Sharp EL-9900 Handbook Vol. 2 Operation 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

11. Ordinary Differ ential Equations 20

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12. Analysing with One-way Layout Method 22

13. Calculating Parabolic Motion 25

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A. Using calculator keys

●

Creating a new programme:

1. Press

to display the programme menu.

2. Press

to select the new programme menu. (See right)

3. Enter the programme title, then press

.

4. Enter the programme.

5. Press

to finish programming.

●

Editing a programme:

1. Press

to display the programme menu.

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

3. Press

to finish editing.

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.

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.

(See right)

ENTER

PRGM

B

2nd F

QUIT

2nd F QUIT

ENTER

C

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 “

*

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

and

keys.

X

÷

2. Executing a programme:

1. Press to display the execute menu.

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

execute.

3. Follow the instructions.

●

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.

ENTER

PRGM

3. Deleting a programme:

Press and then choose to select the programme to 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.

C

5

OPTION

2nd F

4. Using the keys:

Press to use secondary functions (in yellow).

To select “

x

-1

”: ➔ Displayed as follows:

Press to use the alphabet keys (in violet).

To select F:

➔ Displayed as follows:

Press to continue input of violet letters.

To input ABC:

or

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

2nd F

F

2nd F

x

2

x

-1

ALPHA

x

2

ALPHA

2nd F

A-LOCK

ALPHA

ALPHA ALPHA

ALPHA

A

B

C

ABC

2nd F

A-LOCK

x

-1

F

(See right)

A

(See right)

5. Troubleshooting:

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

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

Error code

Error message

* 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

N

INVO

Calculation of involute

Name of parameter D, R, T, J S

Z

4

(Inverse Involute)

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

f'(θ)

tanθ

f(θi)

FLOWCHART

Start

start

Y

S = 1

N

S = 2

Entry of initial

Y

value and

involute value

CALPRESS

Calculation of

angle of obliquity

8

int(10

Display of angle of obliquity

End

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

i - θi -a

tan2 θ

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

ANGLE

Y

D) 0

N

θ

i +1 = θi -= θi -

f (θ) = a - invθSP : involute curve

Selection of type

Entry of angle

of obliquity

value (display)

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

2nd F

Specify the program mode. Select the title INVOLUTE.

Select involute calculation.

Content angle of obliquity involute value input and output of angle

Enter the initial value and the

input of initial value

involute value.

(Display of angle of obliquity)

Select inverse involute calculation.

Enter the value of the angel of obliquity.

(Display of involute value)

1B

10

8 D)≠0 Goto CALPRESS

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

1

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

2

3

4

5

CL

1C

PRGM

A

ENTER

1

ENTER

01

0005091•

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) D =

(A + B + C)

2

A

C

B

FLOWCHART

PARAMETERS

PROGRAMME LIST

(REAL MODE)

Calculation of area

Display of area

Calculation of D

Entry of sides

Start

End

Enter sides A, B and C.

Value of D calculated.

Area of triangle displayed.

Area S calculated.

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

Name of parameter A B C

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

Name of parameter D S

Content value of D area

Exercise

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

Key OperationStep

Display

1

2

Specify the programme mode. Select the title HERON.

The area is approximately 350cm

2

.

3

(Display of area)

Enter the values A, B and C.

1

2

ENTER

ENTER ENTER

035

40

PRGM

A

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

FLOWCHART

PARAMETERS

PROGRAMME LIST

(REAL MODE)

Calculation of tensions

Display of tensions

Calculation of denominator

Entry

Start

Enter angles and weight A, B and W.

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

Tensions T and S displayed.

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

Name of parameter A B C

Content angle A angle B sin(A+B)

Name of parameter S T W

Content tension S tension T weight

T

sin B

=

S

sin A

=

W

sin (A+B)

sin B

sin (A+B)

T = W

sin A

sin (A+B)

S = W

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

A

B

S

W

T

A

vertical line

T

G

S

W

B

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

Title : TENSION

2

EL-9900 Graphing Calculator

3

DisplayStep

Key Operation

1

2

Specify the programme mode. Select the title TENSION.

Tension T is 21.840kg and S is 23.795kg.

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.

4

Enter the values of angles A and B.

Enter the value of weight.

3

CL2C

SET UP

2nd F

3D

1B

3

PRGM

A

ENTER

0152

0

2

7

4

54

0

4

0

•

motomotomotomoto

moto

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:

FLOWCHART

PARAMETERS

PROGRAMME LIST

(REAL MODE)

Selection of type

Entry of initial

value and

involute value

Calculation of

angle of obliquity

Display of angle of obliquity

Start

End

start

Y

ANGLE

INVO

CALPRESS

Y

N

Calculation of involute

value (display)

Entry of angle

of obliquity

Enter 1 or 2.

To calculation of involute.

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.

To inverse involute calculation Returns to START if entry neither 1 nor 2.

