Sharp EL9900C - Graphing Calc With 2 Sided Keypad Lrg 22 CHAR/8 Line Display 64KB Operation Manual

EL-9900

MODEL

GRAPHING CALCULATOR

OPERATION MANUAL

®

In the U.S.A.

Declaration of Conformity

Graphing Calculator: EL-9900

This device complies with Part 15 of the FCC Rules. Operation is subject to the following two
conditions: (1) This device may not cause harmful interference, and (2) this device must accept
any interference received, including interference that may cause undesired operation.

Responsible Party:

SHARP ELECTRONICS CORPORATION
Sharp Plaza, Mahwah, New Jersey 07430-1163

TEL: 1-800-BE-SHARP

Tested To Comply With FCC Standards

FOR HOME OR OFFICE USE

WARNING — FCC Regulations state that any unauthorized changes or modifications to this
equipment not expressly approved by the manufacturer could void the user’s authority to
operate this equipment.

Note: This equipment has been tested and found to comply with the limits for a Class B digital
device, pursuant to Part 15 of the FCC Rules.
These limits are designed to provide reasonable protection against harmful interference in a
residential installation. This equipment generates, uses, and can radiate radio frequency energy
and, if not installed and used in accordance with the instructions, may cause harmful interfer­ence to radio communications.
However, there is no guarantee that interference will not occur in a particular installation. If this
equipment does cause harmful interference to radio or television reception, which can be
determined by turning the equipment off and on, the user is encouraged to try to correct the
interference by one or more of the following measures:

— Reorient or relocate the receiving antenna.
— Increase the separation between the equipment and receiver.
— Connect the equipment into an outlet on a circuit different from that to which the receiver is

connected.

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

Note: A shielded interface cable is required to ensure compliance with FCC regulations for Class B
certification.

FOR YOUR RECORDS...

For your assistance in reporting this product in case of loss or theft, please
record the model number and serial number which are located on the bottom
of the unit.
Please retain this information.

Model Number
Serial Number
Date of Purchase
Place of Purchase

Introduction

This graphing calculator can handle many types of mathematical formulas and
expressions for you. It is powerful enough to process very complex formulas used in
rocket science, but yet so compact that it fits in your coat pocket. The main features of
this graphing calculator are as follows:

•Reversible Keyboard to suit the needs of students’ levels, ranging from middle­school level arithmetic to high-school calculus, and beyond,

•Graphing Capability to help you visualize what you are working on,

• Slide Show Function to help you understand common formulas, prepare for presen­tations,

• Large memory capacity, with fast processing speed, and more.

We strongly recommend you read this manual thoroughly. If not, then browse through
the very first chapter “Getting Started”, at least. Last, but not least, congratulations on
purchasing the Graphing Calculator!

NOTICE

• The material in this manual is supplied without representation or warranty of any
kind. SHARP assumes no responsibility and shall have no liability of any kind,
consequential or otherwise, from the use of this material.

• SHARP strongly recommends that separate permanent written records be kept of all
important data. Data may be lost or altered in virtually any electronic memory
product under certain circumstances. Therefore, SHARP assumes no responsibility
for data lost or otherwise rendered unusable whether as a result of improper use,
repairs, defects, battery replacement, use after the specified battery life has expired,
or any other cause.

• SHARP assumes no responsibility, directly or indirectly, for financial losses or claims
from third persons resulting from the use of this product and any of its functions, the
loss of or alteration of stored data, etc.

• The information provided in this manual is subject to change without notice.

• Screens and keys shown in this manual may differ from the actual ones on the
calculator.

• Some of the accessories and optional parts described in this manual may not be
available at the time you purchase this product.

• Some of the accessories and optional parts described in this manual may be
unavailable in some countries.

• All company and/or product names are trademarks and/or registered trademarks of
their respective holders.

i

Introduction

Reversible Keyboard

This calculator comes equipped with a reversible keyboard. Reverse the keyboard to
select Basic Mode or Advanced Mode.

Basic Mode

A green background color keyboard with basic mathematical functions. This mode is
suitable for learning mathematics in lower grades.

ii

Introduction

Advanced Mode (Default mode)

A blue background color keyboard with advanced mathematical functions. This mode
is suitable for learning or studying mathematics in higher grades.

iii

Contents

Caring for Your Calculator...............................................................................................1

Chapter 1

Getting Started .............................................................................................................. 2

Before Use ......................................................................................................................2

Using the Hard Cover ..................................................................................................... 3

Part Names and Functions .............................................................................................4

Main Unit ................................................................................................................. 4

Reversible Keyboard ............................................................................................... 6

Basic Key Operations .....................................................................................................8

Changing the Keyboard ..................................................................................................9

Quick Run-through: Basic Mode...................................................................................10

Chapter 2

Operating the Graphing Calculator ......................................................................... 13

Basic / Advanced Keyboard..........................................................................................13

Basic Key Operations - Standard Calculation Keys .....................................................13

1. Entering numbers ............................................................................................. 14

2. Performing standard math calculations ............................................................15

Cursor Basics ...............................................................................................................15

Editing Entries ..............................................................................................................17

Second Function Key....................................................................................................18

ALPHA Key ...................................................................................................................19

Math Function Keys ......................................................................................................20

MATH, STAT, and PRGM Menu Keys ...........................................................................23

SETUP Menu ................................................................................................................24

SETUP Menu Items ......................................................................................................25

Precedence of Calculations..........................................................................................27

Error Messages ............................................................................................................ 28

Resetting the Calculator ...............................................................................................29

1. Using the reset switch....................................................................................... 29

2. Selecting the RESET within the OPTION menu .............................................. 30

Chapter 3

Basic Calculations — Basic Keyboard.................................................................... 31

1. Tr y it!........................................................................................................................31

2. Arithmetic Keys .......................................................................................................33

3. Calculations Using Various Function Keys .............................................................35

4. Calculations Using MATH Menu Items ................................................................... 42

iv

Contents

Chapter 4

Basic Graphing Features — Basic Keyboard ......................................................... 50

1. Tr y it!........................................................................................................................50

2. Explanations of Various Graphing Keys .................................................................52

3. Other Useful Graphing Features.............................................................................58

Substitution feature...............................................................................................63

Chapter 5

Advanced Calculations — Advanced Keyboard .................................................... 66

1. Tr y it!........................................................................................................................66

2. Various Calculation Keys ........................................................................................67

3. Calculations Using MATH Menu .............................................................................70

4. More Variables: Single Value Variables and LIST Variables ...................................80

5. TOOL Menu.............................................................................................................81

6. SETUP Menu ..........................................................................................................83

Chapter 6

Advanced Graphing Features — Advanced Keyboard .......................................... 84

1. Tr y it!........................................................................................................................84

2. Graphing Parametric Equations..............................................................................87

3. Polar Graphing ........................................................................................................88

4. Graphing Sequences ..............................................................................................89

5. The CALC Function ................................................................................................93

6. Format Setting ........................................................................................................95

7. Zoom Functions ......................................................................................................96

8. Setting a Window ....................................................................................................98

9. Tables ......................................................................................................................99

10. The DRAW Function .............................................................................................102

11. Substitution Feature ..............................................................................................114

Chapter 7

SLIDE SHOW Feature .............................................................................................. 115

1. Tr y it!..................................................................................................................... 115

2. The SLIDE SHOW menu ......................................................................................118

Chapter 8

Matrix Features ........................................................................................................ 120

1. Tr y it!..................................................................................................................... 120

2. Entering and Viewing a Matrix ............................................................................. 122

Editing keys and functions..................................................................................123

3. Normal Matrix Operations ..................................................................................... 124

4. Special Matrix Operations..................................................................................... 125

Calculations using OPE menus ......................................................................... 125

Calculations using MATH menus ....................................................................... 129

Use of [ ] menus.................................................................................................. 130

v

Contents

Chapter 9

List Features ............................................................................................................ 131

1. Tr y it!..................................................................................................................... 131

2. Creating a list ....................................................................................................... 133

3. Normal List Operations .........................................................................................133

4. Special List Operations .........................................................................................135

Calculations using the OPE menu functions ..................................................... 135

Calculations using MATH Menus ....................................................................... 139

5. Drawing multiple graphs using the list function ................................................... 141

6. Using L_DATA functions ........................................................................................142

7. Using List Table to Enter or Edit Lists .................................................................. 143

How to enter the list ............................................................................................ 143

How to edit the list ..............................................................................................144

Chapter 10

Statistics & Regression Calculations.................................................................... 145

1. Tr y it!..................................................................................................................... 145

2. Statistics Features ................................................................................................149

1. STAT menus ..................................................................................................149

2. Statistical evaluations available under the C CALC menu .......................... 150

3. Graphing the statistical data ................................................................................ 153

1. Graph Types .................................................................................................. 153

2. Specifying statistical graph and graph functions ......................................... 157

3. Statistical plotting on/off function ................................................................. 157

4. Trace function of statistical graphs .............................................................. 158

4. Data list operations ...............................................................................................159

5. Regression Calculations .......................................................................................160

6. Statistical Hypothesis Testing .............................................................................. 165

7. Distribution functions ............................................................................................177

Chapter 11

Financial Features ................................................................................................... 183

1. Tr y it! 1.................................................................................................................. 183

Tr y it! 2.................................................................................................................. 187

2. CALC functions .....................................................................................................189

3. VARS Menu.......................................................................................................... 193

Chapter 12

The SOLVER Feature ................................................................................................194

1. Three Analysis Methods: Equation, Newton, and Graphic.................................. 194

2. Saving/Renaming Equations for Later Use ......................................................... 200

3. Recalling a Previously Saved Equation ............................................................... 201

vi

Contents

Chapter 13

Programming Features ........................................................................................... 202

1. Tr y it!..................................................................................................................... 202

2. Programming Hints ...............................................................................................204

3. Variables .............................................................................................................. 206

Setting a variable ................................................................................................206

4. Operands ............................................................................................................. 206

Comparison operands ........................................................................................206

5. Programming commands ......................................................................................207

A PRGM menu ....................................................................................................207

B BRNCH menu..................................................................................................209

C SCRN menu ....................................................................................................209

D I/O menu......................................................................................................... 209

E SETUP menu ..................................................................................................210

F FORMAT menu ................................................................................................211

G S_PLOT menu ................................................................................................213

6. Flow control tools ..................................................................................................214

7. Other menus convenient for programming .......................................................... 216

H COPY menu ....................................................................................................216

VARS menu ....................................................................................................... 217

8. Debugging ............................................................................................................ 219

9. Sample programs..................................................................................................220

Chapter 14

OPTION Menu ........................................................................................................... 222

Accessing the OPTION Menu ....................................................................................222

1. Adjusting the screen contrast ...................................................................... 222

2. Checking the memory usage ....................................................................... 222

3. Deleting files.................................................................................................. 224

4. Linking to another EL-9900 or PC ............................................................... 224

5. Reset function ...............................................................................................227

Appendix................................................................................................................... 228

1. Replacing Batteries ...............................................................................................228

2. Troubleshooting Guide ..........................................................................................231

3. Specifications ....................................................................................................... 233

4. Error Codes and Error Messages ........................................................................ 235

5. Error Conditions Relating to Specific Tasks ........................................................ 237

1. Financial ....................................................................................................... 237

2. Error conditions during financial calculations .............................................. 239

3. Distribution function ......................................................................................239

6. Calculation Range.................................................................................................241

1. Arithmetic calculation ....................................................................................241

2. Function calculation ......................................................................................241

vii

Contents

3. Complex number calculation........................................................................ 245

7. CATALOG Feature ................................................................................................246

8. List of Menu/Sub-menu Items .............................................................................. 247

1. MATH menus .................................................................................................247

2. LIST menus ...................................................................................................249

3. STAT menus ..................................................................................................251

4. STAT PLOT menus ........................................................................................253

5. DRAW menus ................................................................................................254

6. ZOOM menus ................................................................................................255

7. CALC menus .................................................................................................257

8. SLIDE SHOW menus ....................................................................................258

9. PRGM menus ................................................................................................258

10. MATRIX menus .............................................................................................261

11. FINANCE menus ...........................................................................................262

12. TOOL menus ................................................................................................. 263

13. SOLVER menus ............................................................................................264

INDEX ........................................................................................................................ 265

viii

Caring for Your Calculator

Caring for Your Calculator

• Do not carry the calculator around in your back pocket, as it
may break when you sit down. The display is made of glass and
is particularly fragile.

•Keep the calculator away from extreme heat such as on a car
dashboard or near a heater, and avoid exposing it to exces­sively humid or dusty environments.

• Since this product is not waterproof, do not use it or store it
where fluids, for example water, can splash onto it. Raindrops,
water spray, juice, coffee, steam, perspiration, etc. will also
cause malfunction.

• Clean with a soft, dry cloth. Do not use solvents.

• Do not use a sharp pointed object or exert too much force when
pressing keys.

•Avoid excessive physical stress.

1

Chapter 1

Getting Started

Before Use

Inserting
batteries ­resetting the
memory

1. Open the battery cover
located on the back of the
calculator. Pull down the
notch, then lift the battery
cover up to remove it.

2. Insert the batteries, as
indicated. Make sure that the
batteries are inserted in the
correct directions.

3. Pull off the insulation sheet
from the memory backup
battery.

4. Place the battery cover
back, and make sure that the
notch is snapped on.

5. Press O and you will
see the following message on the display:

PRESS [CL] KEY TO CLEAR ALL DATA
PRESS [ON] KEY TO CANCEL

Note: If the above message does not appear, check the direction of the

batteries and close the cover again. If this does not solve the
problem, follow the instruction described in "Resetting the
Calculator - 1. Using the reset switch" on page 29.

