenuMATH Menu

To display the

MATH menu, press .

MATH NUM CPX PRB 1: 4Frac 2: 4Dec

‡(

‡ Calculates the x

6: fMin( 7: fMax( 8: nDeriv( 9: fnInt( 0: Solver...

4Frac,

Frac, 4Dec

Frac, Frac,

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

Frac with real or complex numbers, expressions, lists, and matrices. If the answer

Dec

DecDec

Displays the answer as a fraction. Displays the answer as a decimal. Calculates the cube. Calculates the cube root.

root. Finds the minimum of a function. Finds the maximum of a function. Computes the numerical derivative. Computes the function integral. Displays the equation solver.

Chapter 2: Math, Angle, and Test Operations 57

cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use 4

value 4Frac

Frac following value.

4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real or complex numbers, expressions, lists, and matrices. You can only use 4 following

value 4Dec

Cube,

Cube, Cube Root

Cube, Cube,

(cube) returns the cube of value. You can use 3 with real or complex numbers,

value.

Cube Root

Cube RootCube Root

Dec

expressions, lists, and square matrices.

value

‡( (cube root) returns the cube root of value. You can use 3‡( with real or complex

numbers, expressions, and lists.

‡(value)

Chapter 2: Math, Angle, and Test Operations 58

‡ (Root)

(Root)

(Root) (Root)

‡ (xth root) returns the x

root of value. You can use

‡ with real or complex numbers,

expressions, and lists.

xthroot

‡value

fMin(, fMax(

fMin(, fMax(fMin(, fMax(

fMin( (function minimum) and fMax( (function maximum) return the value at which the

local minimum or local maximum value of between accuracy is controlled by

fMin(expression,variable,lower,upper[,tolerance]) fMax(expression,variable,lower,upper

Note:

lower and upper values for variable. fMin( and fMax( are not valid in expression. The

tolerance (if not specified, the default is 1âL5).

[,tolerance])

In this guidebook, optional arguments and the commas that accompany them are

expression with respect to variable occurs,

enclosed in brackets ([ ]).

Chapter 2: Math, Angle, and Test Operations 59

nDeriv(

nDeriv(nDeriv(

nDeriv( (numerical derivative) returns an approximate derivative of expression with respect

variable, given the value at which to calculate the derivative and H (if not specified, the

default is 1âL3).

nDeriv(expression,variable,value[,H])

nDeriv( is valid only for real numbers.

nDeriv(

uses the symmetric difference quotient method, which approximates the

numerical derivative value as the slope of the secant line through these points.

fx ε+()fx ε–()–

′ x()

------------------------------------------= 2ε

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

You can use

nDeriv( once in expression. Because of the method used to calculate nDeriv(,

the TI-84 Plus can return a false derivative value at a nondifferentiable point.

Chapter 2: Math, Angle, and Test Operations 60

fnInt(

fnInt(fnInt(

fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of

expression with respect to variable, given lower limit, upper limit, and a tolerance (if not

specified, the default is 1âL5).

fnInt(expression,variable,lower,upper[,tolerance])

To speed the drawing of integration graphs (when fnInt( is used in a Y= equation),

Note:

increase the value of the

Using the Equation Solver

Using the Equation SolverUsing the Equation Solver

Solver

SolverSolver

Solver displays the equation solver, in which you can solve for any variable in an

equation. The equation is assumed to be eq ua l to zer o . numbers.

fnInt( is valid only for real numbers.

Xres window variable before you press s.

Solver is valid only for real

When you select

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

• The interactive solver editor is displayed when an equation is stored in

Chapter 2: Math, Angle, and Test Operations 61

Solver, one of two screens is displayed.

eqn is empty.

eqn.

Entering an Expression in the Equation Solver

Entering an Expression in the Equation SolverEntering an Expression in the Equation Solver

To enter an expression in the equation solver, assuming that the variable follow these steps.

1. Select

0:Solver from the MATH menu to display the equation editor.

2. Enter the expression in any of three ways.

• Enter the expression directly into the equation solver.

• Paste a Y= variable name from the

• Press yK, paste a Y= variable name from the

VARS Y-VARS menu to the equation solver.

VARS Y-VARS menu, and

press Í. The expression is pasted to the equation solver.