θ

i +1

= θi -=

θi

-

f(θi)

f'(θ)

tan2 θ

i

tanθ

i

- θi -a

f (θ) = a - inv

θ

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

Name of parameter D, R, T, J S

Z

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

S = 2

int(10

8

D) 0

S = 1

0

q

Rg

P

S

a

θ

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

Title : INVOLUTE

4

EL-9900 Graphing Calculator

3

DisplayStep Key Operation

1

2

Specify the programme mode. Select the title INVOLUTE.

(Display of angle of obliquity)

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.

4

(Display of involute value)

5

Select involute calculation.

Select inverse involute calculation.

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

Enter the initial value and the involute value.

Enter the value of the angle of obliquity.

5

CL

1B

SET UP

2nd F

1C

PRGM

A

ENTER

0

005091•2

ENTER

1

ENTER

0

1

ENTER

2

ENTER

14

1

•

motomoto

EL-9900 Graphing Calculator

Calculating Illuminance and Luminous Intensity

Enter the luminous intensity of the luminous source, the distance, and the angle between the perpendicular line and light ray, to find the illuminance of the illuminated side. Conversely, find the luminous intensity of the source from the illuminance of the illuminated side.

Calculation

FLOWCHART

PARAMETERS

PROGRAMME LIST(REAL MODE)

Selection of type

To subroutine To subroutine

Start

End

Return

Subroutine

start

CANDELA

LUX

DISTANCE

Y

N

Entry of

luminous intensity

Calculation of

luminous intensity

Entry of

illuminance

Calculation of

illuminance

Display of

illuminance

Display of

luminous intensity

Entry of distance and angle

Enter 1 or 2.

To calculation of luminous intensity.

To calculation of illuminance.

Jumps to subroutine DISTANCE.

Enter illuminance or luminous intensity.

Illuminance or luminous intensity calculated.

Illuminance or luminous intensity displayed.

Subroutine for entry of distance and angle.

Returns to calling program.

Entry.

l : luminous intensity [candela] i : illuminance [lux] r : distance [m] θ: angle [˚ ]

Name of parameter I K R S

Content illuminance of illuminated side luminous intensity of luminous source distance

selecting calculation type (S=1:

calculation of luminous intensity

)

(S=2: calculation of illuminance)

Name of parameter

θ

A L D C

Content angle input of angle input and calculating luminous intensity input of distance input and calculating illuminance

Deg Label START ClrT Print "CANDELA=1 LUX=2 Print "SELECT 1 or 2 Input S If S=1 Goto CANDELA If S=2 Goto LUX Goto START Label CANDELA Gosub DISTANCE Print "Input LUX Input L L I R

2

I/cos θ C Print "CANDELA Print C End Label LUX Gosub DISTANCE Print "Input CANDELA Input C C K K cos θ /R

2

L Print "LUX Print L End Label DISTANCE Print "Input DISTANCE Input D D R Print "Input ANGLE Input A A θ Return

S = 2

S = 1

i =

r

2

l cos θ

l =

cos θ

r

2

i

r

A

Illuminance i

Luminous Intensity l

θ

Title : CAND LUX

6

EL-9900 Graphing Calculator

3

DisplayStep

Key Operation

1

2

Specify the programme mode. Select the title CAND LUX.

(Display of luminous intensity)

Exercise

(1) Find the luminous intensity of the luminous source of distance 10m, angle 60˚ and illuminance 20 lux. (2) Find the illuminance of the illuminated side of distance 10m, angle 60˚ and luminous intensity 4000 candela.

Set up condition: decimal point in Float Pt Mode.

4

(Display of illuminance)

Select calculation of luminous intensity.

Select calculation of illuminance. Enter the values of distance, angle, and luminous intensity.

Enter the values of distance, angle, and illuminance.

7

CL

SET UP

2nd F

1C

PRGM

A

ENTER

1

ENTER

1

0

2

0

60

ENTER ENTER

ENTER

10 6

0

4

0

00

2

EL-9900 Graphing Calculator

Calculating Simple Harmonic Oscillation

Enter period, amplitude and time to calculate displacement at specified time, acceleration, angular velocity, and velocity. Also, display the changes during the entered time period on a graph.

Calculation

FLOWCHART

PROGRAMME LIST

(REAL MODE)

Entry of period

and amplitude

Entry of time

Start

CALC

Calculation of

angular velocity, etc.

A : amplitude t : time [sec] T : period [sec] ω : angular velocity [rad/sec]

angular velocity : ω = acceleration : a = -ω

2

x velocity : v = A ω cos (ω t)

T

displacement : x = A sin (ω t)

Ax

0

ωt

v

0

v ax

2π

A

2π

+

ωt

Display of

calculation result.