6. Press C to reset the calculator’s memory. The memory will
be initialized. Press any key to set the calculator ready for
normal calculation mode.

2

Chapter 1: Getting Started

Adjusting
display contrast

Turning the
calculator OFF

Since the display contrast may vary with the ambient temperature
and/or remaining battery power, you may want to adjust the
contrast accordingly. Here’s how:

1. Press @, then p.

2. Adjust the contrast by using the + and - keys.

+: increases the contrast

-: decreases the contrast

3. When done, press C to exit the mode.

Press @ o to turn the calculator off.

Automatic power off function

• The calculator is automatically turned off when there is no key
operation for approximately 10 minutes (The power-off time
depends on the conditions.)

• The calculator will not automatically power off while it is
executing calculations (“■” flashes on the upper right corner of
the display.)

Using the Hard Cover

To open the cover: When in use:

When not in use:

3

Chapter 1: Getting Started

Part Names and Functions

Main Unit

2 Power ON/

OFF key

1 Display screen

4 Graphing keys

3 Key operation

keys

5 Cursor keys

4

Chapter 1: Getting Started

1 Display screen:

Displays up to 132 pixels wide by 64 pixels tall of graphs and texts.

2 Power ON/OFF key:

Tu r ns calculator ON. To turn off the calculator, press @, then o.

3 Key operation keys:

These keys are used to change the key functions.

@: Changes the cursor to “2”, and the next keystroke enters the

function or mode printed above each key in yellow.

A: Changes the cursor to “A”, and the next keystroke enters the

alphabetical letter printed above each key in purple.

Note: Press @ . to lock the specific keys in the alphabet

entering mode. (ALPHA-LOCK)

4 Graphing keys:

These keys specify settings for the graphing-related mode.

Y: Opens the formula input screen for drawing graphs.
G:Draws a graph based on the formulas programmed in the Y

window.

T: Opens a Table based on the formulas programmed in Y.
W: Sets the display ranges for the graph screen.
Z: Changes the display range of the graph screen.
U: Places the cursor pointer on the graph for tracing, and displays

the coordinates.

,: Displays the substitution feature.
": Displays both a graph and a table at the same time.
y: Opens the table setup screen.
d:Draws items on the graph. Use this key also to save or recall the

graph/pixel data.

f: Sets the operations of the graph screen.
k: Calculates specific values based on formulas programmed in

Y

5

Chapter 1: Getting Started

5 Cursor keys:

Enables you to move the cursor (appears as _, ■, etc. on the screen) in four
directions. Use these keys also to select items in the menu.

Reset switch (in the battery compartment):

Used when replacing batteries or clear the calculator memory.

# key: Returns calculator to calculation screen.
p key: Sets or resets the calculator settings, such as LCD contrast and memory

usage.

n key: Obtains the screen for the slide show.
l key: Accesses list features.

] key: Creates your own slide shows.
[ key: Sets the statistical plotting.

Reversible Keyboard

Basic keyboard Advanced keyboard

Basic Operation keys

E: Used when executing calculations or specifying commands.

C / q: Clear/Quit key

B: Backspace delete key
D: Delete key

i:Toggle input mode between insert and overwrite (in one-line edit

mode).

;: Allows you to set up the basic behavior of this calculator, such as

to set answers in scientific or normal notation.

6

Chapter 1: Getting Started

Menu keys (Function of these keys may vary between basic and advanced mode.)

M: Enter the Math menu with additional mathematical functions.
S: Enter the statistics menu.
P: Enter the programming menu.

z: Enter the menu for calculator specific variables.

Advanced Mode specific keys

V: Converts hexadecimal, decimal, octal and binary numbers or

solves systems of linear equations, finds roots for quadratic and
cubic equations.

m: Enter menu for matrix functions
': Enter screen and menu for Solver features
g: Enter menu for financial solver and functions

Scientific Calculation keys (See each chapter for details.)

Basic Mode specific keys

Q / / / < / >:

Fraction calculation keys

i: Integer division and remainder calculation keys
%:Percentage calculation key

* In Advanced mode, you can access above functions from

CATALOG menu.

Advanced Mode specific keys

s / c / t / s / c / t:

Trigonometric function keys

l / I / 0 / @:

Logarithm and exponential functions.

7

Chapter 1: Getting Started

Basic Key Operations

Since this calculator has more than one function assigned to each key, you will need
to follow a few steps to get the function you need.

Example

-1

x

F

@ x: Specify x

-1

Operation of yA F: Specify character F

y: Specify x

2

• Press “as is” to get the function and number printed on each key.

•To access secondary function printed above each key in yellow, press

@ first, then press the key. Press C to cancel.

•To press the key printed above each key in purple, press A first,

then press the key. When in Menu selection screen however, you do
not have to press A to access the characters. Press C to
cancel.

• If you want enter alphabetical letters (purple) sequentially, use @
.. Press A to return to the normal mode.

• In this manual, alphanumeric characters to be entered are indicated
as they are (without using the key symbols). Use of the key symbol
indicates that it is for selecting the menu specified by the character or
number. The above example also indicates the key notation rules of
this manual.

8

Chapter 1: Getting Started

Changing the Keyboard

This calculator is designed with a reversible keyboard, which by utilizing it will not only
change the appearance, but will also change the internal functions and configurations
of the calculator as well.

To change the
keyboard:

1. Press @ o to turn off the calculator’s power.

2. Open the battery
compartment cover.
Hold the calculator as
illustrated.

3. Slide the keyboard eject
tab (KEYBOARD
EJECT) down.

The keyboard will be
ejected.

Be careful not to drop
the keyboard on the floor, as this may damage it.

4. Turn the keyboard
over, and replace in
the calculator as
illustrated. Secure by
gently pressing the
keyboard until you
hear the notch click.

Note: Clean the edges and contact points of the keyboard and the

keyboard tap before reattaching the keyboard to the main unit.
DO NOT touch the pad portion in the keyboard tap.

5. Replace the battery compartment cover.

6. Press O.

7. Make sure that the message
shown on the right appears.

8. Press O.

9

Chapter 1: Getting Started

When you reverse the keyboard, the following settings are automatically changed.

Basic → Advanced

• Simplifying: Auto (Auto at SIMPLE in SETUP menu)

Advanced → Basic

• Coordinate system: Rectangular coordinates (Rect at COORD
in SETUP menu.)

• Answer mode: Displays a mixed number if ANSWER is set to
complex numbers.

• Angle unit: Set to Deg if DRG is set to Grad.

• Decimal format: Set to FloatPt if FSE is set to Eng.

Quick Run-through: Basic Mode

Here are the major ingredients for 18 doughnuts:

1

cup warm water

4
3

cup warm milk

4
1

cup sugar

3

4 cups all-purpose flour
2 eggs
3 tablespoons butter

Based on these values, solve the following problems using the calculator.

Question If you make 60 doughnuts according to the above recipe,

how many cups of warm milk are required?

At first, you may calculate how many cups of warm milk are
required for 1 doughnut =

3

÷ 18

4

As for the ordinary calculator, the answer is 0.041666666. But
how much is 0.04166666 of a cup of warm milk? The Basic mode
of this graphing calculator is initially set to the fraction answer
mode instead of the decimal answer mode. You may easily obtain
the answer in fraction.

10

Chapter 1: Getting Started

Set up the
calculator
before
calculation

Enter fractions

1. Press # to enter the

calculation screen.

2. Press C to clear the

display.

3. Press 3 b 4 '.

4. Press b 18 '.

5. Press E.

Now we have found

1

of a cup of warm milk is required per one

24

doughnut, how many cups are required for 60 doughnuts?
If you want to use the answer of the previous calculation, press

b and you do not have to reenter the value.

6. Press @ b |, or directly | (multiplication).

“Ans×” is displayed. ANS is a calculator specific variable which
indicates the answer of calculations just before.

* When you enter

+ (addition), – (subtraction), × (multiplication),

÷ (division), it is not required to press b.

7. Press 60.

8. Press E.

1

Answer:

2

2

cups of warm milk are required for making 60 doughnuts.

11

Chapter 1: Getting Started

On the Basic Mode, you can toggle between decimal values,
mixed values, and improper fractions using >, /, and
<, respectively.

1. Press > E.

2. Press < E.

3. Press / E.

Change answer
mode from
fractions to
decimals

1. Press @ ;.

2. Select F ANSWER and

press 1.

3. Press C.

Now the answer mode is set to the decimal answer mode and 2.5
is displayed.

12

Chapter 2

Operating the Graphing
Calculator

Basic / Advanced Keyboard

This calculator comes equipped with a reversible keyboard to support two different
keyboard configurations: Basic and Advanced keyboard. By reversing the keyboard,
the calculator switches its set of functions and behaviors as well as its visual aspect.

The Basic keyboard, with its key frame colored in dark green, is designed to be used
by students at lower grades of math classes. Functions associated with complex
calculations, such as matrix functions and various trigonometric functions, are not
included in this layout to avoid confusing students. Menu items are also carefully
chosen to meet the educational needs of the students at lower grades.

With the Advanced keyboard however, all functions and features are accessible for
higher grade math students and various professionals in the fields of architecture,
finance, mathematics, and physics.

How to switch the keyboard

See page 9.

Basic Key Operations - Standard Calculation Keys

The standard calculation keys, located at the bottom four rows of the keyboard,
enable you to access the basic functions of the calculator.

13

Chapter 2: Operating the Graphing Calculator

1. Entering numbers

Use the number keys (0 ~ 9), decimal point key (.), and negative
number key (_) to enter numbers into the calculator. To clear the screen entry,
press C.

Number entry

Note: $ can be used to enter a value in scientific notation.

Example

Type 10.23456789 onto the
Calculation screen.

1. Enter the Calculation screen,

then clear the screen entry:
# C

2. Enter numbers with the number keys and decimal point key, as

follows:
10 . 23456789

Example

6.3

× 10

8

+ 4.9 × 10

7

# C 6.3 $ 8 + 4.9
$ 7

Entering a
negative value

Note: Do not use the - key to specify a negative value. Doing so

The negative number key _ can be used to enter numbers,
lists, and functions with negative values. Press _ before
entering the value.

will result in an error.

Example

Type -9460.827513 into the
Calculation screen.

# C _ 9460.827513

14

Chapter 2: Operating the Graphing Calculator

2. Performing standard math calculations

By utilizing the + - | and = keys, you can perform the standard
arithmetic calculations of addition, subtraction, multiplication, and division. Press
E to perform each calculation.

Perform an
arithmetic
calculation

Using
parentheses

Example

Obtain the answer to “6

× 5 + 3

– 2”.

# C 6 | 5 + 3

- 2 E

With the ( and ) keys, parentheses (round brackets)
can be added to group sections of expressions. Sections within
the parentheses will be calculated first. Parentheses can also be
used to close the passings of values in various functions, such as
“round(1.2459,2)”.

Example

Obtain the answer to “(9
(5 – 3)”.

# C ( 9 + 7
) | ( 5 - 3

+ 7) ×

) E

Note: The multiplication sign “

be abbreviated if it proceeds a math function, a parenthesis “(”, or
a variable. Abbreviating “(1
error.

×”, as the one in the above example, can

+ 2) × 3” to “(1 + 2) 3” will result in an

Cursor Basics

The cursor indicates where the next entry will be placed. The cursor may be placed
automatically to different areas by various functions and tools, or can be moved
around by using the ; ' { } keys. Use the cursor keys to select a
menu item, select a cell item in a matrix, and trace along a graph.

15

Chapter 2: Operating the Graphing Calculator

Example

Enter “

4

65536

×

3

” in the Calculation screen. Jump the cursor

8

to the beginning of the expression (just for this exercise), then
press E to calculate.

1. Press #, then C to clear the display.

2. Enter 4 for the root’s depth, then press @ _.

The root figure is entered, with the cursor automatically placed
below the figure.
For detailed instructions of how to use the @ key, refer to
“Second Function Key” and “ALPHA Key” in this chapter.

3. Enter 65536.

At this moment, the cursor is still placed under the root figure.

4. Press ' to move the cursor out of the area, then enter

| at the cursor.

5. Press @ _ again. Notice that the cursor is automati-

6. Press E to obtain the

Cursor appear­ance and input

The cursor also displays information regarding the calculator’s
input method. See the following diagram.

method

Mode Symbol Remarks

Normal mode

When A is pressed

cally placed so that you can specify the depth of this root
figure. Type 3, }, and 8.

answer.

The appearance of the cursor pointer

may vary according to the mode or

position. The major shapes and the

definitions are as follows:

When @ is pressed

* , and appear at the insertion point within the functions such as a/b and a.

16

: Insert mode

: Overwrite mode

Editing Entries

Chapter 2: Operating the Graphing Calculator

Editing modes

Cursor naviga­tion

The calculator has the following two editing modes: equation
mode, and one line mode.
You can select one from the G EDITOR menu of the SETUP
menu.

Equation editor One line editor

* See page 26 for details.

Use ; ' { } to move the cursor around, and
use the D B C keys to edit entries.

• D key deletes an entry AT THE CURSOR.

• B key erases one BEFORE THE CURSOR.

About the Insert
mode

• Use C to clear the entire entry line.

When the editing mode is set to one-line, insert mode needs to
be manually specified. Press and release @, then i to
set the insert mode. Press @ i again to return to the
overwrite mode.