The expression is stored to the variable

eqn as you enter it.

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

eqn is empty,

• The equation stored in

Chapter 2: Math, Angle, and Test Operations 62

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

• Variables in the equation are listed in the order in which they appear in the

equation. Any values stored to the listed variables also are displayed.

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

(

bound={L1â99,1â99}).

•A $ is displayed in the first column of the bottom line if the editor continues

beyond the screen.

Note: To use the solver to solve an equation such as K=.5MV

, enter eqn:0=KN.5MV2 in

the equation editor.

Entering and Editing Variable Values

Entering and Editing Variable ValuesEntering and Editing Variable Values

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

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

You can store equations to any

VARS Y-VARS variables, such as Y1 or r6, and then

reference the variables in the equation. The interactive solver editor displays all variables of all Y= functions referenced in the equation.

Chapter 2: Math, Angle, and Test Operations 63

Solving for a Variable in the Equation Solver

Solving for a Variable in the Equation SolverSolving for a Variable in the Equation Solver

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

eqn, follow these steps.

1. Select

0:Solver from the MATH menu to display the interactive solver editor, if not

already displayed.

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

3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-84 Plus will attempt to display the solution that is closest to your guess.

Chapter 2: Math, Angle, and Test Operations 64

upper lower+()

The default guess is calculated as .

----------------------------------------2

4. Edit

bound={lower,upper}. lower and upper are the bounds between which the TI-84 Plus

searches for a solution. This is optional, but it may help find the solution more quickly. The default is

bound={L1â99,1â99}.

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

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

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

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

• The values of the variables are updated in memory.

•

leftNrt=diff is displayed in the last line of the editor. diff is the difference between

the left and right sides of the equation. A solid square in the first column next to

Chapter 2: Math, Angle, and Test Operations 65

leftNrt indicates that the equation has been evaluated at the new value of the

variable for which you solved.

Editing an Equation Stored to eqn

Editing an Equation Stored to eqnEditing 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

Equations with Multiple RootsEquations with Multiple Roots

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

Further Solutions

Further SolutionsFurther Solutions

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

leftNrt=diff disappear . Move the cursor

to the variable for which you now want to solve and press ƒ\.

Controlling the Solution for Solver or solve(

Controlling the Solution for Solver or solve(Controlling the Solution for Solver or solve(

The TI-84 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions.

Chapter 2: Math, Angle, and Test Operations 66

Using solve( on the Home Screen or from a Program

Using solve( on the Home Screen or from a ProgramUsing solve( on the Home Screen or from a Program

The function solution (root) of within which the solution is sought. The default for L1â99.

solve(expression,variable,guess[,{lower,upper}])

expression guess may be a value or a list of two values. Values must be stored for every variable in expression, except variable, before expression is evaluated. lower and upper must be entered in

solve( is available only from CATALOG or from within a program. It returns a

expression for variable, given an initial guess, and lower and upper bounds

lower is L1â99. The default for upper is

solve( is valid only for real numbers.

is assumed equal to zero. The value of variable will not be updated in memory.

list format.

Chapter 2: Math, Angle, and Test Operations 67

MATH NUM (Number) Operations

MATH NUM (Number) OperationsMATH NUM (Number) Operations

MATH NUM Menu

MATH NUM MenuMATH NUM Menu

To display the

MATH NUM menu, press ~.

MATH NUM CPX PRB 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: lcm( 9: gcd(

abs(

abs(abs(

abs( (absolute value) returns the absolute value of real or complex (modulus) numbers,

Absolute value Round Integer part Fractional part Greatest integer Minimum value Maximum value Least common multiple Greatest common divisor

expressions, lists, and matrices.

abs(value)

Chapter 2: Math, Angle, and Test Operations 68

Note: abs( is also available on the MATH CPX menu.

round(

round(round(

round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals

is omitted,

round(value[,#decimals])

iPart(, fPart(

iPart(, fPart(iPar t(, fPart(

iPart( (integer part) returns the integer part or parts of real or complex numbers,

value is rounded to the digits that are displayed, up to 10 digits.

expressions, lists, and matrices.

iPart(value)

(fractional part) returns the fractional part or parts of real or complex numbers,

fPart(

expressions, lists, and matrices.