Graph display

Display clear

Calculation of

range and scale

Rad Print "Input PERIOD Input P P F Print "Input AMPLITUDE Input A A D Label CALC Print "Input TIME Input T T E 2 π/F W D sin (W E) H

-(W2) H B D W cos (W E) V Print "ANGULAR VELOCITY Print W Print "MAGNITUDE Print H Print "ACCELERATION Print B Print "VELOCITY Print V Wait E/10 X scl D/5 Y scl 0 Xmin:E Xmax

-D Ymin:D Ymax Draw D sin (W X) Wait ClrT ClrG Goto CALC

Angular velocity, displacement, acceleration and velocity calculated.

W = angular velocity H = displacement B = acceleration, V = velocity

Calculation result of angular velocity, displacement, acceleration and velocity displayed.

Text and graph display cleared.

Range set and graph displayed. Function: Y = D sin (W X) X is time increase. Xmin

...

0, Xmax

...

E, Xscl

...

E/10

Ymin

...

-D, Ymax

...

D, Yscl

...

D/5

Title : OSCILLAT

8

Name of parameter B E V W H Xscl Yscl

Exercise

Content acceleration time velocity angle of velocity (ω) displacement x-axis scale y-axis scale

PARAMETERS

Name of parameter A P T D F X

EL-9900 Graphing Calculator

Content input of amplitude input of period input of time amplitude period time increase

Calculate angular velocity, etc., using period

ππ

π, amplitude 1 and time 3 seconds and

ππ

display the changes on a graph.

Set up condition: decimal point in Float Pt Mode.

Specify the programme mode.

1

Select the title OSCILLAT.

Enter the values of period,

2

amplitude, and time.

3

(Display of angular velocity) (Display of displacement) (Display of acceleration) (Display of velocity)

2nd F

SET UP

E

1

C

CL

1

Key Operation

PRGM

A

2nd F

ENTER

π

ENTER

1

ENTER

DisplayStep

3

4

(Display of graph of simple harmonic oscillation)

5

ENTER

9

EL-9900 Graphing Calculator

Electric Power Consumed on an AC Circuit

Enter the voltage effective value, frequency and resistance value to find the power value of the circuit with resistance R. Draw a graph of the changes in power over a period of time.

Calculation

FLOWCHART

PARAMETERS

PROGRAMME LIST

(REAL MODE)

Data entry

Calculation of power

Calculation of range

Display of power

Display of graph

Start

End

Enter data (resistance, voltage and frequency).

Power calculated. W = angular velocity M = maximum voltage N = maximum current I = effective value of current Z = power

Range for graph calculated. Xmax, Xscl, Ymax, Yscl

Power displayed. (value of Z)

Function: Y = N M (sin (W X))

2

Rad Print "Input RESISTANCE Input R Print "Input VOLTAGE Input V Print "Input FREQUENCY Input F R T V D F S 2 π S W D √2 M M/T N N/√2 I D I Z 1/S Xmax Xmax/10 Xscl N M Ymax Ymax/10 Yscl Print "WATT= Print Z Wait 0 Xmin 0 Ymin Draw N M (sin (W X))

2

End

P : power consumption I : effective value of current V : effective value of voltage

Name of parameter S I T D W N M Xmax

Content frequency effective value of current resistance value effective value of voltage angular velocity maximum value of current maximum value of voltage maximum value of x-axis

Name of parameter Xscl Ymax Yscl V R F Z

Content scale of x-axis maximum value of y-axis scale of y-axis input of voltage input of resistance value input of frequency value of power

I0 = N

•

sin ω

•

t V0 = M

•

sin ω

•

t P0 = l0

•

V0 P0 : change in amount of power with time I

0 : change in amount of current with time

V

0: change in amount of voltage with time

N: maximum value of current M: maximum value of voltage ω: angular velocity (2 π S) t : time S : frequency

R

I

V

Title : AC POWER

10

EL-9900 Graphing Calculator

DisplayStep

Key Operation

1

2

Specify the programme mode. Select the title AC POWER.

Exercise

Find the power value of an A C cir cuit with r esistance value 150 Ω, voltage effective value 100V and frequency 50Hz and display on a graph the changes in power over a period of time.

Set up condition: decimal point in Float Pt Mode.

(Display of value power)

Enter the resistance value, voltage effective value, and frequency.

11

PRGM

A

0

ENTER

15

0

ENTER

10

0

ENTER

5

CL

SET UP

2nd F

1

C

1

E

3

(Display of graph)

ENTER

EL-9900 Graphing Calculator

A

ngle of Vector

Use the matrix operation feature to find the angle θ which forms the standard vector and vector. The angle can be calculated at one time against the multiple vectors.

Calculation

FLOWCHART

PROGRAMME LIST

(MATRIX MODE)

Entry of number

of vectors

Definition of arrays

Start

End

K = K + 1

Calculation of

component of

standard vector

Calculation of

inner product

Entry of standard

vector data

Enter no. of vectors for which angles are calculated.