The C key clears all screen entries in the Calculation screen,
as well as clearing error messages. It also clears a single line
equation in the Y screen. For more information on the Y
key, refer to Chapters 4 and 6 of the manual.

Example

Type 3096, then change 3 to 4. When done, jump the cursor to
the very end of the numbers.

# C 3 0 9 6 ;
; ; ; D 4
' ' '

17

Chapter 2: Operating the Graphing Calculator

Example

Type 4500000, then remove 500.

# C 4 5 0 0 0 0 0 ;
; ; B B
B

Tips: You can jump the cursor to the beginning or the end of line by

using the @ and ; ' keys. Likewise, press @

} to jump the cursor all the way to the bottom. Press @
{ to jump the cursor to the top. To learn about how to use the
@ key and its functions, refer to the section “Second Function

Key” of this chapter.

Second Function Key

Use @ to call up the calculator’s extended key functions, math functions and
figures.

All functions associated with @ are color coded light yellow, and are printed above
each key.

Note: Available Second function keys differ between the Basic keyboard

and the Advanced keyboard. For example, a second function “
is not accessible within the Basic keyboard.

Example

Enter “2π” on the screen.

1. Press # C to clear the screen, then enter “2” by

pressing 2.

2. Press @. When the key

is released, the cursor on
the screen changes,
indicating that a second
function is now ready to be
called up.

x

e

”

3. Press $. The entry

appears on the screen.

18

Chapter 2: Operating the Graphing Calculator

ALPHA Key

Use A to enter an alphabet character. With the Basic keyboard, all 26 alphabet
characters from “A” up to “Z”, and space can be typed; the Advanced keyboard has all
26 characters accessible, as well as “

All functions associated with A are color coded purple, and are printed above
each key.

Note: Do not type out math figures (

names (Y1, Y2, etc.), list names (L1, L2, etc.), or matrix names
(mat A, mat B, etc.), etc. with A keys. If “SIN” is entered from
A mode, then each alphabet character — “S”, “I” and “N” —
will be entered as a variable. Call up the figure and equation
names from within the second functions and various menus
instead. If a colon (:) is used, data may continue to be entered in
more than one term.

Entering one
Alphabet
character

Example

Enter 2

1. Press # C to clear

× A on the screen.

the screen. Enter “2
pressing 2 |.

θ

”, “=”, “ : ”, and space.

sin, log

×” by

, etc.), graph equation

Entering 1 or
More Alphabet
characters

2. To enter “A”, press A;

the cursor pattern changes
to “A_” upon releasing the key.

3. Press A to call “A” at the
cursor.
After the entry, the cursor
pattern changes back to
normal.

To type more than one alphabet character, use @ then A
to apply the “ALPHA-LOCK”. When done, press A to escape
from the mode.

19

Chapter 2: Operating the Graphing Calculator

Math Function Keys

Basic keyboard

Advanced keyboard

Mathematical functions can be called up quickly with the Math Function keys. The
Math Function key sets for both the Basic and Advanced Keyboards are designed to
suit the needs of calculations at each level.

Math Function keys for the
Basic keyboard:

Q Reduces a fraction

/ Converts a number to a mixed fraction, if possible

< Converts a number to an improper fraction

> Converts a number to decimal form

i Gives an answer in quotient and remainder

% Specifies a percentage number

x Enters an variable “

Math Function keys for the

x” at the cursor

Advanced keyboard:

s Enters a sine function at the cursor

s Enters an arc sine function at the cursor

c Enters a cosine function at the cursor

20

Chapter 2: Operating the Graphing Calculator

c Enters an arc cosine function at the cursor

t Enters a tangent function at the cursor

t Enters an arctangent function at the cursor

l Enters a logarithm function at the cursor

0 Enters “10 to the

I Enters a natural logarithm function at the cursor

@ Enters “

“x”

X Enters a variable “

determined according to the calculator’s coordinate setup: “
rectangular, “θ” for polar, “T” for parametric, “n” for sequential.

Common Math Function
keys for both keyboards:

y Enters “

x Enters “

power

d Enters a mixed number.

xth power”, then sets the cursor at the “x”

e-constant to the power of x”, then sets the cursor at the

x”, “

θ

”, “T”, or “n”. The variable is automatically

x” for

2

” at the cursor, to raise a number to the second power

-1

” at the cursor, to raise a number to the negative first

b Enters a fraction.

a Enters an exponent.

_ By itself enters a “root” figure; the cursor will be set at “a”, the

depth.

21

Chapter 2: Operating the Graphing Calculator

Note: If a number precedes d b a and _, then the

number will be set as the first entry of the figure. Else, the first
entry is blank and the cursor flashes.

Examples

2 d 3 }
4 '

d
; 2 ' 3 } 4 '

+ Enters a “root” figure at the cursor

, Enters “ , ” (a comma) at the cursor

R Stores a number or a formula into a variable

r Recalls an item stored in a variable

z Brings up the VARS menu.

22

Chapter 2: Operating the Graphing Calculator

MATH, STAT, and PRGM Menu Keys

By using the M, S, and P keys, you can access many menu items for
complex calculation tasks. The appendix “List of Menu/Sub-menu Items” shows the
contents of each, with detailed descriptions of each sub-menu item.

Note that the contents of menu items differ drastically between the Basic keyboard
and the Advanced keyboard. For example, the P menu for the Basic mode
contains only one item (A EXEC), while in the Advanced mode there are three menu
items (A EXEC, B EDIT, and C NEW).

Example

Round the following number beyond the decimal point: 34.567

1. Press # C, then
M. The MATH menu
takes over the screen, as
shown to the right. MATH
menu items are displayed on
the left side of the screen.

Note: The example above is simulated on the Basic mode. There are

more menu items available with the Advanced mode.

2. Use the { and } keys to move the cursor up and
down the menu. As you scroll, you will see the corresponding
sub-menu contents (shown on the right side of the screen)
change.

3. Set the cursor at B NUM.
Menu items can also be selected by using shortcut keys (A

through H); in this example, simply press B to select B
NUM. There is no need to use A for this operation.

4. Press a shortcut key 2
to select 2 round(. The
screen now goes back to the

calculation screen, as
follows:

Another way of selecting the sub-menu item is to press '
(or E) on the menu item B NUM. The cursor will be
extended into the sub-menu on the right. Now, move the
cursor on the sub-menu down to 2 round(, then press E.

23

Chapter 2: Operating the Graphing Calculator

5. Type 3 4 . 5 6 7 ,
0 ), and press E.

SETUP Menu

Use this menu to verify basic configurations, such as to define the calculator’s editing
preferences, and scientific and mathematical base units.

Checking the
calculator’s
configuration

Tips: Using the arrow keys, move the cursor down to the C FSE

To check the current configuration of the calculator, press @,
then ;.

By entering menu items (B
DRG through H SIMPLE),
various setups can be changed.
To exit the SETUP menu, press
C.

Example

Display the calculation result of “1000

2

” in scientific notation.

1. Press @, then ;.
Within the SETUP menu,
press C, then 3 to
select 3 Sci under the C
FSE menu.

position, press E, and then move the cursor down to the 3
Sci position. Press E to select the sub-menu item.

2. The display goes back to the
SETUP menu’s initial screen.

3. Press C to exit the
SETUP menu.

24

4. Press # C to clear

the Calculation screen, type
1 0 0 0 y, then E.

SETUP Menu Items

DRG: For trigonometric calculations and coordinate conversions,

various angle units can be selected:

Deg Angle values to be set in degrees (default for Basic

mode)

Rad Angle values to be set in radians (default for Advanced

Chapter 2: Operating the Graphing Calculator

mode)

Grad Angle values to be set in gradients (for Advanced mode

only)

FSE: Various decimal formats can be set:

FloatPt Answers are given in decimal form with a floating

decimal point (default).

Fix Answers are given in decimal form. The decimal point

can be set in the TAB menu.

Sci Answers are given in “scientific” notation. For example,

“3500” is displayed as “3.500000000E3”. The decimal
point can be set in the TAB menu.

Eng Answers are given in “engineering” notation with

exponents set to be multiples of 3. “100000” will be

Note: If the value of the mantissa does not fit within the range

displayed as “100.0000000E3”, and “1000000” will be
shown as “1.000000000E6”. The decimal point can be
set in the TAB menu. (for Advanced mode only)

±0.000000001 to ±9999999999, the display changes to
scientific notation. The display mode can be changed
according to the purpose of the calculation.

25

Chapter 2: Operating the Graphing Calculator

TAB: Sets the number of digits beyond the decimal point (0 through 9).

The default is “9”.

COORD: Sets the calculator to various graph coordinate systems.

Rect Rectangular coordinates (default)

Param Parametric equation coordinates (for Advanced mode

only)

Polar Polar coordinates (for Advanced mode only)

Seq Sequential graph coordinates (for Advanced mode

only)

ANSWER: Sets the answer preference to various number formats.

Decimal (Real) Answers will be given in decimal form (default for

Advanced mode)

Mixed (Real) Answers will be given in mixed fractions, whenever

appropriate (default for Basic mode)

Improp (Real) Answers will be given in improper fractions, whenever

appropriate

x±yi (Complex) Answers will be given in complex rectangular form (for

Advanced mode only)

r∠θ (Complex) Answers will be given in complex polar form (for

Advanced mode only)

EDITOR: Sets the editing style to one of two available formats.

Equation Formulas can be

entered in a "type it
as you see it ap-

One line Formulas will be

26

proach" (default
setting).

displayed on one line.

Chapter 2: Operating the Graphing Calculator

Notes: Immediately after changing the EDITOR, the calculator will return

to the calculation screen and the following data will be cleared.

• ENTRY memory

• Equations stored in the graph equation window (Y)

• Equations temporally stored in the SOLVER window (@

')

* Resetting to the default settings (@ p E 1)

will also clear the above data.

Expression of up to 114 bytes can be entered in the Equation edit
mode. If the expression exceed the screen width, it is horizontally
extended.

Expression of up to 160 bytes can be entered in One-line edit
mode. if the expression exceed the screen width, it goes to the
next line.

SIMPLE: Sets the preference for handling reducible fractions.

Auto Fractions will automatically be reduced down (default)

Manual Fractions will not be reduced unless Q is pressed

Note: All the procedures in this manual are explained using the default

settings unless otherwise specified.

Precedence of Calculations

When solving a mathematical expression, this calculator inter­nally looks for the following figures and methods (sorted in the
order of evaluation):

1) Fractions (1/4, a/b,

2) Complex angles (∠)

3) Single calculation functions where the numerical value occurs
before the function (X2, X

, etc.)

-

1

, !, “ ° ”, “ r ”, and “ g ”)

4) Exponential functions (ab, a, etc)

5) Multiplications between a value and a stored variable/con-

6) Single calculation functions where the numerical value occurs

stant, with “×” abbreviated (2π, 2A, etc.)

after the function (sin, cos, tan, sin

-

1

, cos

-

1

, tan

ex, , abs, int, ipart, fpart, (–), not, neg, etc.)

-

1

, log, 10x, ln,

27

Chapter 2: Operating the Graphing Calculator

7) Multiplications between a number and a function in #6
(3cos20, etc. “cos20” is evaluated first)

8) Permutations and combinations (nPr, nCr)

9) ×, ÷

10

) +, –

11

) and

12

)or, xor xnor

13

) Equalities and nonequalities (<, ≤, >, ≥, ≠, =, →deg, →dms,

etc.)

Example

The key operation and calculation precedence

5 + 2 | s 30 + 25 | 5 a 3 E

3rd

• If parentheses are used, parenthesized calculations have

precedence over any other calculations.

Error Messages

The calculator will display an error message when a given
command is handled incorrectly, or when instructions cannot be
handled correctly such that the task cannot be processed further.
Various types of error messages are given to inform users the
types of situations to be remedied.
For example, performing the
following key strokes:

2nd

1st

4th

5th

6th

5 | E

will result in an error, and the
error message will be displayed.

In such a situation, you can go back to the expression to correct
its syntax by pressing ; or ', or you can erase the
entire line to start over by pressing C.

For a list of various error codes and messages, refer to the
appendix.

28

Chapter 2: Operating the Graphing Calculator

Resetting the Calculator

Use the reset when a malfunction occurs, to delete all data, or to set all mode values
to the default settings. The resetting can be done by either pressing the reset switch
located in the battery compartment, or by selecting the reset in the OPTION menu.

Resetting the calculator’s memory will erase all data stored by the user; proceed with
caution.

1. Using the reset switch

1. Pull down the notch to open the battery cover located on the
back of the calculator.

2. Place the battery cover back until the notch is snapped on.

3. Press O.
The verification window will

appear on the screen.

4. Press C to clear all the
stored data. Press O to
cancel resetting. After C
is pressed, the calculator's
memory will be initialized.
Press any key to display the
calculation screen.

Note: If the above verification window does not appear, remove the

battery cover and gently push the RESET switch with the tip of a
ball-point pen or a similar object.

DO NOT use a tip of a pencil
or mechanical pencil, a
broken lead may cause a
damage to the button mecha­nism.

29

Chapter 2: Operating the Graphing Calculator

• The message on the right may
occasionally appear. In this
case, repeat the procedure
from step 1 to prevent loss of
data.

2. Selecting the RESET within the OPTION menu

1. Press @, then p.

The OPTION menu appears.

2. While in the OPTION menu,

press E to select E
RESET; the RESET sub­menu items should appear on
the right side of the screen.

