Sharp EL-9900 User Manual

Graphing Calculator

EL-9900

Handbook Vol. 2

Programmes

For Advanced Levels For Basic Levels

Contents

1. Heron's Formula 1

2. Calculating Tension 2

3. Involute (Inverse Involute) 4

4. Calculating Illuminance and Luminous Intensity 6

5. Calculating Simple Harmonic Oscillation 8

6. Electric Power Consumed on an AC Circuit 10

7. Angle of Vector 12

8. Linear Transformation 14

9. Moving Average 16

10. Creating a Graph of Experimental Data 18

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11. Ordinary Differ ential Equations 20

12. Analysing with One-way Layout Method 22

13. Calculating Parabolic Motion 25

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Read this first

This handbook was produced for practical application of the SHARP EL-9900 Graphing Calculator. This
calculator includes a highly convenient programming function, which enables automatic processing of
both simple and complex calculations any number of times.

1. Entering and Editing a Programme (Advanced keyboard mode only):

Programmes can be entered and edited either by pressing the calculator keys or by downloading from a PC.
To download programmes from a PC, you will need the CE-LK2 PC link software (sold separately).

In this handbook, we use the symbol “
division. Please follow this convention when entering and editing programmes via the PC-Link software.
When entering programmes directly through the EL-9900’s keypad, meanwhile, please use the

keys.

÷

” to represent multiplication, and the symbol “/” to represent

*

X

and

A. Using calculator keys

●

Creating a new programme:

1. Press

2. Press

3. Enter the programme title, then press

to display the programme menu.

PRGM

to select the new programme menu. (See right)

ENTER

C

.

ENTER

4. Enter the programme.

5. Press

●

Editing a programme:

1. Press

2. Press and choose the number of the programme you wish to edit.

3. Press

to finish programming.

2nd F

QUIT

to display the programme menu.

PRGM

B

to finish editing.

2nd F QUIT

(See right)

B. Downloading from PC

●

Creating a new programme:

1. Using the CE-LK2, select New from the File menu.

2. Enter a programme name in Title:.

3. Enter a programme. (For details on entering a programme, refer to
the operation manual.) (See right)

●

Programmes can also be downloaded from Sharp’s website at

http://sharp-world.com/products/calculator/education/program/index.html

instead of creating a new programme.

●

Sending programmes from a PC:

1. Using the CE-LK2, select the Communication Port from
the Link menu and click on the port to be used.

2. Turn off the EL-9900 and connect it to the PC.

3. Turn on the EL-9900

4. Select Send… from the Link menu of the CE-LK2

5. Specify the kind of drive, folder, and file, then select the file
to be sent from the file list, and click on the Select button.

6. Click on the OK button.

Note : For further details refer to the manual.

2. Executing a programme:

(See right)

1. Press to display the execute menu.

2. Press and choose the number of the programme you wish to

PRGM

A

ENTER

execute.

3. Follow the instructions.

3. Deleting a programme:

Press and then choose to select the programme to

2nd F

OPTION

C

5

be deleted.

Note: Do not try to erase a programme by resetting all memories to the initial condition as

programme data to be stored will also be deleted. Also, it is advised to use the CE­LK2 PC link software to back up any programmes not to be erased.

4. Using the keys:

Press to use secondary functions (in yellow).

2nd F

To select “

Press to use the alphabet keys (in violet).

ALPHA

To select F:

-1

x

”: ➔ Displayed as follows:

➔ Displayed as follows:

ALPHA

2nd F

F

2

x

-1

x

2

x

ALPHA

(See right)

-1

x

2nd F

F

Press to continue input of violet letters.

2nd F

A-LOCK

To input ABC:
(To return to the normal function, press again.)

or

ALPHA

ALPHA ALPHA

A

B

C

ALPHA

2nd F

A-LOCK

ABC

5. Troubleshooting:

Following is a list of error codes and error messages.
When errors occur, refer to pages 233 and 234 of the manual.