Arrays defined.

Counter for data entry.

Enter x component and Y component of standard vector.

Product of matrices A and B calculated.

Length component of standard vector (scalar) calculated.

Calculating vector inner product a• b = | a | | b | cos θ Use the above expression to derive the following expression

←

←←

←←←

θ = cos

-1

a• b

matA, matB, matC.

Vector data entry

Enter x component and Y component of each vector.

Entry repeated by no. of vectors.

Y

N

Angle calculated and displayed.

I = I + 1

Counter for calculation of angle.

I > M

Y

N

Calculation repeated by no. of vectors.

Length component of vector (scalar) calculated.

Calculation of

component of vector

Calculation of angle and display of angle

Print " Input NUMBER Input N N M {M,2} dim (mat A) {2,1} dim (mat B) {M,1} dim (mat C) For K, 1, M, 1 Print " Input VECTOR Print K Input X X mat A(K,1) Input Y Y mat A(K,2) NEXT Print "Input FUNDAMENTAL VECTOR Input X X mat B(1,1) Input Y Y mat B(2,1) √ (mat B(1,1)

2

+mat B(2,1)2) B mat A mat B mat C For I, 1, M, 1 √ (mat A(I,1)

2

+mat A(I,2)2) A

cos

-1

(mat C(I,1) / (A B)) θ Print "ANGLE OF VECTOR Print I Print "θ= Print θ Wait NEXT End

| a | | b |

Title : VECTOR

K

≤

M

12

EL-9900 Graphing Calculator

3

DisplayStep

Key Operation

1

2

Specify the programme mode. Select the title VECTOR.

Exercise

Calculate the angle formed by the following 3 vectors and standard vector (2,3).

vector 1 (5, 8) vector 2 (7, 4) vector 3 (9, 2)

Set up condition: angle unit in Deg mode, and decimal point in Float Pt

mode.

4

5

(Display of angle of vector 1)

6

(Display of angle of vector 2)

(Display of angle of vector 3)

PARAMETERS

Name of parameter A B I K M X Y

Content vector scalar quantity standard vector scalar quantity calculating counter input counter number of vectors input of x component input of y component

Name of parameter

θ

K N mat A mat B mat C

Content vector angle display input of number of vectors vector components standard vector components vector inner product

Enter the number of vectors.

Enter the values of vector 1.

Enter the values of vectors 2 and 3.

Enter the value of standard vector.

13

CL

1

B

SET UP

2nd F

1

C

PRGM

A

3

ENTER

5

ENTER

8

ENTER

7

ENTER

4

ENTER

9

ENTER

2

ENTER

2

ENTER

3

ENTER

EL-9900 Graphing Calculator

Linear Transformation

Use the matrix to find four types of the linear transformation of x-axis symmetric transformation, y-axis symmetric transformation, similar transformation and revolution around the origin.

Calculation

1. Symmetric transformation to x-axis (Case 1)

X'

() ()

Y'

1 0

=

() ()

0 -1

X Y

2. Symmetric transformation to y-axis (Case 2)

X'

() ()()

Y'

Start

Array declaration

Entry of coordinates (X,Y)

Entry of type

s = 1

s = 2

s = 3

s = 4

Label XSYMMETRY

Transformation data set

Label SIMRATIO

Entry of ratio of similitude

Data set of transformation

Display of coordinates after transformation

-1 0

=

01

Y

N

Y

N

Y

N

Y

N

Coordinate transformation

X Y

FLOWCHART

TYPE

To label XSYMMETRY

To label YSYMMETRY

To label SYMRATIO

To label ROTATE

Label YSYMMETRY

Transformation data set

Label ROTATE

Entry of angle

Data set of transformation

End

3. Similar transformation with ratio of similitude K around origin (Case 3)

X' Y'

=

K0

0 K

X

()()

Y

4. Transformation revolving around only angle B at the origin (Case 4)

X'

(())()

Y'

Declare array size, etc. matH(2,2), matD(2,1), matA(2,1) Enter coordinates before transformation.

Type of transformation specified with no from 1 to 4.

Jumps to destination corresponding to entered number.

XSYMMETRY Data set of x-axis symmetric transformation matH(1,1) = 1, matH(1,2) = 0, matH(2,1) = 0, matH(2,2) = -1

YSYMMETRY Data set of y-axis symmetric transformation matH(1,1) = -1, matH(1,2) = 0, matH(2,1) = 0, matH(2,2) = 1

SIMRATIO Data set of similar transformation Entry of ratio of similitude (R) matH(1,1) = K, matH(1,2) = 0, matH(2,1) = 0, matH(2,2) = θ

Data set of transformation by revolving Entry of angle (A) matH(1,1) = cos B, matH(2,1) = sin B, matH(1,2) = -sin B, matH(2,2) = cos B,

Matrix H multiplied by matrix D.