3. The first item 1 default set will initialize only the SETUP and

FORMAT settings, while the second item 2 All memory will
erase all memory contents and settings. To reset the memory,
select 2 All memory by pressing 2. The verification
window will appear.

4. Press the C key to clear

all data stored on the
calculator.
Press any key to continue.

30

Chapter 3

Basic Calculations —
Basic Keyboard

In this chapter, we explore more features of this calculator using the Basic Keyboard.
Features such as fraction to decimal conversion and the quotient-remainder key, as
well as basic arithmetic calculations, will be covered in this chapter.

Note: To try the examples in the chapter, it is required that the Basic Keyboard is

already set up by the user. To learn how to set up the Basic Keyboard, read
“Changing the Keyboard” in Chapter 1.

1. Try it!

The speed of light is known to be 186,282
miles (approximately 300,000 kilometers) per
second. That means light can go around the
earth 7 and a half times within a second!

Suppose you are standing at the equator.
While the earth rotates over the period of one
day, you also rotate around the globe at a
certain speed. Knowing the facts above, can
you figure out how fast you are traveling, in
miles per hour?

Since distance traveled = average speed
following equation can be formed to find out the circumference of
the earth (x miles):

x

× 7.5 = 186282

Then,

× time taken, the

Since you know the earth turns around once a day (which means,
in 24 hours), divide the above “x” with 24 to get a value in miles
per hour.

x = 186282 ÷ 7.5

24

× v = x

x

v =

24

31

Chapter 3: Basic Calculations — Basic Keyboard

CONCEPT

1. Enter a math expression, then perform the calculation.

2. Save a number into a variable, then recall the value later.

PROCEDURE

1. First, press #, then C to clear any screen entries.

2. Type 186282 = 7.5,

then press E. The
circumference of the earth is
thus obtained.

3. Store the answer in a variable. A variable is a symbol under

which you can store a numerical value.
We will use variable A to

store the circumference of
the earth. Press R to set
the “store” mode. Press
A A, then E to
store the answer. To call up
the stored answer, press A A E again.

Note: While checking the stored values, you may see “0”; this means

that no value is stored in the variable.

4. Now, since the value you

have stored under “A” is the
distance you will be travel­ling in 24 hours, divide the
number by 24. Press A
A = 24, then E.

So, you are travelling at 1034.9 miles/hour. That is fast!

32

Chapter 3: Basic Calculations — Basic Keyboard

2. Arithmetic Keys

Performing
addition,
subtraction,
multiplication
and division

E Executes an expression.

A Note about
expressions

There are various keys for arithmetic calculations. Use the +

- | =, _, ( and ) keys to perform
basic arithmetic calculations. Press E to solve an equation.

Example

• Calculate 1

# C 1 + 2 E

An expression is a mathematical statement that may use num­bers and/or variables that represent numbers. This works just like
a regular word sentence; one may ask “how are you?”, and you

+ 2.

may answer “okay.” But what if an incomplete sentence is thrown,
such as “how are”? You’ll wonder, “how are... what?”; it just
doesn’t make sense. A math expression needs to be complete as
well. 1 + 2, 4x, 2sinx + cosx form valid expressions, while “1
“cos” do not. If an expression is not complete, the calculator will
display an error message upon pressing the E key.

+ Enters a “+” sign for addition.

Example

• Calculate 12 + 34.

# C 1 2 + 3 4
E

- Enters a “–” sign for subtraction.

Example

• Subtract 21 from 43.

4 3 - 2 1 E

+” and

33

Chapter 3: Basic Calculations — Basic Keyboard

| Enters a “×” sign for multiplication.

Example

• Multiply 12 by 34.
1 2 | 3 4 E

= Enters a “÷” sign for division.

Example

• Divide 54 by 32.
5 4 = 3 2 E

When to leave
out the “×” sign

The multiplication sign can be left out when:
a. It is placed in front of an

b. It is followed by a variable or

c. It is followed by a scientific

Entering a number
with a negative value

_ Sets a negative value.

Example

open parenthesis.

a mathematical constant (π,
e, etc.):

function, such as sin, log,
etc.:

• Calculate
_ 1 2 | 4 E

Note: Do not use the - key to enter a negative value; use the

_ key instead.

34

-12 × 4.

Chapter 3: Basic Calculations — Basic Keyboard

( Enters an open parenthesis. Use with “)” as a pair, or the calcula-

tion will result in an error.

) Enters a closing parenthesis; a parenthesis left open will result in

an error.

Example

• Calculate (4 + 6) ÷ 5.

( 4 + 6 ) =
5 E

Note: Functions, such as “round(”,

automatically include an open parentheses. Each of these
functions needs to be closed with a closing parenthesis.

3. Calculations Using Various Function Keys

Use the calculator’s function keys to simplify various calculation tasks. The calculator’s
Basic Keyboard is specially designed to help you learn/solve fraction calculations
easier.

Q Simplifies a given fraction stored in the ANSWER memory.

(Set the SIMPLE mode to Manual in the SETUP menu to use this
key.)

Specifying no common factor

Simplify the fraction using the lowest common factor other than 1.

Example

1 b 12 ' + 5
b 12 E

Q E (Simplified by 2,

the lowest common factor of 12
and 6.)

Q E (Simplified by 3,
the lowest common factor of 6
and 3.)

35

Chapter 3: Basic Calculations — Basic Keyboard

Specifying a common factor

Simplify the fraction using the specified common factor.

Example

1 b 12 ' + 5
b 12 E

Q 6 E (Manually

specify 6, the Greatest Com­mon Factor of 12 and 6, to
simplify the fraction.)

Note: If the wrong number is specified for a common factor, an error will

occur.
Q is effective in a fraction calculation mode only (when the

ANSWER mode is set to Mixed or Improp in the SETUP menu).

/ Converts an improper fraction to a mixed number.

Example

• Change

12

to a mixed

5

number.
12 b 5 ' /

E

< Converts a mixed number to an

improper fraction.

Example

2

• Change

2

to an improper fraction.

5

< E

> Converts a fraction to a decimal

number.

Example

• Change

12

to a decimal

5

number.
> E

Note: Above three conversions will not affect the ANSWER settings in

the SET UP menu.
If a decimal number is not rational, fraction conversion will not

function and display the answer in decimal format.

36

Chapter 3: Basic Calculations — Basic Keyboard

i Performs an integer division, and returns a quotient and a

remainder.

Example

• Get a quotient and a remain­der of 50

÷ 3.

50 i 3 E

* Quotient value is set to Ans

memory and remainder is not
stored.

y Squares the preceding number.

Example

• Obtain the answer to 122. (= 144)
12 y E

Note: When no base number is entered, the base number area will be

left blank and just the exponent appear.

C y ;1 2 ' E

d Enters a mixed number.

Example

5

• Enter

4

6

4 d 5 ' 6 E

Note: When no value is entered prior to this key, the number areas will

be left blank.
* If the calculator is set to one-line mode, d enters “ ”

(integer-fraction separator) only. Use d in combination with
b as follows.

5

• Enter

4

in one-line mode

6

4 d 5 b 6 E

* Integer part of the mixed

number must be a natural
number. A variable can not be
used. Equation or use of parenthesis, such as (1

+2) 2

¬

3 or

(5) 2¬3, causes syntax error.

* When a numerator or a denominator is negative, the calculator

will cause error.

37

Chapter 3: Basic Calculations — Basic Keyboard

b Enters a fraction, setting the preceding number as its numerator.

* If the calculator is set to one-line mode, then “¬” will be entered

instead. For example, “2¬5” indicates “

Example

2

• Calculate

3

+

5

.

4

2 b 5 ' + b
3 ' 4 ' E

a Enters an exponent, setting the preceding number as its base.

Example

• Raise 4 to the 5th power. (= 1024)

4 a 5 E

2

”.

5

Note: When no base value is entered, “a

b

” will be entered with both

number areas left blank.

C a ; 4 ' 5 E

When calculating x to the power of m-th power of n, enter as
follows;

2

• Calculate 2

3

(= 512)

2 a 3 a 2 E

2

The above calculation is interpreted as 2

3

= 29.

If you wish to calculate (23)2 = 82, press ( 2 a 3 '

) a 2 E.

, Enters a comma “ , ” at the cursor. A comma is required in some

of the MATH functions. For more information, refer to the next
section “Calculations Using MATH Menu Items” in this chapter.

R Stores a number in a variable.

Example

• Let A = 4, and B = 6.

Calculate A + B.
4 R A A E
6 R A B E
A A + A B E

38

Chapter 3: Basic Calculations — Basic Keyboard

x Enters an “x”, an unknown variable. Use this key when working

with graph equations. Refer to Chapter 4 “Basic Graphing
Features” to learn how to use this feature.

Second
functions

To access the second function of a key (printed above the keys in
yellow), press and release @, then press the key you want to
use.

% Set the preceding value as a percentage.

Example

• Get 25% of 1234.
1 2 3 4 | 2 5 @

% E

*Percentage must be a positive

value equal to or less than

100.

-

x Enters “x

1

”, and returns an inverse by raising a value to the -1

power. The inverse of “5”, for example, is “

Example

• Raise 12 to the

-1 power. (= 0.083333333)

1

”.

5

1 2 @ x E

-

Note: When no base number is entered, “x

1

” will be entered, with “x” left

blank.

C @ x ;1 2 E

_ Enters “a”.

Example

•Bring 4 to the 5th root. (= 1.319507911)
5 @ _ 4 E

Note: When no depth of power is entered, “a” is entered, with both

number areas left blank.

C @ _ 5 ' 4 E

+ Enters a square root symbol.

Example

• Obtain the square root of 64. (= 8)
@ + 6 4 E

39

Chapter 3: Basic Calculations — Basic Keyboard

r Recalls a variable.

Example

• Set C = 8.

8 R A C E
Recall the value of C.

@ r A C E

z Accesses the VARS menu. Refer to chapters 4 and 6 to learn how

to use each item in this menu.

{ } Enter braces to group numbers as a list.

b Recalls the previous answer. Use this key to incorporate the

answer to the previous calculation into an expression.

Example

•Perform 3

× 3.

3 | 3 E
Subtract the value of the

previous answer from “10”.
1 0 - @ b E

Note: b can be considered as a variable; its value is automatically

set when E is pressed. If b is not empty, then pressing
+, -, |, or = will recall “Ans” and places it at
the beginning of an expression. If “1” was the previous answer,
then pressing + 4 E will result in “5”.

40

Chapter 3: Basic Calculations — Basic Keyboard

e Recalls the previous entry. This is useful when you want to modify

the previous entry, rather than reenter the whole expression over.

Example

• Calculate 4

× 6.

4 | 6 E
Next, calculate 4 × 8.
@ e B 8 E

Note: Executed expressions are stored in a temporary memory in the

executed order. If the temporary memory is full, the oldest data is
automatically deleted. Be aware that e may not function on
these occasions.

A maximum of 160 bytes can be stored in the temporary memory.
The capacity may vary when there are division codes between
expressions.

When switching from equation edit mode to one-line edit mode in
the SETUP menu, all the numerical and graph equations stored in
the temporary memory are cleared and cannot be recalled.

$ Enters “pi”. Pi is a mathematical constant, representing the ratio

of the circumference of a circle to its diameter.

Example

• Enter “2π”. (= 6.283185307)
2 @ $ E

j Calls up the CATALOG menu. From the CATALOG menu, you can

directly access various functions in the menus.

• Functions are listed in alphabetic order.

•Move the cursor using the {/} keys and press E
to access or enter the function.

• Press A and an appropriate alphabetic key (A to Z) to
navigate the catalog.

• Press A

+ {/} to scroll the catalog page by page

and press @ + {/} to jump to the beginning or the
end of the catalog.

• See page 246 for details.

41

Chapter 3: Basic Calculations — Basic Keyboard

4. Calculations Using MATH Menu Items

The MATH menu contains functions used for more elaborate math concepts, such as
trigonometry, logarithms, probability, and math unit/format conversions. The MATH
menu items may be incorporated into your expressions.

Note: The default angle measurement unit while using the calculator’s

Basic Keyboard is degrees. If you wish to work in radians, then
the configuration must be changed in the SET UP menu. For
more information, see page 25.

A Note about
Degrees and
Radians

Note: The following examples show keystrokes with keyboard shortcuts.

1 sin Enters a sine function to be used in a trigonometric calculation.

The degree and radian systems are two of the basic methods of
measuring angles. There are 360 degrees in a circle, and “2-pi”
radians. 1 degree is equal to pi/180 radians. “Then, what’s this
pi?”, you may ask. Pi, or to use its symbol “π”, is the ratio of the
circumference of a circle to its diameter. The value of π is the
same for any circle “3.14...”, and it is believed to have an infinite
number of digits beyond the decimal point.

A CALC

The CALC sub-menu contains items to be used in calculations
containing trigonometric and logarithmic functions.

It is also possible to select a sub-menu item using the cursor
keys.

Example

• Calculate sine 90°.

M A 1 9 0 E

2 cos Enters a cosine function to be

used in a trigonometric calcula­tion.

Example

• Calculate cosine 60°.

M A 2 6 0 E

42

Chapter 3: Basic Calculations — Basic Keyboard

3 tan Enters a tangent function to be used in a trigonometric calcula-

tion.

Example

• Calculate tangent 45°.
M A 3 4 5 E

4 log Enters a “log” function for a logarithmic calculation

Example

• Calculate log 100.

M A 4 1 0 0
E

5 10xEnters a base of 10, setting the

cursor at the exponent.