Error
code

Error message

01 Syntax Syntax error found in equation/programme.
02 Calculate Calculation-related error found (division by 0, calculation beyond range, etc.).
03 Nesting Cannot nest more than 14 numerical values, or 32 functions during execution.
04 Invalid Matrix definition error or entering an invalid value.
05 Dimension Matrix dimension, or STAT list dimension, inconsistent.
07 Invalid DIM Size of list/matrix exceeds calculation range.
08 Argument Inconsistency found in argument of the structured function.
09 Data Type Invalid data type used in calculation.
10 No Sign Change Financial calculation error found.
11 No define Undefined list/matrix used in calculation.
12 Domain Argument definition outside of domain.
13 Increment Increment error found.
16 Irr Calc More than two inflection points for Irr calculation.
17 Stat Med Med-Med law (statistic) error found.
20 No Argument Argument missing.
21 Not pair ∫ dx ∫ and dx are not used in a pair.
22 Not pair [ ] Brackets are not used in a pair.
23 Not pair ( ) Parentheses are not used in a pair.
24 Not pair { } Braces are not used in a pair.
25 Line over Line is over the capacity.
26 Not delete Unable to delete a selected item.
27 Buffer over Input/equation exceeds buffer capability.
30 Edit type Invalid editor type found.*
31 Continue = “ = ” exists in equation that has been recalled (RCL).
32 No data Data does not exist.
33 Graph Type Graph type setting incorrect.
34 Too many var. Too many variables assigned in the SOLVER.
35 No variable No variable specified in the SOLVER.
36 No solution No solution found.
37 No title No title entered.
38 Too many obj More than 30 objects selected.

Error content

Error
code

Error message

40 Lbl duplicate Labels with identical name found in programme.
41 Lbl undefined Goto/Gosub encountered with no defined label.
42 Lbl over More than 50 labels found in programme.
43 Gosub stack Nesting of more than 10 subroutines found.
44 Line too long Line contains more than 160 characters.
45 Can’t return Return used without jumping from subroutine.
46 Storage full Cannot create more than 99 files.
47 Coord type Invalid coordinate system for command.
48 Without For For is missing corresponding to the Next command.
49 Without WEnd WEnd is missing corresponding to the While command.
50 Without While While is missing corresponding to the WEnd command.
51 Without Then Then is missing corresponding to the If command.
52 Without EndIf EndIf is missing corresponding to the If command.
53 Without If If is missing corresponding to the EndIf command.
70 I/O device Communication error found among devices.
71 Wrong Mode Wrong communication mode set.
90 Memory over Memory is full; cannot store data as requested.
99 System error System error found; user memory space is insecure.

Low battery Operation interr upted due to low batter y power.
BREAK!! Operation break specified.

Error content

* The following operations may cause Editor type error. Correct the Editor type to continue.

•Recall the SOLVER equations (EQTN) or Graph data (G_DATA) stored in a different EDITOR mode
than currently in use.

•Receive the Graph equation (Y1 and others) entered in a different EDITOR mode than currently in use.

6. Page Layout

Introduction

Brief explanation and
purpose of the section

Calculation

The formula to be used
in calculation and
definition of terms

Flowchart

Summary of steps from
start to end

Parameters

Definition of the
parameters used in the
programme

Involute

Use the involute function for calculating gears etc. to find the angle of obliquity
from the initial value and involute value.

Calculation

Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:

θ

f (θ) = a - inv

Selection of type

N

INVO

Calculation of involute

Name of parameter
D, R, T, J
S

Z

4

f'(θ)

i +1 = θi -= θi -

f(θi)

θ

Start

S = 1

N

S = 2

Entry of initial

Y

involute value

CALPRESS

Calculation of

angle of obliquity

Display of angle of obliquity

Entry of angle

of obliquity

value (display)

End

(Inverse Involute)

tanθ

i - θi -a

tan2 θ

SP : involute curve
S : involute starting point
θ : angle of obliquity of point P

FLOWCHART

start

Y

ANGLE

value and

Y

8

int(10

D) 0

N

Content
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity

Step

A step-by-step guide to solving the problems
and an explanation of the display

i

Enter 1 or 2.

To calculation of involute.
To inverse involute calculation

Returns to START if entry
neither 1 nor 2.

Calculation of involute.
Enter initial value and
involute value.