Coordinates displayed.

cos B -sin B

=

sin B cos B

X Y

PROGRAMME LIST

Title : LINE TRN

{2, 2} dim(mat H) {2, 1} dim(mat D) {2, 1} dim(mat A) Print "Input POINT Input X Input Y X mat D(1, 1) Y mat D(2, 1) Label TYPE Print "SELECT 1, 2, 3, 4 Input S ClrT If S=1 Goto XSYMMETRY If S=2 Goto YSYMMETRY If S=3 Goto SIMRATIO If S=4 Goto ROTATE GotoTYPE Label XSYMMETRY 1 mat H(1, 1) 0 mat H(2, 1) 0 mat H(1, 2)

-1 mat H(2, 2) Goto TRANS Label YSYMMETRY

-1 mat H(1, 1) 0 mat H(2, 1) 0 mat H(1, 2) 1 mat H(2, 2) Goto TRANS Label SIMRATIO Print "Input Input R R K K mat H(1, 1) 0 mat H(2, 1) 0 mat H(1, 2) θ mat H(2, 2) Goto TRANS Label ROTATE Print "Input ANGLE Input A A B cos B mat H(1, 1) sin B mat H(2, 1)

-sin B mat H(1, 2) cos B mat H(2, 2) Label TRANS mat H mat D mat A Print "mat A(1, 1) Print mat A(1, 1) Print "mat A(2, 1) Print mat A(2, 1) End

SIMILITUDE RATIO

14

EL-9900 Graphing Calculator

3

DisplayStep

Key Operation

1

2

Specify the programme mode. Select the title LINE TRN.

Exercise

1. Transform symmetrically the point (3, 5) to the x-axis.

2. Rotate the point (2, 6) at 45˚ around the origin.

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

PARAMETERS

Name of parameter B K S

X

Content angle ratio of similitude selecting type (S=1: case 1, S=2: case 2, S=3: case 3, S=4: case 4) x-coordinate

Name of parameter Y A R mat A mat H mat D

Content

y-coordinate

input of angle

input of ratio of similitude

coordinate after transformation

transformation data

x,y-coordinate

4

5

Select symmetric transformation to x-axis (case 1).

Select transformation revolving around only angle B at the origin (case 4).

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

Enter the values of the point.

Enter the angle value.

15

CL

1B

SET UP

2nd F

1C

PRGM

A

3

ENTER

5

ENTER

1

ENTER

2

ENTER

6

ENTER

4

ENTER

5

ENTER

4

ENTER

EL-9900 Graphing Calculator

Moving Average

Plot a moving average graph which helps to understand how the results change over a specified period. The progress of sales and amounts of consumption and production can also be seen.

Calculation

FLOWCHART

PROGRAMME LIST

Entry of number of divisions

Start

End

COUNT

MOVINGSUM

Setting of calculation range

Enter unit for calculating average.

Returns to entry of no. of divisions if the number of divisions more than no. of data.

Range for graph set.

I = 0, K = int (M/2)

First calculation. Jumps to subroutine.

Jumps to subroutine. Number of calculation times of moving sum judged.

Repeated until calculation of no. of divisions performed.

X = K, Y = H Jumps to

subroutine.

Subroutine Setting of counter

Subroutine Calculation of moving sum

Subroutine Calculation of average

Jumps to subroutine.

Line displayed.

Judgment of end.

Label MAIN Print "Input DIVISION Input D D M 1_Stats L1 If M≥n Goto MAIN Rem RANGE (xmax-xmin)/10 Yscl 0 Xmin n Xmax 1 Xscl xmin Ymin xmax Ymax 0 I int (M/2) K Gosub COUNT Label LOOP1 Gosub MOVINGSUM If M≥J Goto LOOP1 Gosub AVERAGE Label LOOP2 K X H Y Gosub COUNT Label LOOP3 Gosub MOVINGSUM If (I+M)>J Goto LOOP3 Gosub AVERAGE Line (X, Y, K, H) If K≠(n-int (M/2))

Goto LOOP2 Wait End Label COUNT I+1 I I J 0 S Return Label MOVINGSUM S+L1(J) S J+1 J Return Label AVERAGE S/M H K+1 K Return

Hi = ( I = 1 +

M-1

, 2 +

M-1

, ... , n +

M-1

)

M

Calculation

Gosub count

Gosub MOVINGSUM

N

I = I + 1, J = I, S = 0

Return

AVERAGE

Return

Calculation of moving sum

Calculation of moving average

MAIN

LOOP1

LOOP2

LOOP3

Xi-(M-1) / 2 + ... + Xi + ... Xi+(M-1) / 2

Hi: moving average M : number of divisions X

i

: data

n : number of data

M>=n

Gosub AVERAGE

Gosub COUNT

Gosub MOVINGSUM

Gosub AVERAGE

Display of line

Substitution

N

M>=J

N

Y

(I+M)>J

N

K≠

(n-int(M/2))

2 2 2

Title : MVIN AVG

16

Parameters

EL-9900 Graphing Calculator

name of parameter H I J K M

content moving average counter counter counter number of divisions

name of parameter S X Y Yscl B

content moving sum starting point (x) starting point (y) scale of y-axis input of number of divisions

Exercise

Find the moving average every three months (number of divisions: 3) fr om the follo wing table of monthly sales.