Example

• Calculate 5

× 10

5

.

5 | M A 5 5 E

B NUM

Use the NUM sub-menu items when converting between various
number systems.

1 abs( abs(

Returns an absolute value.
*A real number, a list, matrix, variable, or equation can be used

as values.

Example

• Find an absolute value of
“

-40.5”.

M B 1 _ 4 0
. 5 E

value

)

43

Chapter 3: Basic Calculations — Basic Keyboard

2 round( round(

Returns the rounded value of the term in parentheses. A rounding
point can be specified.

*A real number, a list, matrix, variable, or equation can be used

as values.

Example

• Round off 1.2459 to the nearest hundredth. (= 1.25)

M B 2 1 . 2 4 5 9 , 2 ) E

3 ipart ipart

Returns only the integer part of a decimal number.

*A real number, a list, matrix, variable, or equation can be used

as values.

Example

• Discard the fraction part of 42.195. (= 42)

M B 3 4 2 . 1 9 5 E

value [, digit number of decimals]

value

)

4 fpart fpart

Returns only the fraction part of a decimal number.

*A real number, a list, matrix, variable, or equation can be used

as values.

Example

• Discard the integer part of 32.01. (= 0.01)

M B 4 3 2 . 0 1 E

5 int int

value

Rounds down a decimal number to the closest integer.

Example

• Round down 34.56 to the nearest whole number. (= 34)

M B 5 3 4 . 5 6 E

value

44

Chapter 3: Basic Calculations — Basic Keyboard

6 min( min(

Finds and returns the minimum value within a list of numbers. To
define a list of more than two numbers, group the numbers with
brackets (@ { and @ }), with each element
separated by a comma.

Example

• Find the smallest value among 4, 5, and

M B 6 @ { 4 , 5 , _ 9
@ } ) E

7 max( max(

Finds and returns the maximum
value within a list of numbers.

Example

• Find the largest value among 4, 5, and

M B 7 @ { 4 , 5 , _ 9
@ } ) E

list

list

)

-9.

)

-9.

8 lcm( lcm(

Returns the least common multiple of two integers.

Example

• Find the least common multiple of 12 and 18.
M B 8 1 2 , 1 8 ) E

9 gcd( gcd(

number

Returns the greatest common
divisor of two integers.

Example

• Find the greatest common divisor of 16 and 36.
M B 9 1 6 , 3 6 ) E

natural number, natural number

natural number, natural

)

)

45

Chapter 3: Basic Calculations — Basic Keyboard

0 remain

natural number

Returns the remainder of a division.

Example

• Obtain the remainder when
123 is divided by 5.

1 2 3 M B 0 5

E

CPROB

Use the PROB sub-menu items for probability calculations.

1 random random

Returns a random decimal number between 0 and 1.

Example

• Make a list with three random
numbers.

remain

natural number

[(number of trial)]

Note: Set the “FSE” to “Fix” and “TAB”

to “0”.

@ { M C
1 | 100 , M C 1 | 100 ,
M C 1 | 100 @ } E

Note: The random functions (random, rndInt(, rndCoin, and rndDice)

will generate different numbers every time when the display is
redrawn. Therefore, the table values of the random functions will
be different every time. When in case of random-based graphing
calculations, the tracing values and other parameters of the graph
will not match the graph's visual representation.

2 rndInt( rndInt(

minimum value, maximum value [, number of trial]

Returns a specified number of random integers, between a
minimum and a maximum value.

Example

• Produce eight random integers, ranging between values of 1

)

and 6.
M C 2 1 , 6 , 3 ) E

* Minimum value: 0 ≤

Maximum value: 0 ≤ x
Number of trial: 1 ≤ n ≤ 999

46

x

min

max

≤ 10

≤ 10

10

10

Chapter 3: Basic Calculations — Basic Keyboard

3 rndCoin rndCoin

Returns a specified number of random integers to simulate a coin
flip: 0 (head) or 1 (tail). The size of the list (i.e., how many times
the virtual coin is thrown) can be specified. (The same as rndInt
(0, 1, number of times))

Example

• Make the calculator flip a
virtual coin 4 times.

M C 3 ( 4
) E

4 rndDice rndDice

Returns specified number of random integers (1 to 6) to simulate
rolling dice. The size of the list (i.e., how many times the die is
thrown) can be specified. (The same as rndInt (1, 6, number of
times))

Example

[(number of trial)]

[(number of trial)]

• Make the calculator roll a virtual die 11 times.
M C 4 ( 11 ) E

5 nPr Returns the total number of different arrangements (permuta-

tions) for selecting “r” items out of “n” items.

nPr

=

n!

(n – r)!

Example

•How many different ways can
4 people out of 6 be seated in
a car with four seats?

6 M C 5 4 E

47

Chapter 3: Basic Calculations — Basic Keyboard

6 nCr Returns the total number of combinations for selecting “r” item out

of “n” items.

nCr

=

n!

r!(n – r)!

Example

•How many different groups of
7 students can be formed with
15 students?

1 5 M C 6 7

E

7 ! Returns a factorial.

Example

• Calculate 6

× 5 × 4 × 3 × 2 × 1.

6 M C 7 E

D CONV

CONV sub-menu items are to be used when converting a number
in decimal form (degrees) to a number in sexagesimal form

Sexagesimal
and Degree
System

1 →deg Ta kes a number in sexagesimal form, and converts it into a

(degrees, minutes, seconds), or vice versa.

The “base 60” sexagesimal system, as well as the minutes­second measurement system, was invented by the Sumerians,
who lived in the Mesopotamia area around the fourth millennium
B.C.(!) The notion of a 360 degrees system to measure angles
was introduced to the world by Hipparchus (555-514 B.C.) and
Ptolemy (2nd cent. A.D.), about 5000 years later. We still use
these ancient systems today, and this calculator supports both
formats.

decimal number.

Example

• Convert 34° 56’ 78” to
degrees.

3 4 M E 1 5 6

M 2 7 8 M
3 M D 1
E

48

Chapter 3: Basic Calculations — Basic Keyboard

2 →dms Tak es a number in decimal form (in degrees), and converts it into

a sexagesimal number. To enter a number in sexagesimal form,
use items in the “ANGLE” sub-menu, described in the next
subsection of this Chapter.

Example

• Show 40.0268 degrees in
degrees, minutes, and
seconds.

4 0 . 0268 M D
2 E

E ANGLE

The Basic mode has two angle modes: Deg (degree) and Rad
(radian). Use the E ANGLE menu to enter a degree value in Rad
mode or a radian value in Deg mode. (The gradient mode is not
included in the Basic mode. Refer to Chapter 5 for details.)

1 ° Inserts a degree, and sets the preceding value in degrees.

2 ’ Inserts a minute, and sets the preceding value in minutes.

3 ” Inserts a second, and sets the preceding value in seconds.

Example

• Enter 34° 56’ 78”.
3 4 M E 1
5 6 M 2 ← “E ANGLE” remains selected;
7 8 M 3 type the number to enter the symbols.

E

4 r Enters an “r”, to enter a number in radians.

Example

•Type 2 radian.
2 M E 4 E

49

Chapter 4

Basic Graphing Features
— Basic Keyboard

This chapter takes the knowledge you have gained in Chapter 3 several steps further.
Note: To try the examples in this chapter, it is required that the Basic Keyboard is

already set up by the user. To learn how to set up the Basic Keyboard, read
“Changing the Keyboard” in Chapter 1.

1. Try it!

There are two taxi cab companies in your city, Tomato Cab and Orange Cab,
with different fare systems. The Tomato Cab charges $2.00 upon entering the
taxi cab, and $1.80 for each mile the taxi travels. The Orange Cab, on the other
hand, charges $3.50 plus $1.20 per mile. This means that taking the Tomato
Cab will initially cost less than
going with the Orange Cab, but
will be more expensive as you
travel longer distances.

Suppose you need to go to a place
3 miles away from where you are
now. Which cab company should
you take to save money?

Two math expressions can be derived from the above fare
systems. If “y” represents the cost, while “x” represents the
mileage, then:

y = 2 + 1.8x.................... Tomato Cab’s fare system

y = 3.5 + 1.2x ................ Orange Cab’s fare system

Use the calculator’s graphing capabilities to figure out the
approximate point where the Orange Cab gets ahead of the
Tomato Cab, in terms of cost performance.

50

CONCEPT

PROCEDURE

Chapter 4: Basic Graphing Features — Basic Keyboard

1. By using two linear graphs, the approximate crossing point

can be found.

2. The exact crossing point can be found with the TABLE

function.

1. Press Y to enter the Graph Equation window. Six equa-

tion entry areas appear, from “Y1=” to “Y6=”. Since we need
only two equations in this exercise, let’s use “Y1=” and “Y2=”.

2. By default, the cursor should be placed on the right side of the

“Y1=” equation, next to the equal sign. If this is not so, use the
cursor keys to bring the cursor to the “Y1=” line, then press the
C key to clear any entries. The cursor will automatically be
placed to the right of the equal sign.

3. Enter the first equation, “2

+ 1.8X”, to represent the Tomato

Cab’s fare system.
2 + 1 . 8 x
Use the x key to enter the “x”, representing the distance

in miles.

4. When the equation line is complete, press E. The first

equation is now stored, and the cursor automatically jumps to
the second line, where the second equation can be entered.

5. At the second line, press

C to clear any entries,
then enter “3.5

+ 1.2X” to

represent the Orange Cab’s
fare system. When done
entering the equation, press
E. The two equations are now ready to graph.

6. Press G to draw the graphs.

To draw a graph, “=” must be highlighted. If not, move the
cursor to “=” of the targeted equation and press E to draw
a graph, and press E again not to draw a graph.

51

Chapter 4: Basic Graphing Features — Basic Keyboard

Graph Basics

The graph examples in this exercise are called X-Y graphs. An
X-Y graph is quite useful for clearly displaying the relationship
between two variables.

7. Let’s take a look at the
graph. The vertical axis
represents the Y value, while
X is represented by the
horizontal axis. It appears
that the two diagonal lines
cross at the point where the X value is somewhere between 2
and 3, indicating that Orange Cab costs less than the other,
after 3 miles of traveling.

8. Next, press T to find the
values per graph increment.
When the traveling distance
is 2 miles, the Tomato Cab
charges 30 cents less overall
than the Orange Cab, but it
costs 30 cents more at 3 miles. To make the X increment
smaller, press @ y.

9. When the Table setting window appears, move the cursor
down to “TBLStep”, type . 5, and press E. Now
the Y values will be sampled at every 0.5 mile.

10

. Press T to show the

table again. It indicates that
when the X value is 2.5, both
Y1 and Y2 values are 6.5. It
is now clear that if you are
traveling 2.5 miles or more,
the Orange Cab costs less.

2. Explanations of Various Graphing Keys

Y: Displays the Graph Equation window. Up to 10 different equations

can be entered.
After the graph expression is entered, press E to store the
equation.

52

Chapter 4: Basic Graphing Features — Basic Keyboard

= : The expression can be represented as a graph.

= : The expression cannot be drawn as a graph.

•Move the cursor pointer to the “=” sign and press E to

change between to-draw and not-to-draw.

Note: To switch the window back to the calculation screen, simply press

the # key.

G: Draws a full-screen graph based on the equation(s) entered in the

Graph Equation window. To cancel the graph drawing, press
O.

Note: If no equations are entered in the Graph equation window, only

the vertical (Y) and horizontal (X) axis will be displayed upon
pressing the G key.

T: Displays the graph values in a table. The default sample incre-

ment value of the graph’s X axis is “1”.

Z: Displays the ZOOM menu. Within the ZOOM menu, various

preferences can be set for the graph appearance on zooming in/
out .
The menu items with each function and the sub-menu items are
described below:

A ZOOM

There are a myriad of tools under this menu item, by which the
graph can be zoomed in/out in various styles. Press “A” within the
ZOOM menu to select this menu item.

1 Auto According to the WINDOW setup, the graph will be

zoomed in by adjusting the “Ymin” (the minimum Y
value) and “Ymax” (the maximum Y value) according to
the “Xmin” (the minimum X value) and “Xmax” (the
maximum X value). When this item is selected, the

Note: The “Auto” sub-menu item is directly affected by how the WIN-

DOW items are set up. Refer to the W key section in this
chapter to learn how to set up the Xmin and Xmax items.

graph will automatically be redrawn.

53

Chapter 4: Basic Graphing Features — Basic Keyboard

2 Box A box area can be specified with this sub-menu tool so

that the area within the box will be displayed full
screen.

To select a box area to zoom:

1. While the ZOOM menu item is selected within the

ZOOM window, press 2 to select 2 Box.

2. The graph appears on the screen. Use the cursor
keys to position the cursor at a corner of the
required box area. Press E to mark the point as
an anchor.

3. Once the initial anchor is set, move the cursor to a
diagonal corner to define the box area. When the
required area is squared off, press E.
If a mistake is made, the anchor can be removed by
pressing the C key.

4. The graph will automatically be redrawn.

3 In A zoomed-in view of the graph will be displayed, sized

according to the B FACTOR set up under the ZOOM
menu. For example, if the vertical and horizontal zoom
factors are set to “2”, then the graph will be magnified
two times. Refer to the B FACTOR segment of this
section for more information.

4 Out The graph image will be zoomed out according to the B

FACTOR setup under the ZOOM menu.