Chapter 2: Math, Angle, and Test Operations 69

fPart(value)

int(

int(int(

int( (greatest integer) returns the largest integer  real or complex numbers,

expressions, lists, and matrices.

int(value)

For a given value, the result of int( is the same as the result of iPart( for nonnegative

Note:

numbers and negative integers, but one integer le ss than the re sult of

iPart( for negative

noninteger numbers.

min(, max(

min(, max(min(, max(

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

elements. If

list and value are compared, min( compares each element in list with value.

Chapter 2: Math, Angle, and Test Operations 70

max( (maximum value) returns the larger of valueA and valueB or the largest element in list.

listA and listB are compared, max( returns a list of the larger of each p air 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)

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

lcm(, gcd(

lcm(, gcd(lcm(, gcd(

lcm( returns the least common multiple of valueA and valueB, both of which must be

nonnegative integers. When each pair of elements. If

list and value. gcd( returns the greatest common divisor of valueA and valueB, both of which must be

list and value are specified, lcm( finds the lcm of each elemen t in

nonnegative integers. When

max(valueA,valueB) max(list) max(listA,listB) max(list,value)

listA and listB are specified, lcm( returns a list of the lcm of

listA and listB are specified, gcd( returns a list of the gcd of

Chapter 2: Math, Angle, and Test Operations 71

each pair of elements. If list and value are specified, gcd( find s the gcd of ea ch element i n

list and value.

lcm(valueA,valueB) lcm(listA,listB) lcm(list,value)

Entering and Using Complex Numbers

Entering and Using Complex NumbersEntering and Using Complex Numbers

Complex-Number Modes

Complex-Number ModesComplex-Number Modes

The TI-84 Plus displays complex numbers in rect angular form and polar form. To select a complex-number mode, press z, and then select either of the two modes.

•

a+bi (rectangular-complex mode)

•

re^qi (polar-complex mode)

gcd(valueA,valueB) gcd(listA,listB) gcd(list,value)

Chapter 2: Math, Angle, and Test Operations 72

On the TI-84 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements.

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

ln(L1) returns an error; in a+bi mode ln(L1)

returns an answer.

Real mode

a+bi mode

Entering Complex Numbers

Entering Complex NumbersEntering Complex Numbers

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

Note about Radian Versus Degree Mo de

Note about Radian Versus Degree Mo deNote about Radian Versus Degree Mo de

Radian mode is recommended for complex number calculations. Internally, the TI-84 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.

Chapter 2: Math, Angle, and Test Operations 73

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

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

Interpreting Complex Results

Interpreting Complex ResultsInterpreting Complex Results

e^(i45) = cos(45) + i sin(45) is treated internally as

Complex numbers in results, including list elements, are disp layed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polar-complex (

Rectangular-Complex Mode

Rectangular-Complex ModeRectangular-Complex Mode

re^qi) and Radian modes are set.

Rectangular-complex mode recognizes an d disp lays a complex n umber in the form where

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

1–

To enter a complex number in rectangular form, enter the value of Ã or ¹, enter the value of

real component(+ or N)imaginary component i

Chapter 2: Math, Angle, and Test Operations 74

b (imaginary component), and press y V (constant).

a (real component), press

a+bi,

Polar-Complex Mode

Polar-Complex ModePolar-Complex Mode

Polar-complex mode recognizes and displays a complex number in the form is the magnitude,

1–

To enter a complex number in polar form, enter the value of (exponential function), enter the value of q (

e is the base of the natural log, q is the angle, and i is a constant equal to

r (magnitude), press y J

angle), press y V (constant), and then

press ¤.

magnitudee^(anglei)

re^qi, where r

Chapter 2: Math, Angle, and Test Operations 75

MATH CPX (Complex) Operations

MATH CPX (Complex) OperationsMATH CPX (Complex) Operations

MATH CPX Menu

MATH CPX MenuMATH CPX Menu

To display the

MATH NUM CPX PRB 1: conj( 2: real( 3: imag( 4: angle( 5: abs( 6: 4Rect 7: 4Polar

conj(

conj(conj(

conj( (conjugate) returns the complex conjugate of a complex number or list of complex

numbers.

conj(a+bi) returns aNbi in a+bi mode. conj(re^(

MATH CPX menu, press  ~ ~.