Month Sales[$]

Jan. 300

Feb.

326

Mar.

323

Apr.

344

May.

300

Jun. 401

Jul.

398

On the graph, Xmax = 8, Ymin = 300, and Ymax = 450. Set up condition: decimal point in Float Pt Mode.

Enter statistical data into L1.

1

2nd F

SET UP

1

C

CL

Key Operation

STAT

ENTER

A

Aug.

450

DisplayStep

Specify the programme mode.

2

Select the title MVIN AVG.

Enter the number of divisions(3).

3

0

03623

ENTER

43

ENTER

93

ENTER

PRGM

3

ENTER

4

8

A

23

ENTER

04

ENTER

3

1

ENTER

4

003

05

17

EL-9900 Graphing Calculator

Creating a Graph of Experimental Data

Graph the results of an experiment and examine the trends. (Example: examined data relating to water vapour pressure and temperature.)

FLOWCHART

PROGRAMME LIST

Graph plot

Start

Enter statistical data using statistics feature before executing program.

Counter

Data as coordinates (starting point and finishing point).

Line drawn between set coordinates.

Y

N

End

ClrG Rem DRAWING SD 2 -Stats L1,L2 Rem RANGE xmin Xmin xmax Xmax ymin Ymin ymax Ymax (Xmax-Xmin) / 10 Xscl (Ymax-Ymin) / 10 Yscl Rem BROKEN LINE For I, 1, n-1, 1 L1(I) X L2(I) Y L1(I+1) Z L2(I+1) W Line(X,Y,Z,W) NEXT Wait End

DRAWLOOP

I = I + 1

Graph plotted using automatic scaling.

Setting of

coordinates

of line

Display of line

Whether or not lines of no. of data drawn judged. Repeated until lines drawn by the no. of data.

PARAMETERS

Name of parameter I X Z

Content counter x of line starting point x of line finishing point

Name of parameter Y W

Content

y of line starting point y of line finishing point

*n = number of statistical data

I < N

Title : XY GRAPH

18

EL-9900 Graphing Calculator

3

DisplayStep

Key Operation

1

2

Enter statistical data into L1 and L2.

…

Exercise

The following table shows examined water vapour pressure. Draw a graph of this data.

Set up condition: decimal point in Float Pt Mode.

Temperature [˚C] Pressure [mmHg]04.581109.2052017.5323031.8264055.3395092.55860149.4770223.7980355.2990525.90

100

760.00

…

4

Specify the programme mode. Select the title XY GRAPH.

(Drawing of graph)

(Other numbers not shown)

19

SET UP

2nd F

CL1C

ENTER

ST A T

A

PRGM

A

00

1

0

ENTER

01

Enter the value for temperature.

Enter the value for pressure.

0

ENTER

6

7

1

ENTER

854

•

▲

ENTER

EL-9900 Graphing Calculator

20

Ordinary Differential Equations

Enter the initial conditions (X, Y) with the step H and interval T. Use Runge Kutta Gill method to solve the ordinary differential equation of first order.

Calculation

FLOWCHART

PROGRAMME LIST

(REAL MODE)

Entry of data

Initial setting

Start

Gosub

Enter Data.

Data for calculation set. Calculation executed.

Use the following four steps of Runge Kutta Gill method to find the equation X

n + 1

and Y

n - 1

from Xn and Yn. Input Qo = 0 at the

starting point X

0

.

MAIN

Calculation of step 1.

Judgment of calculation end. If calculation result of I smaller than value of increase of I, calculation repeated again.

Z <= I

1. K0 = Hf (Xn , Yn), R1 = (1/2) (K0-2Q0), Y

(1)

= Yn +R

1

2. Q1 = Q0 + 3R1- (1/2)K

0

K1 = Hf (Xn + H/2, Y

(1)

), R2 = (1 - 1/2) (K1-Q1), Y

(2)=Y(1)

+ R

2

3. Q2 = Q1 + 3R2 - (1 - 1/2) K

1

K2 = Hf (Xn + H/2, Y

(2)

), R3 = (1 + 1/2) (K2 -Q2),Y

(3)

= Y

(2)

+ R

3

4. Q3 = Q2 + 3R3- (1 + 1/2) K

2

K3 = Hf (X

n+1

, Y

(3)

), R4 = (1/6) (K3-2Q3), Y

n+1

= Y

(3)

+ R

4

Q4 = Q3 + 3R4 - (1/2)K

3

X1X2X

3

X

Y

1

Y

2

Y

3

Y

0

h

Initial coordinates (X, Y), step of x (H), and interval of solutions (T)

Jumps to subroutine.