5 Default The graph will be displayed with default graph setting

(Xmin =

-10, Xmax = 10, Xscl = 1, Ymin = -10, Ymax =

10, Yscl = 1)

6 Square Set the same scale for X and Y axes. The Y-axis scale

7 Dec Sets the screen dot as 0.1 for both axes. The graph will

8 Int Sets the screen dot as 1.0 for both axes. The graph will

9 Stat Displays all points of statistical data set.

54

is adjusted to the current X-axis scale. The graph will
be redrawn automatically.

then be redrawn automatically.

then be redrawn automatically.

Chapter 4: Basic Graphing Features — Basic Keyboard

B FACTOR

Use this menu to set the vertical and horizontal zooming factor.
The factor set under this menu directly affects the zoom rate of
the 3 In and 4 Out sub-menu tools under the ZOOM menu, as
described above.

To set the zooming factor, do the following:

1. Within the
B FACTOR menu,
press E to
activate the setup
tool.

2. When the “Zoom factor” window appears, the cursor
is automatically placed at “X_Fact=”. The default
zoom factor is 4; enter the required value here.

C POWER

2

1

x

–1

x

2

3

x

D EXP

3. Pressing E after entering a value will switch the
cursor position to “Y_Fact=”. Enter the required
zooming factor, and press E.

4. To go back to the ZOOM menu, press the Z
key.

Use this zooming tool when the equation contains a
form of “x2”.

Use this zooming tool when the equation contains a

-

form of “

1

x

”.

Use this tool to zoom correctly when the equation
contains a form of “x”.

1 10

2 log X Use this tool when the equation contains a form of “log

X

Use this tool when the equation contains a form of

x

“10

”.

x”.

55

Chapter 4: Basic Graphing Features — Basic Keyboard

E TRIG

1 sin X Use this when the equation contains a sine function.

2 cos X Use this when the equation contains a cosine function.

3 tan X Use this when the equation contains a tangent func-

tion.

F STO

Under this menu item there is one tool that enables the storing of
graph window settings.

1 StoWin By selecting this sub-menu item, the current graph

window setup will be stored.

Note: The actual graph image will not be stored with this tool.

G RCL

Under this menu item there are two tools that enable the recalling
of the previous graph window setup:

1 RclWin On selecting this sub-menu item, the previously stored

window setup will be recalled, and the graph will be
redrawn accordingly. If no window setup has been
stored previously, the default graph window setup will
be used.

2 PreWin On selecting this sub-menu item, the window setup

prior to the current zoom setup will be recalled, and the
graph will be redrawn accordingly.

56

Chapter 4: Basic Graphing Features — Basic Keyboard

U: Press this button to trace the graph drawn on the screen, to

obtain the X-Y coordinates:

1. While the graph is displayed,

press the U key. The
cursor appears, flashing on
the graph line, with the
present X-Y coordinates.

2. Trace the graph using the ; or ' keys. The ; key
decreases the value of x, while the ' key increases it.

3. Pressing the U key again will redraw the graph, with the
cursor at the center of the screen. If the cursor is moved
beyond the range of the screen, pressing the U key will
redraw the screen centered around the cursor.

4. When done, press the C key to escape the tracing
function.

If more than one graph is displayed on the screen, use the {
or } keys to switch the cursor from one graph to the other.

Note: If the U key is not activated, the cursor will not be bound to

the graph. Pressing the ;, ', {, or } keys will
position the free-moving flashing cursor on the graph display.

W: Displays the graph window setup. The setup values — the

minimum/maximum X/Y values, and X/Y-axis scale — can be
changed manually:

1. While the graph is displayed
on the screen, press the
W key. The following
window appears, with the
cursor set at “Xmin=”.

2. The required X-minimum value can be entered here. This
limits the left boundary of the graph window. For example, if

3. Once the “Xmin=” value is entered (“0”, for example), press

“Xmin=” is set to “0”, then the portion of the graph’s Y-axis to
the left will not be displayed.

E. The left limit of the graph is now set, and the cursor
moves to “Xmax=”.

57

Chapter 4: Basic Graphing Features — Basic Keyboard

4. Now the right boundary of the graph can be set. Enter the

required value here (“3”, for example), and press E.

Note: The “Xmax=” value cannot be set equal to or smaller than the

value of “Xmin”. If so done, the calculator will display an error
message upon attempting to redraw the graph, and the graph will
not be displayed.

5. The next item “Xscl=” sets the frequency of the X-axis indices.
The default value is “1”. If, for example, the value is set to
“0.5”, then indices will be displayed on the X-axis at incre­ments of 0.5. Enter the required “Xscl=” value (“0.5”, for
example), and press E.

6. The “Ymin=”, “Ymax=”, and “Yscl=” can be set, as was
described for “Xmin=”, “Xmax=”, and “Xscl=” above.

7. When done, press the G key to draw the graph with the
newly configured window setup.

3. Other Useful Graphing Features

": Splits the display vertically, to show the graph on the left side of

the screen while showing the X-Y values in a table on the right.
The cursor is positioned on the table, and can be scrolled up/
down using the { or } keys.

Graph and table Graph and equation

• When @ " are pressed on the graph screen, the graph

and table are displayed on the same screen.

• When @ " are pressed on the equation input screen,

the graph and equation are displayed on the same screen.

58

Chapter 4: Basic Graphing Features — Basic Keyboard

The following illustration shows these relationships.

Y

G

G@ " Y@ "

GY

@ "

• The split screen is always in the trace mode. Therefore, the
cursor pointer appears on the graph. Accordingly, the coordi­nate values are displayed reverse in the table and in the
equation at which the cursor pointer is located is also displayed
reversely.

• Using ; or ', move the cursor along the graph.
(Values displayed reverse in the table are also changed
accordingly.)

• When two or more graphs are displayed on the screen, the
desired graph is selected using { or }. (The table or
equation on the right of the screen is also changed accordingly.)

• The table on the split screen does not relate to the table
settings on the full-screen table.

• The table on the split screen is displayed in units of trace
movement amount based on the cursor pointer position on the
graph screen. When the full-screen table is displayed by
pressing T, a different table may appear on the screen.

• When the EXPRES or Y’ is set to ON on the FORMAT menu,
the equation or coordinates are displayed on the graph screen.

• Only equations to be graphed are displayed on the split screen.

• Press G or T on the split screen to display the full­screen of the graph or table. To exit the split screen, press any
of other function keys.

59

Chapter 4: Basic Graphing Features — Basic Keyboard

k: Calculations can be performed on the entered graph equation(s).

Press @ k to access. The following 6 sub-menu tools are
available:

1 Value With this sub-menu tool, the Y value can be obtained

by entering an X value. The flashing graph cursor will
then be placed in that position on the graph. If more
than one graph equation is set, use the { or
} keys to switch to the equation you wish to work
with.

Note: If the entered X value

is incalculable, an
error message will be
displayed. Also, if the
Y value exceeds the
calculation range, then “----” will be displayed instead.

2 Intsct With this tool, the intersection(s) of two or more graphs

can be found, where the flashing cursor will be placed.
When the intersection is found, then the X-Y coordi­nates of the intersection will be displayed at the bottom
of the screen. If there is more than one intersection,
the next intersection(s) can be found by selecting the
tool again.

Note: If there is only one

graph equation
entered there will be
no other graph(s) to
form an intersection,
so selecting this tool
will result in an error.

3 Minimum Finds the minimum of the given graph, and places the

Note: If the given graph has

60

flashing cursor at that position.

no minimum value,
an error message will
be displayed.

Chapter 4: Basic Graphing Features — Basic Keyboard

4 Maximum Finds the maximum of the given graph, and places the

flashing cursor at that position.

Note: If the given graph has

no maximum value,
an error message will
be displayed.

5 X_Incpt Finds an X-intercept (a crossing point of the graph on

the X-axis) of the given graph, and places the flashing
cursor at that position. If there is more than one X­intercept, the next X-intercept can be found by select­ing the tool again.

Note: If the graph has no X-

intercept, an error
message will be
displayed.

6 Y_Incpt Finds an Y-intercept of the given graph, and places the

flashing cursor at that position.

Note: If the graph has no Y-

intercept, an error
message will be
displayed.

Note: The result may be different when the ZOOM function is

used.

d: There is an extensive set of features under this menu item that

enhance the graphing capabilities of the calculator. Only the
shading function will be covered here; refer to Chapter 6 “Ad­vanced Graphing Features — Advanced Keyboard” in this manual
for more information.

To access the DRAW menu, press @ d.

An inequation can be expressed with the calculator’s graphing
capability. Here’s how:

1. Set up a simple graph within the Graph Equation window.

Enter “X

2

” for Y1, for example.

61

Chapter 4: Basic Graphing Features — Basic Keyboard

2. Press @, and d to enter the DRAW menu, then press

G to select G SHADE. The SHADE sub-menu appears.

3. Press 1 to select 1 SET.

The “Set shade” window
appears.

4. Using the cursor keys, move
the cursor pointer to the
appropriate position.

5. Press @ z A.

6. Press 1 to select Y1.

7. When the value is set, press
the G key. The graph will
be redrawn.

8. Let’s add another inequation,
so that the area where the
two inequality overlap can be shaded. Press the Y key,
and enter another simple graph equation such as “X

+ 4” for

“Y2”.

9. Now, return to the SHADE menu by pressing @ d,
and G. Press 1 to select “1 SET”.

10

. Within the “Set shade” window, add the second equation at the

right of the topmost inequation. Use the ' or ; key to
position the underscore cursor, then select “Y2” using the
VARS menu.

11

. Press the G to redraw the graph with the new shading

appearance.

62

Chapter 4: Basic Graphing Features — Basic Keyboard

f: The graph appearance can be set and verified under this menu.

Press @ f to access.

A –––––– Displays the current FORMAT settings. The default

setting is:

OFF (for the graph equation to be displayed

on the graph)

OFF (for displaying numeric derivatives on

the graph)

ON (for displaying the X/Y axis on the

graph)

OFF (for displaying a grid on the graph)

B EXPRES This sets whether or not graph equations are displayed

on the graph screen (in the trace mode, etc.). To
display the equations on the graph, select 1 ON by
pressing 1 at this menu item.

C Y’ The numeric derivative (dx/dy) can be displayed on the

graph screen (in the trace mode, etc.). To activate this
function, select 1 ON by pressing 1 at this menu
item.

D AXIS The graph axis can be set invisible with this menu item.

To hide the X/Y axis of the graph, select 2 OFF by
pressing 2 at this menu item.

E GRID The graph display can be backed with an X-Y grid. To

show the grid on the graph, select 1 ON by pressing
1 at this menu item.

Substitution feature

• The substitution feature allows you to input an equation using characters and
variables, and then substitute numeric values for the characters to draw the graph.

• The substitution feature is valid only in the rectangular coordinate system.
Using this feature, any number of numeric value sets can be substituted while
referring to the graph drawing screen. This clearly shows the changes in the graph
depending on numeric values.
For example, the graph for “Y1 = AX
numeric values for variables A, B, C, and D of the equation.

3

+ BX2 + CX2 – D” is drawn by substituting

63

Chapter 4: Basic Graphing Features — Basic Keyboard

• 22 kinds of variables (characters), A to Z except for R, T, X, and Y can be used for
the substitution feature.

• Up to seven variables (characters) can be used for one equation. (If the equation
contains more than seven variables (characters), up to seven characters from the
top of the equation are determined as variables and subsequent characters are
ignored.)

• If you attempt to execute an equation containing no variables, the substitution
feature becomes invalid and the error message, “NO VARIABLE”, appears on the
screen.

•To input the equation, there are the following two methods after Y has been
pressed. After the equation has been input, the same operations apply to subse­quent steps.

Example

Substitute numeric values under the conditions that “Y1 = AX

2

+

BX + C” and “Y2 = AX” have been input.
Equation Entry screen

The cursor pointer is located at
Y1. Drawing of both graphs Y1
and Y2 is valid.

1. Press @ ,.

The substitution feature
screen will appear. The
equation on which the cursor
pointer is located and its
variables are displayed on
the right of the screen.
If variables (characters) contain no values, the graph is not
drawn.
If independent memories A to C contain any numeric values,
the graph is drawn based on these values.

* If the equation (in this example, Y1) on which the cursor is

located contains no variables, the substitution feature screen
will not appear.

64

Chapter 4: Basic Graphing Features — Basic Keyboard

2. Press 2 E.

(2 is input to A.)
The graph for “Y1 = 2X

2

” is
drawn. (Since B and C have
no values, they are ignored.)
At this time, the graph for Y2
is also drawn. Y2 also uses variable A which is used in Y1.
Therefore, the drawing of the graph for Y2 is also valid.

* If you need to draw only the graph for Y2, it is necessary to

change variables (characters) or make the graph drawing for
Y1 invalid.

3. Press 1 E.

(1 is input to B.)
The graph is changed from
“Y1 = 2X

2

” to “Y1 = 2X2 +

1X”.

4. Press _ 3 E.

(

-3 is input to C.)

Now, the graph for “Y1 = 2X

2

+ 1X – 3” is drawn on the

screen.

Next, change variable A from 2 to 5 and see how the graph
changes.

1. Press { { 5 E.

(The cursor is moved from C
to A and 5 is input.)
The slope of the graph
becomes sharp.

*Move the cursor accordingly and substitute other numeric

values for variables to view how the graph changes.

* The trace function cannot be used in the substitution feature.

(When U is pressed, the full-screen graph will appear.)

65

Chapter 5

Advanced Calculations —
Advanced Keyboard

Note: To try the examples in the chapter, it is required that the Advanced Keyboard is

already set up by the user. To learn how to set up the Advanced Keyboard, read
“Changing the Keyboard” in Chapter 1.