Returns the complex conjugate. Returns the real part. Returns the imaginary part. Returns the polar angle. Returns the magnitude (modulus). Displays the result in rectangular form. Displays the result in polar form.

qi)) returns re^(Lqi) in re^qi mode.

Chapter 2: Math, Angle, and Test Operations 76

real(

real(real(

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

real(a+bi) returns a. real(re^(

imag(

imag(imag(

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

qi)) returns r†cos(q).

complex numbers.

imag(a+bi) returns b. imag(re^(qi)) returns r†sin(q).

angle(

angle(angle(

angle( returns the polar angle of a complex number or list of complex numbers,

calculated as tan

(b/a), where b is the imaginary part and a is the real part. The

calculation is adjusted by +p in the second quadrant or Np in the third quadrant.

Chapter 2: Math, Angle, and Test Operations 77

angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp<q<p.

abs(

abs(abs(

abs( (absolute value) returns the magnitude (modulus),

22imag+real()

, of a complex

number or list of complex numbers.

abs(a+bi) returns abs(re^(qi)) returns r (magnitude).

4Rect

Rect

RectRect

Rect (display as rectangular) displays a complex result in rectangular form. It is valid

a2 b2+()

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

complex result8Rect returns a+bi.

Chapter 2: Math, Angle, and Test Operations 78

4Polar

Polar

PolarPolar

Polar (display as polar) displays a complex result in polar form. It is valid only at the end

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

complex result8Polar returns re^(qi).

MATH PRB (Probability) Operations

MATH PRB (Probability) OperationsMATH PRB (Probability) Operations

MATH PRB Menu

MATH PRB MenuMATH PRB Menu

To display the

MATH NUM CPX PRB 1: rand 2: nPr 3: nCr 4: ! 5: randInt( 6: randNorm( 7: randBin(

Chapter 2: Math, Angle, and Test Operations 79

MATH PRB menu, press  |.

Random-number generator Number of permutations Number of combinations Factorial Random-integer generator Random # from Normal distribution Random # from Binomial distribution

rand

randrand

rand (random number) generates and returns one or more ran dom numbers > 0 and < 1.

To generate a list of random-numbers, specify an integer > 1 for trials). The default for

rand[(numtrials)] Note: To generate random numbers beyond the range of 0 to 1, you can include rand in

an expression. For example,

numtrials is 1.

rand5 generates a random number > 0 and < 5.

numtrials (number of

With each for a given seed value. The TI-84 Plus factory- set seed valu e for different random-number sequence, store any nonzero seed value to the factory-set seed value, store 0 to

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

nPr, nCr

nPr, nCrnPr, nCr

nPr (number of permutations) returns the number of permu tations of items taken number at

a time.

items nPr number

Chapter 2: Math, Angle, and Test Operations 80

rand execution, the TI-84 Plus generates the same random-number se quence

rand is 0. To generate a

rand. To restore

rand or reset the defaults (Chapter 18).

items and number must be nonnegative integers. Both items and number can be lists.

nCr (number of combinations) returns the number of combinations of items taken number

at a time.

items and number must be nonnegative integers. Both items and number can be

lists.

items nCr number

Factorial

FactorialFactorial

! (factorial) returns the factorial of eith er an integer or a multiple of .5. For a list, it returns

factorials for each integer or multiple of .5.

value!

The factorial is computed recursively using the relationship (n+1)! = n…n!, until n is

Note:

value must be ‚L.5 and  69.

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

n!=n…(nN1)…(nN2)… ... …2…1, if n is an integer ‚ 0 n!= n…(nN1)…(nN2)… ... …1à2…‡p, if n+1à2 is an integer ‚ 0 n! is an error, if neither n nor n+1à2 is an integer ‚ 0.