Gosub

Jumps to subroutine.

Calculation of step 2.

Gosub

Jumps to subroutine.

Calculation of step 3.

Gosub

Jumps to subroutine.

Calculation of step 4.

N

Y S = I

O = J

Z ≠ I

N

Y

Processing

in case of inequality

Following calculation performed when calculation result of x not equal to the value of increase of X.

P =

(Z - S) (J - O)

+ O,

M = Z N = P

Display of result

SUB1

Processing for

next calculation

Prior processing for next calculation Z = Z + T, S = X, O = J

FORMULA

Subroutine

Subroutine for

calculating

built-in function

Subroutine for calculating built-in function

f = -I J

(Another equation can be used.)

Return

SUB2

Rem INITIAL Print " Input X0 Input X Print " Input Y0 Input Y X I Y J Print " Input H Input H Print " Input T Input T 1+√(2

-1

) A

1- √(2

-1

) B I+T Z O Q I S Label MAIN Rem 1 Gosub

FORMULA H F K (K-2 Q) /2 R J+R J Q+3 R-K/2 Q

I+H/2 I Rem 2 Gosub

FORMULA H F K B (K-Q) R J+R J Q+3 R-B K Q Rem 3 Gosub

FORMULA H F K A (K-Q) R J+R J Q+3 R - A K Q I+H/2 I Rem 4 Gosub

FORMULA H F K (K - 2 Q) /6 R J+R J Q+3 R - K/2 Q If Z≤I Goto

NEXT I S J O

Goto MAIN Label NEXT If Z≠I Goto

SUB2 I M J N Label SUB1 ClrT Print "XN= Print M Print "YN= Print N Wait Z+T Z I S J O Goto MAIN Label SUB2 (Z-S) (J-O) /H+O

P Z M P N Goto SUB1 Label

FORMULA

-I J F Return

H

Title : RUNGE

EL-9900 Graphing Calculator

PARAMETERS

Name of parameter A B F H K O P Q R

Content value of 1+ (1/2) value of 1- (1/2) f (I,J) step calculating working area value of Yn-1 increase of J value of Qn value of Rn

Name of parameter S T I J Z X Y M N

Content value of Xn-1 interval Xn Yn value of increase of X input of X

0

input of Y

0

indicates Xn indicates Yn

4

DisplayStep

Key Operation

1

3

Specify the programme mode. Select the title RUNGE.

(Display of X2) (Display of Y2)

Exercise

Initial settings: Y = 10 when X = 0. F ind J when H = 0.01, T = 0.03 and I = 0.03, 0.06

...

.

(The built-in differential equation is F = -I J.)

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

5

(Display of X3) (Display of Y3)

(Display of X1) (Display of Y1)

Similar operation is performed hereafter.

2

Enter the values of X0, Y0, H and T.

21

CL2B

SET UP

2nd F

1

C

2nd F

PRGM

A

1

ENTER

00

• 3

0

•

0

ENTER

10

ENTER

EL-9900 Graphing Calculator

A

nalysing with One-way Layout Method

Use the one-way layout method to verify whether there is a relation to the results achieved based on one condition. Analysis of variance is carried out with this method.

Calculation

FLOWCHART PROGRAMME LIST

(STAT MODE)

Entry of number of levels

and repeat frequency

Start

End

Enter no. of levels and repeated frequency.

One variable statistic (Stat X) declared.

Data and square of data accumulated.

Judgment of repeated frequency

ΣX (sum of levels) displayed. ΣX obtained with

statistics feature. Square of ΣX accumulated.

Repeated frequency corresponding to no. of levels judged.

X, Y and Z calculated. Sum of squares (E, M, P)

calculated and displayed. Sum of degree of freedom

(Q, R, D) calculated and displayed.

Variance (V, U) calculated and displayed.

Variance ratio (F) calculated and displayed.

Rem INPUT Print "Input LEVEL Input L L A Print "Input TIMES Input T T N 0 W 0 B 0 C For S, 1, A, 1 N dim(L1) For K, 1, N, 1 ClrT S L K T Print "Input DATA Print "LEVEL Print L Print "TIME Print T Input I I L1(K) B+I B C+I

2

C NEXT 1_Stats L1 Σx J Print "Σx= Print J Wait W+(Σx)

2

W NEXT Rem CALCULATE B

2

/A/N X W/N Y C Z

Analysis of variance chart of one-way layout method

Declaration of one

variable statistic

Display of ΣX

(sum of levels)

Accumulation of data

Accumulation of

square of data

Entry of data

K = K + 1

LOOP2

LOOP1

[X] = (Σ Σ Xij)2 ÷ AN [A] = Σi (Σj Xij)