1. Try it!

The Mendocino Tree, a coast redwood growing in Montgomery Woods State
Reserve in California, is known to be the tallest living tree in the world. You are
to find out how tall the tree is by using the following factors:

• The distance from you to the bottom of the
tree is exactly 505.8 feet, and the tree
stands vertically.

• The angle of elevation between the top
and the bottom of the tree is 36 degrees

CONCEPT

If the base length of the right triangle is 505.8 feet, and the angle
of elevation is 36 degrees, then the following expression can be
derived:

the height of the Mendocino tree (ft.) = 505.8 ft.

1. Verify/change the calculator’s angle unit.

× tan(36°)

2. Use the calculator’s trigonometric function key on the
Advanced keyboard to enter/perform the calculation.

66

PROCEDURE

Chapter 5: Advanced Calculations — Advanced Keyboard

1. Since the angle of elevation is measured in degrees, the
calculator’s angle setting will
need to be matched with
that. Press @ ; to
bring up the SETUP menu.

2. On the right side of the
SETUP menu, the current
setup will be displayed.
Make sure that the top line is
indicated as Deg (i.e.,
degrees). If not, then the
angle system will need to be
changed. Press B to
select B DRG, then press
1 to select 1 Deg.

3. Now, let’s work on the actual calculation part. Press the #
key to enter the Calculation screen, and press C to clear
any screen entries.

4. Press 505.8 | t

36. Press E to execute
the calculation.

2. Various Calculation Keys

The calculator’s Advanced Keyboard is designed so that various advanced-level
expressions can be written quickly with few strokes of the keys.

Note: The default angle unit for the Advanced mode is radians. The

examples hereafter will therefore feature the radian angle system,
unless otherwise specified.

The keys with each associated math function are described
below. Refer to the usage diagram in the Appendix for the
parameters for each sub-menu item.

67

Chapter 5: Advanced Calculations — Advanced Keyboard

s Enters a sine function to be used in a trigonometric expression.

c Enters a cosine function to be used in a trigonometric expression.

t Enters a tangent function to be used in a trigonometric expres-

sion.

l Enters a common logarithm function.

I Enters a natural logarithm function.

Example

4

e

• Calculate In

.

I @ @ 4 E.

y Raises the preceding value to the 2nd power.

If no preceding value exists, then the base value will be left blank.

d Enters a mixed number, with all elements left blank. If a preceding

number exists, then the number is assumed as the integer part of
the mixed number. (See page 37.)

b Enters a fraction. Sets the preceding value as its numerator while

the denominator left blank. (See page 38.)
If no preceding value exists, then both the numerator and the

denominator will be left blank.

a Raises the preceding value to a power. The exponent value can

subsequently be entered.
If no preceding value exists, then both the base and the exponent

area will be left blank. (See page 38.)

68

Chapter 5: Advanced Calculations — Advanced Keyboard

The following math functions can be accessed with the use of @ key. To learn the
basic steps of how to access the second function of each key, refer to the section
“Second Function Key” of Chapter 2.

s Enters an arcsine function to be used in a trigonometric expres-

sion.

Example

• Calculate arcsine 1.

@ s 1 E.

c Enters an arccosine function to

be used in a trigonometric
expression.

Example

• Calculate arccosine 0.5.

@ c 0.5 E.

t Enters an arctangent function to be used in a trigonometric

expression.

Example

• Calculate arctangent 1.

@ t 1 E.

Note: Expressions with inverse trigonometric functions evaluate in the

following ranges.

θ

= sin-1x, θ = tan-1x

Deg: 0 ≤ |

θ

| ≤ 90 Deg: 0 ≤ |θ | ≤ 180

Rad: 0 ≤ |θ | ≤

π

2

θ

= cos-1x

Rad: 0 ≤ |θ | ≤ π

Grad: 0 ≤ |θ | ≤ 100 Grad: 0 ≤ |θ | ≤ 200

0 Raises 10 to the power of x.

@ Enters the Euler Number

e (2.71…) to a power. The cursor will

then be placed at the exponent.

Example

• Obtain a value of e3.

@ @ 3 E.

69

Chapter 5: Advanced Calculations — Advanced Keyboard

x Raises a preceding value to the power of -1. If no value is

preceded, then the cursor will be placed at the base.

th

_ Enters an a

root of a base. When a value precedes, then the
value will be incorporated as the index number. Otherwise, both
entry areas will be left blank.

+ Enters a square root; sets the cursor at the base entry area.

$ Enters π (3.14…).

θ

~ Sets the following value as

, assuming the preceding value is the

radius of the polar coordinates.

# Enters i (representing

), to make imaginary or combination

-1

numbers.

3. Calculations Using MATH Menu

The Advanced keyboard has considerably more MATH menu items to choose from
than that of the Basic keyboard:

A CALC Contains sub-menu tools for advanced calculations. To access

each sub-menu item, make sure that this A CALC menu item is
selected. Pressing the ' cursor key will extend the cursor to
the sub-menu items. Items can then be highlighted by scrolling
with {, }, ; or ', and selected by pressing
E, or simply use the short cut key stroke (i.e., select 01 by
pressing 0 and 1).

A sub-menu item with open parenthesis will need to be completed
by the closing parenthesis; failure to do so will result in an error.

01 log

70

log2

2

value

Enters a base-2
logarithm (log

).

2

Chapter 5: Advanced Calculations — Advanced Keyboard

02 2

X

2

value

Raises 2 to a power. Sets the cursor to exponent.

03 fmin( fmin(

equation, lower limit of x, upper limit of x

Returns the value of
variable x when the
equation Y has the
minimum value within
the specified range of
x.

04 fmax( fmax(equation,

Return the value of variable x when the equation Y has
the maximum value within the specified range of x.

05 d/dx( d/dx(

equation, value of x [, tolerance]

Returns derivative of
equation Y at the

lower limit of x, upper limit of x

)

)

)

specified X value
using the tolerance (if
not specified, default
value is 1E–5).

06 ∫∫

Calculates an integral
value of equation Y
from the lower limit to
the upper limit using
the specified toler­ance (if not specified,
default value is 1E–5). Use in conjunction with the 07
dx sub-menu item.

• Press the keys as follows in the Equation edit mode.

equation, lower limit, upper limit [, tolerance]

dx

M A 0 6 2 { 8 ' (
X a 3 ' - 0.5 X y +

07 dx Enters a differential “

6 ) , 0.001 M A 0 7
E

dx

” in an integration expression.

71

Chapter 5: Advanced Calculations — Advanced Keyboard

08 ∑( ∑(

expression, initial value, end value [, increment]

Returns the cumula­tive sum of a given
expression from an
initial value to an end
value in the specified
increment value (if
not specified, default increment is 1).

09 sec sec

Enters a secant
function to be used in
a trigonometric
expression.

10 csc csc

Enters a cosecant (cosec) function to be used in a
trigonometric expression.

)

value

value

11 cot cot

Enters a cotangent (cotan) function to be used in a
trigonometric expression.

-1

12 sec

sec

Enters an inverse
secant.

-1

13 csc

csc

Enters an inverse
cosecant.

-1

14 cot

cot

Enters an inverse cotangent.

15 sinh sinh

Enters a hyperbolic
sine.

value

-1

value

-1

value

-1

value

value

16 cosh cosh

17 tanh tanh

72

value

Enters a hyperbolic cosine.

value

Enters a hyperbolic tangent.

Chapter 5: Advanced Calculations — Advanced Keyboard

18 sinh

-1

sinh

-1

value

Enters an inverse
hyperbolic sine.

19 cosh

-1

cosh

-1

value

Enters an inverse
hyperbolic cosine.

20 tanh

-1

tanh

-1

value

Enters an inverse hyperbolic tangent.

B NUM Use the sub-menu items below to convert a value. Refer to

“Chapter 3: Basic Calculation — Basic Keyboard” to learn how
these tools can be used.

1 abs( Returns the absolute value of a given number.

2 round( Returns a rounded value of a given term in parenthe-

ses. A rounding point can be specified.

3 ipart Returns only the integer part of a decimal number.

4 fpart Returns only the fraction part of a decimal number.

5 int Rounds a decimal number to the closest integer.

6 min( Finds and returns the minimum value within a list of

numbers.

7 max( Finds and returns the maximum value within a list of

numbers.

8 lcm( Returns the least common multiple of two integers.

9 gcd( Returns the greatest common divisor of two integers.

73

Chapter 5: Advanced Calculations — Advanced Keyboard

C PROB These sub-menu items are useful for probability calculations.

Refer to “Chapter 3: Basic Calculations — Basic Keyboard” for
details. A comprehensive list of menu items can be found in the
Appendix.

1 random Returns a random number form between 0 and 1.

2 rndInt( Returns a list of random integers, between a minimum

and a maximum value.

3 nPr Returns the total number of permutations for selecting

“r” items out of “n” items.

4 nCr Returns the total number of combinations for selecting

“r” items out of “n” items.

5 ! Returns a factorial.

D CONV These tools deal with conversions between different angle units

and between rectangular and polar coordinates.

1 →deg

2 →dms

Rectangular/polar coordinate conversion

This calculator is equipped with rectangular coordinates and polar
coordinates conversion capabilities.

value (sexagesimal number)

Takes a number in sexagesimal form, and converts it
into a decimal number.

value (degrees)

Takes a number in decimal form (in degrees), and
converts it into a sexagesimal number. To enter a
number in sexagesimal form, use items in the ANGLE
sub-menu, described in Chapter 3.

→dms

→deg

x

74

y

r

θ

Chapter 5: Advanced Calculations — Advanced Keyboard

Rectangular to polar coordinate conversion functions

Conversion formulas: r = (x2 + y2)

3 xy→r( xy→r(

x coordinate, y coordinate

Returns polar
coordinate radius
value from X-Y
rectangular coordi­nates.

4 xy→

θθ

θ(xy→

θθ

θθ

θ(

x coordinate, y coordinate

θθ

Returns polar
coordinate θ value
from X-Y rectangular
coordinates.
The following ranges
are used to find θ.

Degree mode: 0 ≤ |θ| ≤ 180

1/2

,

θ

=

tan-1(y/x)

)

)

Radian mode: 0 ≤ |θ| ≤ π
Gradient mode: 0 ≤ |θ| ≤ 200

Polar to rectangular coordinate conversion functions

Conversion formulas: x = rcos

θθ

5 r

θ→x( r

θθ

θθ

θ→x(

r coordinate,

θθ

θ

, y = rsin

θθ

θ

coordinate

θθ

θ

)

Returns rectangular
coordinate X value
from r-θ polar
coordinates.

θθ

6 r

θ→y( r

θθ

θθ

θ→y(

r coordinate,

θθ

θθ

θ

coordinate

θθ

)

Returns rectangular
coordinate Y value
from r-θ polar
coordinates.

75

Chapter 5: Advanced Calculations — Advanced Keyboard

E ANGLE Use these tools to enter the symbols to specify angle units.

1 ° Inserts a symbol for “degrees”.

2 ’ Inserts a symbol for “minutes”.

3 ” Inserts a symbol for “seconds”.

4 r Enters an “r” symbol, to enter a number in radians.

5 g Enters an “g” symbol, to enter a number in gradients.

F INEQ Use the equality/inequality figures to compare two values. These

sub-item tools return 1 (true) or 0 (false).

1 = Tests whether a

preceding value and
a following value are
equal.

2

Tests whether a
preceding value and a following value are not equal.

3 > Tests whether a preceding value is larger than a

following value.

4

Tests whether a
preceding value is
larger than OR equal
to a following value.

5 < Tests whether a

preceding value is smaller than a following value.

6 Tests whether a preceding value is smaller than OR

equal to a following value.

76

Chapter 5: Advanced Calculations — Advanced Keyboard

G LOGIC Use the LOGIC sub-menu items to perform boolean operations.

In the N-base calculation mode (binary, octal, decimal and
hexadecimal), A LOGIC will directly appear when M is
pressed.
The following is the truth table of the combination of input A and
B:

AB
11
10
01
00

A and B

1
0
0
0

A or B

1
1
1
0

A xor B

0
1
1
0

A xnor B

1
0
0
1

A notA
10
01

The following examples show the answer screen when
executing a boolean operation for AND, OR, XOR,
XNOR between “1100” and “1010” in binary mode.
Compare the results (binary) to the above table.

1. Press # @ V A E to enter the binary,

octal, and hexadecimal calculation mode.

2. Press } } } to select the binary mode.

1 and

value A

and

value B

Enters an “AND” logic
figure.
1100 M 1
1010 E

2 or

value A

Enters an “OR” logic
figure.
1100 M 2
1010 E

3 not not

Enters a “NOT” logic
figure.

M 3 10
E

value

or

value B

77

Chapter 5: Advanced Calculations — Advanced Keyboard

4 neg neg

value

Enters a “neg” logic
figure.

M 4 1
E

Note: “4 neg” menu

appears only in the N-base calculation (binary, octal,
decimal and hexadecimal) mode.

5 xor

value A

xor

Enters an Exclusive­OR (xor) logic figure.
1100 M 5
1010 E

6 xnor

value A

xnor

Enters an Exclusive­NOR (xnor) logic

value B

value B

figure.
1100 M 6
1010 E

H COMPLX In order to use the sub-menu items within the COMPLX menu,

the calculator must be set up to handle complex numbers.
Otherwise the result will be a data type error.