Chapter 2: Math, Angle, and Test Operations 81

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

randInt(

randInt(randInt(

randInt( (random integer) generates and displays a random integer within a range

specified by specify an integer > 1 for

randInt(lower,upper[,numtrials])

randNorm(

randNorm(randNorm(

randNorm( (random Normal) generates and displays a random real number from a

lower and upper integer bounds. To generate a list of random numbers,

numtrials (number of trials); if not specified, the default is 1.

specified Normal distribution. Each generated value co uld be any rea l nu mbe r, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for

randNorm(m,s[,numtrials])

numtrials (number of trials); if not specified, the default is 1.

Chapter 2: Math, Angle, and Test Operations 82

randBin(

randBin(randBin(

randBin( (random Binomial) generates and displays a random integer from a specified

Binomial distribution.

numtrials (number of trials) must be ‚ 1. prob (probability of success)

must be ‚ 0 and  1. To generate a list of random numbers, specify an integer > 1 for

numsimulations

randBin(numtrials,prob[,numsimulations])

The seed value stored to rand also affect s randInt(, randNorm(, and randBin(

Note:

(number of simulations); if not specified, the default is 1.

instructions.

Chapter 2: Math, Angle, and Test Operations 83

ANGLE Operations

ANGLE OperationsANGLE Operations

ANGLE Menu

ANGLE MenuANGLE Menu

To display the indicators and instructions. The Radian/Degree mode setting affects the TI-84 Plus’s interpretation of

ANGLE 1: ¡ 2: ' 3: r 4: 8DMS 5: R8Pr( 6: R8Pq( Returns q, given X and Y 7: P8Rx( Returns x, given R and q 8: P8Ry(

Entry Notation

Entry NotationEntry Notation

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

seconds must be real numbers ‚ 0.

ANGLE menu, press y;. The ANGLE menu displays angle

ANGLE menu entries.

Degree notation DMS minute notation Radian notation Displays as degree/minute/second Returns r, given X and Y

Returns y, given R and q

'), and the second symbol ("). degrees must be a real number; minutes and

degrees¡minutes'seconds"

Chapter 2: Math, Angle, and Test Operations 84

For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to Degree, you must use ¡ so that the TI-84 Plus can interpret the argumen t as de grees, minutes, and seconds.

Degree mode Radian mode

Degree

DegreeDegree

¡ (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use ¡ to convert degrees to radians.

value¡ {value1,value2,value3,value4,...,value n}¡

¡ also designates

' (minutes) designates minutes (M) in DMS format. " (seconds) designates seconds (S) in DMS format.

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

Radians

RadiansRadians

(radians) designates an angle or list of angles as radians, regardless of the current

angle mode setting. In Degree mode, you can use

Chapter 2: Math, Angle, and Test Operations 85

degrees (D) in DMS format.

to convert radians to degrees.

value

Degree mode

8DMS

DMS

DMSDMS

DMS (degree/minute/second) displays answer in DMS format. The mode setting must be

Degree for

answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid

only at the end of a line.

answer8DMS

RRRR8PPPPrrrr(, R

(, R8PPPPq((((, P

(, R(, R

, P8Rx(, P

Rx(, P8Ry(

, P, P

Rx(, PRx(, P

Ry(

Ry(Ry(

R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq(

converts rectangular coordinates to polar coordinates and returns q.

Chapter 2: Math, Angle, and Test Operations 86

x and y can be lists.

R8Pr(x,y), R8Pq(x,y)

Note:

Radian mode is set.

8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry(

converts polar coordinates to rectangular coordinates and returns

P8Rx(r,q), P8Ry(r,q)

Note: Radian mode is set.

y. r and q can be lists.

Chapter 2: Math, Angle, and Test Operations 87

TEST (Relational) Operations

TEST (Relational) OperationsTEST (Relational) Operations

TEST Menu

TEST MenuTEST Menu

To display the

This operator ... Returns 1 (true) if...

TEST LOGIC 1: = 2: ƒ 3: > 4: ‚ 5: < 6: 

Ä=,

=, ƒ, >,

, >, ‚, <,

=, =,

, >, , >,

Relational operators compare test is false. only ,

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

matrices, both must have the same dimensions.

TEST menu, press y :.

Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to

, <, 

, <, , <,

valueA and valueB and return 1 if the test is true or 0 if the

valueA and valueB can be real numbers, expressions, or lists. For = and ƒ

Chapter 2: Math, Angle, and Test Operations 88

Relational operators are often used in programs to control prog ram flow and in gra phing to control the graph of a function over specific values.

valueA=valueB valueA>valueB valueA<valueB

Using Tests

Using TestsUsing Tests

valueA valueA valueA

ƒvalueB ‚valueB valueB

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

• The expression

2+2=2+3 returns 0. The TI-84 Plus 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-84 Plus performs the relational test first

because it is in parentheses, and then it adds 2, 1, and 3.

Chapter 2: Math, Angle, and Test Operations 89

TEST LOGIC (Boolean) Operations

TEST LOGIC (Boolean) OperationsTEST LOGIC (Boolean) Operations

TEST LOGIC Menu

TEST LOGIC MenuTEST LOGIC Menu

To display the

This operator... Returns a 1 (true) if...

TEST LOGIC 1: and

2: or 3: xor 4: not(

Boolean Operators

Boolean OperatorsBoolean Operators

Boolean operators are often used in programs to contro l program flow and in gr aphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero (true).

and, or, xor

and, or, xorand, or, xor

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. expressions, or lists.

TEST LOGIC menu, press y : ~.

Both values are nonzero (true). At least one value is nonzero (true). Only one value is zero (false). The value is zero (false).

valueA and valueB can be real numbers,

Chapter 2: Math, Angle, and Test Operations 90

valueA and valueB valueA or valueB valueA xor valueB

valueA valueB and or xor

ƒ0 ƒ0 ƒ0

0 0 0 returns 0 0 0

not(

not(not(

not( returns 1 if value (which can be an expression) is 0.

not(value)

Using Boolean Operations

Using Boolean OperationsUsing Boolean Operations

0 returns 0 1 1

ƒ0

returns 1 1 0

returns 0 1 1

Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C.

Chapter 2: Math, Angle, and Test Operations 91

Chapter 3:

Chapter 3:Chapter 3:

Function Graphing

Function GraphingFunction Graphing

Getting Started: Graphing a Circle

Getting Started: Graphing a CircleGetting Started: Graphing a Circle

Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing wind ow. To

graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle.

1. In

Func mode, press o to display the Y= editor.

Press y C the expression Y=‡(100NX

top half of the circle.

100 ¹ „ ¡ ¤ Í to enter

), which defines the

The expression Y=L‡(100NX half of the circle. On the TI-84 Plus, you can define one function in terms of another . To define press Ì to enter the negation sign. Press  ~ to display the Í to select secondary menu is displayed. Press

1:Y1.

Chapter 3: Function Graphing 92

VARS Y-VARS menu. Then press

1:Function. The FUNCTION

) defines the bottom

Y2=LY1,

1 to select

2. Press q quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s.

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

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

5:ZSquare. The functions are replotted and now

appear as a circle on the display.

6 to select 6:ZStandard. This is a

5 to select

4. To see the p and notice the new values for

Ymin, and Ymax.

Defining Graphs

Defining GraphsDefining Graphs

TI-84 Plus—Graphing Mode Similarities

TI-84 Plus—Graphing Mode SimilaritiesTI-84 Plus—Graphing Mode Similarities

Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-84 Plus graphing mode. Chapters 4, 5, and 6 desc rib e as pe cts that are unique to parametric graphing, polar graphing, and sequence graphing.

Chapter 3: Function Graphing 93

ZSquare window variables, press

Xmin, Xmax,

Defining a Graph

Defining a GraphDefining a Graph

To define a graph in any graphing mode, follow these steps. Some ste ps are not always necessary.

1. Press z and set the appropriate graph mode.

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

3. Deselect stat plots, if necessary.

4. Set the graph style for each function.

5. Press p and define the viewing window variables.

6. Press y . and select the graph format settings.

Displaying and Exploring a Graph

Displaying and Exploring a GraphDisplaying and Exploring a Graph

After you have defined a graph, press s to display it. Explore the behavior of the function or functions using the TI-84 Plus tools described in this chapter.

Saving a Graph for Later Use

Saving a Graph for Later UseSaving a Graph for Later Use

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

GDB1 through GDB9, and GDB0; Chapter 8). To recreate the current graph

later, simply recall the graph database to which you stored the original graph. These types of information are stored in a

GDB.