Angle of obliquity
calculated.

Judgment on repetition
of calculation of angle
of obliquity.

Calculation of inverse
involute. Enter angle
of obliquity.

Involute value calculated.
Involute value displayed.

PARAMETERS

Name of parameter

θ

I
A
B

EL-9900 Graphing Calculator

θ

P

q

S

a

θ

Rg

0

PROGRAMME LIST

(REAL MODE)

Title : INVOLUTE

Label START
ClrT
Print "SELECT 1/2
Input S
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE

Exercise

Print "Input BEGIN
Input B
B Z

(1) Find the angle of obliquity when the involute value is 0.0050912 and the initial

Print "Input INVO

value is 10.

Input I
I J

(2) Find the involute value when the angle of obliquity is 14.1.

Label CALPRESS
tan Z T

Set up condition: angle unit in Deg Mode and decimal point in

π Z/180.0 R

2

Float Pt Mode.

(T-R-J)/T

D

180.0 (R-D)/π Z

SET UP

10

8 D)≠0 Goto CALPRESS

If int (
Z A
Print "ANGLE
Print A
End
Label INVO
Print "Input ANGLE
Input A

Specify the program mode.

A θ

1

Select the title INVOLUTE.

tanθ -π θ/180 I
Print "INVOLUTE
Print I
End

Select involute calculation.

2

Content
angle of obliquity
involute value
input and output of angle

Enter the initial value and the

input of initial value

3

involute value.

(Display of angle of obliquity)

Select inverse involute

4

calculation.

Enter the value of the angel

5

of obliquity.

(Display of involute value)

2nd F

1C

1B

CL

PRGM

A

ENTER

1

ENTER

01

0005091•

ENTER

ENTER

ENTER

2

14 1•

ENTER

EL-9900 Graphing Calculator

Programme List

Procedure of data to
be entered

Exercise

Example of problem to be
solved in the section

Set Up Condition

Important set up condition
before starting the exercise
in order to obtain correct

DisplayStep Key Operation

answers

Key Operation

Illustration of the keys to be

2

operated

Display

Illustration of the calculator
screen as it should appear
if each step is carried out

5

correctly

EL-9900 Graphing Calculator

Heron's Formula

Use Heron's formula to find the area of a triangle when the sides (A,B,C) of the
triangle are known.

Calculation

S = D (D - A) (D - B) (D - C)

(A + B + C)

D =

2

FLOWCHART

Start

Entry of sides

Calculation of D

Calculation of area

Display of area

End

Name of parameter
A
B
C

Content
value of side A
value of side B
value of side C

Enter sides A, B and C.

Value of D calculated.

Area S calculated.

Area of triangle
displayed.

PARAMETERS

Name of parameter
D
S

A

C

B

PROGRAMME LIST

Title : HERON

Print "Input LENGTH
Input A
Input B
Input C
(A+B+C)/2 D
(D (D-A) (D-B) (D-C) ) S
Print "S =
Print S
End

Content
value of D
area

(REAL MODE)

Exercise

Find the area of a triangle when sides A, B and C are 20, 35 and 40cm respectively.

Specify the programme

1

mode.
Select the title HERON.

Enter the values A, B and C.

Key OperationStep

PRGM

A

2

ENTER

035

Display

2

(Display of area)

The area is approximately

3

350cm

2

.

ENTER ENTER

40

1

EL-9900 Graphing Calculator

Calculating Tension

Use the law of sines to find the tension when a pole of weight W is suspended with
two strings, and the strings are balanced with the angles from the vertical line A and B.

Calculation

T

vertical line

W

B

S

G

T

sin B

T = W

S = W

T, S : tension W : weight
A, B : angles (6 sexagesimal numbers)

=

sin A

sin (A+B)

sin (A+B)

S

sin B

sin A

=

sin (A+B)

W

A

B

S

W

A

T

FLOWCHART

Start

Entry

Calculation of denominator

Calculation of tensions

Display of tensions

Name of parameter
A
B
C

Content
angle A
angle B
sin(A+B)

Enter angles and weight
A, B and W.

Denominator in law of sines
calculated. C= sin (A + B)

Tensions T and S calculated.
T = W sin B/C
T = W sin A/C

Tensions T and S displayed.