Refer to the section “6. SETUP Menu” in this chapter for chang­ing/verifying the calculator’s setup to enable complex number

answers, in either rectangular or polar coordinates.

1 conj( conj(

complex number

)

Returns the complex
conjugate of the
specified complex
number (or list of
complex numbers).

78

Chapter 5: Advanced Calculations — Advanced Keyboard

2 real( real(

complex number

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

3 image( image(

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

4 abs( abs(

complex number

Returns the absolute
value of a complex
number (or list of

)

complex number

)

)

complex numbers).

5 arg( arg(

complex number

)

Takes the coordi­nates (x

+ yi), and

returns the θ.

Calculations using complex numbers

To calculate using complex numbers, select the sub-menu item 4
x ± yi or 5 r ∠

θ

in the F ANSWER of the SETUP menu items.

The initial screen for the complex number calculation mode is the
same as for the real number mode.

Complex numbers can be noted using either 4 x ± yi (rectangular
coordinates) or 5

r ∠

θ

(polar coordinates).

79

Chapter 5: Advanced Calculations — Advanced Keyboard

Example

• Calculate (3 + 4i) × (4 – 6i)

Note: It is possible to input complex

numbers (i) in the real number
mode, however an error
message will return.

Functions available for complex number calculations

The following function keys are available for complex number
calculations without the limits existing in the real number calculations.

y, x, l, I, 0, @, a, +,
_

The following MATH menu functions are also available for
complex number calculations.

abs(, round(, ipart, fpart, int

4. More Variables: Single Value Variables and
LIST Variables

Additional single value variables (from A to Z, and θ) may be accessed. In addition, six
LIST variables (from L1 to L6) are readily accessible through the second function of
the Advanced Keyboard.

To save a list of numbers, follow the procedure below:

On the Calculation screen (#), create a list of numbers (“1,

1.
2, 3”, in this example). Separate numbers with a comma
(,), and group the numbers with braces ({ and }).

2. Press R, then select
one of the six LIST variables.
To store the list in “L1”, press
@ 1 to call up the
LIST variable.

3. Pressing E will store the
list in the LIST variable. Note
that this procedure will
overwrite the list previously
stored in the LIST variable.

Refer to Chapter 9 “LIST Features” to learn more about how LIST

80

variables can be utilized.

Chapter 5: Advanced Calculations — Advanced Keyboard

5. TOOL Menu

The TOOL menu contains items to help calculating in different number systems, as
well as to help solve both linear and polynomial equation. Press @ V to
access the TOOL menu. Press the # key (or @ q) to escape from the
menu.

A NBASE Calculations can be performed in different number base systems,

while simultaneously converting the calculation result into
hexadecimal, decimal, octal, and binary systems.

1. While this menu item A
NBASE is selected, press
the E key. The NBASE
tool opens, with the cursor
set at HEX: (hexadecimal).

2. Type 1B | 9, for example. When entering the hexadecimal
B, simply press the B key; using the A key will call up
the variable B instead.

3. When done entering the
hexadecimal expression,
press E. The calculation
result will be displayed in
three other number base
systems, as well as in
hexadecimal format.

Note: Numerical values in binary, octal, and hexadecimal modes can be

expressed in the following number of digits:

Binary: 16 digits
Octal: 10 digits

Hexadecimal: 10 digits
If you enter a number exceeding the range specified above for
calculations or conversions, the calculator will return an error.
If the answer exceeds the above range, the calculator will also
return an error.

Decimals can be used for DEC mode only (. cannot be used
in the other modes). If you convert decimal values to binary,
octal, or hexadecimal number, the decimal part is discarded and
only the integer part is converted.

When numerical values of binary, octal, and hexadecimal modes
are negative, the display is switched to complements of 2.

81

Chapter 5: Advanced Calculations — Advanced Keyboard

B SYSTEM With this tool, linear equations containing up to 6 unknown values

(i.e., ax + by + cz + du + ev + fw = g) can be solved.

1. Press B to select B SYSTEM, and select the number of

unknown values. For example, press 2 if values x and y
are unknown.

2. In the next screen, an
equation ax

+ by = c is

displayed, with an entry
table for the known values —
a, b, and c.

3. Enter 2 sets of the known
values, as shown in the
figure. Pressing E at
each entry will store the
value, and sets the cursor at
the next entry area.

4. When done entering the
known values, press @
h. The calculation result
will be displayed on the next
screen.

Pressing C will bring back the previous entry screen.

82

5. To go back to the TOOL menu to perform another calculation,
press @ V.

C POLY This tool is designed so that quadratic (ax

3

(ax

+ bx2 + cx + d = 0) equation may be solved.

1. Press C to select C
POLY, and select the degree.

For example, press 2 if
a quadratic equation is
desired.

2. In the next screen, an equation ax

2

+ bx + c = 0 is displayed,

with an entry area for the known values — a, b, and c.

2

+ bx + c = 0) or cubic

Chapter 5: Advanced Calculations — Advanced Keyboard

3. Enter the values, as shown
in the screen to the right.
Pressing E at each
entry will store the value,
and sets the cursor at the
next entry area.

4. When done, press @ h to execute the calculation.
The results (i.e. the x-intersects) will be displayed.

5. To enter a different set of
numbers for a, b, and c,
press C to go back to
the previous screen. To
select a different degree of
polynomial, press @
V to go back to the TOOL menu.

• If the solution cannot be displayed on the screen, a symbol will
appear at the bottom left corner of the screen. Press } to
scroll the screen.

6. SETUP Menu

Use the SETUP menu to verify the calculator’s current setup for mathematical and
scientific base units and the global editing style, as well as to change each
configuration.

It is very important that each item within this menu is properly set
up, or calculation results may not turn out as expected. For
example, entering 1
as either “1” (when set to degree mode), or “0.893996663” (when
set to radian mode), or “0.98768834” (when set to gradient
mode). Refer to the “SETUP Menu” in Chapter 2 to learn about
each setup configuration.

×

sin90 in the Calculation screen will result

83

Chapter 6

Advanced Graphing Features
— Advanced Keyboard

In this chapter, some real-life situations are featured. You are encouraged to modify
the examples to make your own graph schemes.

Note: To try the examples in this chapter, it is required that the Advanced Keyboard is

already set up by the user. To learn how to set up the Advanced Keyboard, read
“Changing the Keyboard” in Chapter 1.

It should be noted that the following examples assume that the angle mode is
set to Rad (radian), the default angle unit for the Advanced Keyboard. If set to
degree or gradient, some unexpected results will be obtained.

1. Try it!

You have just opened your own bank
account, with an initial deposit amount of
$2,000. Suppose your monthly income is
$3,000, and you will spend 60 percent of
what you have in the account every month,
how much will your balance be after one
year? How much will you have in the
account, 6 months from now?

The example can be expressed as a sequential equation, as
follows:

u

= u

n

where un is the balance of the current month and u
balance of the previous month, and

84

× (1 – 0.6) + 3000

n–1

n

is the month.

is the

n–1

CONCEPT

PROCEDURE

Chapter 6: Advanced Graphing Features — Advanced Keyboard

1. Grasp the idea of sequential equations.

2. Use the graph tracing function to obtain approximate values.

1. First, let us set the calculator
to the appropriate graphing
coordinate mode. Press
@ ; to enter the
SETUP menu, press E
to select E COORD, then
press 4 to select 4 Seq, and press C.

2. We will use the “Time”
sequential graph type within
the FORMAT menu. Press
@ f, press G
to select G TYPE, and 2
to select 2 TIME.

3. Then press Y.
The Graph Equation Entry window will open.

4. Enter a new equation set

u(n-1)

u(n)=

× (1 - 0.6) + 3000 for

. Press @ u
(7) to enter u and
press X for n. Press
E when done entering.

Note: Press C to clear the previous entry.

Using a capitalized “U” or “N” here will result in an error upon
pressing the G key.

5. On the second entry row
(

u(nMin) =

), enter 2000,

6. The v and the w entry sets will not be necessary in this case,

then press E.
The figure is automatically
enclosed by braces.

so press C to clear, then press E to move one row
down. Repeat until the four unnecessary entry rows are
cleared.

85

Chapter 6: Advanced Graphing Features — Advanced Keyboard

7. Press G to draw the graph.

8. If the line is outside of the

graph’s range, press Z
then 1 to select
automatic zoom.
This will only display a small
portion of the graph, so the
graph’s range will need to be changed.

9. Press W. Find

n

Max=

and change the value to 15
(default: 10). Next, find
Xmax= and change the
value to 15 too (default: 10).

10

. Press the G key again.

11

. Use the graph trace function

by pressing U. As '
is pressed several times, the

n

value (=X value, since the
graph is set to “Time” format)
increases, and the Y value
(the balance of your ac­count) will change. Find the
Y value when the

n

value is
6 (after 6 months) as well as
the value when n=12 (after 12 months = 1 year).

You can obtain the value directly from the CALC menu.

1. Press @ k and

select 1 VALUE.

n=

will appear on the bottom

line of the screen.

2. Enter the n value of 6, and

press E.

3. Follow the procedure 1 to 2 to obtain the Y value for 12.

86

Chapter 6: Advanced Graphing Features — Advanced Keyboard

2. Graphing Parametric Equations

A two-dimensional parametric equation assumes that both X and Y are represented
by functions in a third variable T. When set in parametric graphing mode, the calculator
automatically sets up the Graph Equation Entry screen to take one set of X and Y per
each graph, with the equation’s right side variable to be set as “T”.

Example

•Draw a graph: x(t) = 16cos(t), y(t) = 9sin(t).

1. Press @ ; to enter the SETUP menu.

2. Press E to select E

COORD, then 2 to
select 2 Param.

Be sure that the other
settings are as shown on the
right.
To exit the SETUP menu, press C.

3. Press Y to go to the Graph Equation Entry window.

4. Enter 16cos(t) for X1T=.

Press E when done
entering.

5. Enter 9sin(t) for Y1T=. Press

E when done entering.

Note: The right side variable is automatically set to “T”. When the X

key is pressed within the Graph Equation Entry window, it will
enter the variable “T”.

6. Press G to draw the graph.

7. If the graph line extends
beyond the screen, press
Z and select A ZOOM
then 1 AUTO.

Use 3 IN or 4 OUT of the A
ZOOM to adjust the drawing size.

You can also set the drawing size in the WINDOW menu by
determining the maximum and minimum values of T, X and Y.

87

Chapter 6: Advanced Graphing Features — Advanced Keyboard

3. Polar Graphing

Polar coordinates are a different method of specifying a point in two dimensions; the
location of the point is described by the distance from the X-Y intersect “r”, and its
elevation angle “

θ

”.

Example

•Draw a graph: r = 16cos(

1. Press @ ;.

The SETUP menu appears.

2. Press E to select E

COORD, then press 3

θ

r

θ

)sin(θ).

to select 3 Polar. Be sure
that the other settings are as
shown on the right.
To exit the SETUP menu,
press C.

3. Press Y.

The Graph Equation Entry window will appear.

4. At the first entry row R1=,
enter 16cos(
Press E.

5. Press G to draw the
graph.
Press Z, then press
6 to select 6 Square.

θ

) × sin(θ).

88

Chapter 6: Advanced Graphing Features — Advanced Keyboard

4. Graphing Sequences

The sequence graph mode can store and simultaneously draw three graph equations
u(n), v(n), and w(n).

Variables u, v, and w are entered as @ u (or v, w).
Use X to enter the natural number n.

A sequence is an ordered set of numbers with a defined relation­ship. The

recursive

un = u

un = u

sequential formulas can be described as

+ d and/or

n-1

× r

n-1

where un is the n-th term, d is the common difference, and r is the
ratio. In many occasions however, the term before u
term before un) is not known. In such cases, the

(i.e., one

n-1

explicit

formulas

must then be derived as:

u

= u

+ d × (n - 1) and/or

n

1

un = u

× r

1

n-1

where un is the n-th term, u1 is the first term of the sequence, d is
the common difference, and r is the ratio.

A sequence {2, 4, 8, 16, 32, ...} may suggest the following
recursive sequence expression:

u

= 2 × 2

n

n-1

or it may also suggest the following non-recursive expression:

n

un = 2

The calculator can plot sequential graphs in three different
schemes, as follows:

n

-based (Time)

The un values will be plotted
against the n value.

89

Chapter 6: Advanced Graphing Features — Advanced Keyboard

phase-based (uv, uw, or vw)

The un values will be plotted against the vn values (uv).

(n–1

)-based (Web)

The un values will be plotted against the u

Note: • When u

requires two values: the minimum, and the second smallest. For
example, you will need {0, 1} in the

+

u(n–2)

• When Web is selected, n – 2 cannot be referred to. n also

cannot be directly referred to; entering u(n–1) + n will result in
an error.

Before entering graphing sequences, the calculator’s graphing
coordinates will need to be set up:

1. Press @ ;. The SETUP menu appears.

2. Press E to select E COORD, then press 4 to select 4
Seq.

3. Press C to exit the SETUP menu.

value.

n-1

is incorporated in to the equation, the

n–2

u(nMin)

is entered as the equation.

u(nMin)

entry row if

u(n–1)

Example 1:

•Draw a sequential graph of u

n

-based Graphing (Time)

= 2 × 2

n

n–1

.

First, make sure that the graph coordinate mode is set to
sequential (see above.)

1. Press @ f to open the FORMAT menu. The FORMAT
menu allows user to change the graph configurations.

2. When the menu appears, select the item G TYPE.

3. Press 2 to select 2
Time.

90