• Y= functions

• Graph style settings

Chapter 3: Function Graphing 94

• Window settings

• Format settings

You can store a picture of the curr en t gr ap h dis pla y to an y of 10 grap h pic tur e varia ble s (

Pic1 through Pic9, and Pic0; Chapter 8). Then you can superimpose one or more stored

pictures onto the current graph.

Setting the Graph Modes

Setting the Graph ModesSetting the Graph Modes

Checking and Changing the Graphing Mode

Checking and Changing the Graphing ModeChecking and Changing the Graphing Mode

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

The TI-84 Plus has four graphing modes.

Func mode before you enter values for the window

•

Func (function graphing)

•

Par (parametric graphing; Chapter 4)

•

Pol (polar graphing; Chapter 5)

•

Seq (sequence graphing; Chapter 6)

Chapter 3: Function Graphing 95

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

•

Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates.

•

Radian or Degree angle mode affects interpretation of some functions.

•

Connected or Dot plotting mode affects plotting of selected functions.

•

Sequential or Simul graphing-order mode affects function plotting when more than

one function is selected.

Setting Modes from a Program

Setting Modes from a ProgramSetting Modes from a Program

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

1. Press z to display the mode settings.

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

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

The mode is changed when the program is executed.

Defining Functions

Defining FunctionsDefining Functions

Displaying Functions in the Y= Editor

Displaying Functions in the Y= EditorDisplaying Functions in the Y= Editor

To display the Y= editor, press o. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selec ted .

Chapter 3: Function Graphing 96

Defining or Editing a Function

Defining or Editing a FunctionDefining or Editing a Function

To define or edit a function, follow these steps.

1. Press o to display the Y= editor.

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

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

• You may use functions and variables (including matrices and lists) in the

expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.

• The independent variable in the function is X.

To enter X, press „ or press ƒ

Func mode defines „ as X.

[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 th e variable

Yn as a user-defined function

in the Y= editor.

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

Chapter 3: Function Graphing 97

TEXAS INSTRUMENTS TI 84 PLUS User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Important Information

USA FCC Information Concerning Radio Frequency USA FCC Information Concerning Radio Frequency Interference

Chapter 1:Chapter 1: Operating the TI-84 Plus Silver Edition

Documentation Conventions

TI-84 Plus Keyboard

Keyboard Zones

TI-84 Plus

Turning On and T urning Off the TI-84 Plus

Turning On the Graphing Calculator

Turning Off the Graphing Calculator

Batteries

Setting the Display Contrast

Adjusting the Display Contrast

When to Replace Batteries

The Display

Types of Displays

Home Screen

Displaying Entries and Answers

Returning to the Home Screen

Busy Indicator

Display Cursors

Interchangeable Faceplates

Removing a Faceplate

Installing New Faceplates

Using the Clock

Displaying the Clock Settings

Changing the Clock settings

Error Messages

Turning the Clock On

Turning the Clock Off

Entering Expressions and Instructions

What Is an Expression?

Entering an Expression

Multiple Entries on a Line

Entering a Number in Scientific Notation

Functions

Instructions

Interrupting a Calculation

TI-84 Plus Edit Keys

Setting Modes

Checking Mode Settings

Changing Mode Settings

Setting a Mode from a Prog ram

Normal, Sci, Eng

Float, 0123456789

Radian, Degree

Func, Par, Pol, Seq

Connected, Dot

Sequential, Simul

Full, Horiz, G-T

Set Clock

Using TI-84 Plus Variable Names

Variables and Defined Items

Notes about Variables

Storing Variable Values

Storing Values in a Variable

Displaying a Variable Value

Archiving Variables (Archive, Unarchive)

Recalling Variable Valu es

Using Recall (RCL)

ENTRY (Last Entry) Storage Area

Using ENTRY (Last Entry)

Accessing a Previous Entry

Reexecuting the Previous Entry

Multiple Entry Values on a Line

Clearing ENTRY

Using Ans in an Expression

Continuing an Expression

Storing Answers

TI-84 Plus Menus

Using a TI-84 Plus Menu

Displaying a Menu

Moving from One Menu to Another

Scrolling a Menu

Selecting an Item from a Menu

Leaving a Menu without Making a Selection