PARAMETERS

Name of parameter
S
T
W

PROGRAMME LIST

Title : TENSION

Print "Input ANGLE
Input A
Input B
Print "Input WEIGHT
Input W
sin (A+B) C
W sin B/C T
W sin A/C S
Print "TENSION
Print "T=
Print T
Print "S=
Print S
End

Content
tension S
tension T
weight

(REAL MODE)

2

EL-9900 Graphing Calculator

Exercise

Calculate the tension assuming weight=40kg, angle A=30˚ 15' 20", and angle
B=27˚ 45' 40". Enter the angles with sexagesimal numbers.

Set up condition: decimal point digit number in TAB 3 Mode, decimal
point in Fix Mode, and angle unit in Deg Mode.

2nd F

SET UP

3D

Specify the programme mode.

1

Select the title TENSION.

Enter the values of angles

2

A and B.

Enter the value of weight.

3

CL2C

1B

Key Operation

PRGM

A

3

ENTER

2

ENTER

4

•

0152

7

0

•

ENTER

4

54

DisplayStep

0

0

Tension T is 21.840kg and

4

S is 23.795kg.

3

EL-9900 Graphing Calculator

Involute(Inverse Involute)

Use the involute function for calculating gears etc. to find the angle of obliquity
from the initial value and involute value.
Conversely, calculate the involute value from the angle of obliquity.

Calculation

Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:

θ

i +1

= θi -=

f'(θ)

f(θi)

f (θ) = a - inv

Start

Selection of type

S = 1

N

S = 2

Y

INVO

Entry of angle

of obliquity

Calculation of involute

value (display)

θ

N

CALPRESS

angle of obliquity

Display of angle of obliquity

End

FLOWCHART

start

Y

Entry of initial

value and

involute value

Calculation of

int(10

tanθ

i

θi

-

- θi -a

tan2 θ

i

SP: involute curve
S : involute starting point
θ : angle of obliquity of point P

Enter 1 or 2.

To calculation of involute.
To inverse involute calculation

Returns to START if entry
neither 1 nor 2.

Calculation of involute.
Enter initial value and
involute value.

Angle of obliquity
calculated.

Judgment on repetition
of calculation of angle
of obliquity.

Calculation of inverse
involute. Enter angle
of obliquity.

Involute value calculated.
Involute value displayed.

8

D) 0

N

ANGLE

Y

θ

P

S

a

PROGRAMME LIST

q

θ

Rg

0

(REAL MODE)

Title : INVOLUTE

Label START
ClrT
Print "SELECT 1 or 2
Input S
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE
Print "Input BEGIN
Input B
B Z
Print "Input INVO
Input I
I J
Label CALPRESS
tan Z T
π Z/180.0 R
(T-R-J)/T

2

D

180.0 (R-D)/π Z
If int (10ˆ8 D)≠0 Goto CALPRESS
Z A
Print "ANGLE
Print A
End
Label INVO
Print "Input ANGLE
Input A
A θ
tanθ -π θ/180 I
Print "INVOLUTE
Print I
End

Name of parameter
D, R, T, J
S

Z

4

PARAMETERS

Content
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity

Name of parameter

θ

I
A
B

Content
angle of obliquity
involute value
input and output of angle
input of initial value

EL-9900 Graphing Calculator

Exercise

(1) Find the angle of obliquity when the involute value is 0.0050912 and the initial
value is 10.

(2) Find the involute value when the angle of obliquity is 14.1.

Set up condition: angle unit in Deg Mode and decimal point in
Float Pt Mode.

2nd F

SET UP

1B

CL

1C

motomoto

DisplayStep Key Operation

Specify the programme mode.

1

Select the title INVOLUTE.

Select involute calculation.

2

Enter the initial value and the

3

involute value.

(Display of angle of obliquity)

○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○

Select inverse involute

4

calculation.

PRGM

A

ENTER

1

ENTER

01

0

ENTER

ENTER

2

005091•2

ENTER

Enter the value of the angle

5

of obliquity.

(Display of involute value)

14 1

ENTER

•

5