2

÷ N

[AS] = Σi Σj (Xij)

2

A : number of levels N: repeated frequency X: number of data

S = S + 1

Calculation of X,Y and Z

Calculation and display

of variance

Calculation and display

of sum of squares

Calculation and display

of degree of freedom

Calculation and display

of variance ratio

Accumulation

of (ΣX)

2

N

Y

Factor Error Total

Sum of squares (S) SA = [A] - [X] S

E

= [AS] - [A]

S

T

= [AS] - [X]

Degree of freedom (θ)

θA = A - 1 θ

E

= A (N- 1)

θ

T

= AN - 1

Variance (V) VA = SA ÷ θ

A

VE = SE ÷ θ

E

Variance ratio (F) FA = VA ÷ V

E

Rem SUM OF SQUARES Y-X E Z-Y M Z-X P Print "SUM OF SQUARES Print E Print "ERROR SUM OF SQUARES Print M Wait Print "TOTAL SUM OF SQUARES Print P Wait Rem DEGREES OF FREEDOM A-1 Q A (N-1) R A N-1 D Print "DEGREES OF FREEDOM Print Q Print "

DEGREES OF FREEDOM Print R Wait Print "

SUM OF DEGREES OF FREEDOM Print D Wait Rem VARIANCE E/Q V M/R U Print "VARIANCE Print V Print "VARIANCE OF ERRORS Print U Wait Rem VARIANCE RATIO V/U F Print "VARIANCE RATIO Print F End

ABOUT ERRORS

Title : VARIANCE

K ≤ N

S

≤

1

22

EL-9900 Graphing Calculator

PARAMETERS

Name of parameter A I K J N S X Z F E M P

Content number of levels input of data loop 1 counter indicating Σx repeated frequency loop 2 counter (ΣΣ xi)

2

/ a/ n

Σi Σj (xij)

2

variance ratio factor sum of squares factor sum of squares error sum of squares total

Name of parameter V U Y Q R D T L W B C

Content variance factor variance error Σi (Σ jxij)

2

/ n degree of freedom factor degree of freedom error degree of freedom total input and indicating frequency input and indicating number of levels total sum of squares of each level total sum (all data) total sum of squares (all data)

3

DisplayStep

Key Operation

1

2

Specify the programme mode. Select the title VARIANCE.

Exercise

When a mouse is given a dosage of hormone, the relationship between dosage amount and increase of mouse weight is as shown in the following table. Find the analysis of variance. If the value of the variance ratio is larger than the value of the F- distribution table at the 5% level of significance, the relationship between the hormone amount and the increase of mouse weight is a causal relation.

The number of levels (number of columns in the table) is A = 3

The repeated frequency (number of rows in the table ) is N = 5 Set up condition: decimal point in Float Pt Mode.

Increase mouse weight (grams/day)

Hormone

(grams/mouse)

10 20 30

10 882 923 933

20 891 915 939

30 864 923 925

40 888 912 940

50 885 930 932

Enter the number of levels and the repeated frequency.

23

SET UP

2nd F

CL1C

PRGM

A

5

3

ENTER

EL-9900 Graphing Calculator

6

DisplayStep

Key Operation

4

5

(Display of total of hormone 10 g)

(Display of total of hormone 20 g)

(Display of total of hormone 30 g)

7

(Display of sum of squares) (Display of error sum of squares)

8

(Display of sum of squares)

9

(Display of degrees of freedom) (Display of degrees of freedom about errors)

10

(Display of sum of degrees of freedom)

11

(Display of variance) (Display of variance of errors)

12

(Display of variance ratio)

The F-distribution chart shows that the value of F of upper probability P = 5% is 3.89. Since f > 3.98 in this example, the relationship between the hormone amount and the increase of mouse weight is a causal relation with 5% level of significance.

Enter the statistical data in level 1.

Enter the statistical data in level 2.

Enter the statistical data in level 3.

24

2

ENTER

88

4

ENTER

68

8

ENTER

88

3

ENTER

29

5

ENTER

19

2

ENTER

19

3

ENTER

39

9

ENTER

3

9

0

ENTER

49

2

ENTER

39

529

329

588

198

ENTER

0

ENTER

39

EL-9900 Graphing Calculator

Calculating Parabolic Motion

Display on a graph the altitude change and the horizontal distance over a period of time

w

hen an object is thrown at initial velocity V0 and angle θ, and find the horizontal

distance and altitude after t seconds. Specify the angle in Deg.

Calculation

FLOWCHART PROGRAMME LIST

(REAL MODE)

Entry of initial velocity

Start

Enter velocity when thrown. Highest altitude, throwing

distance (horizontal distance), and time (duration of flight) in case of released angle 45˚ calculated and displayed.

Highest altitude, throwing distance (horizontal distance), and time (duration of flight) for entered angle calculated and displayed.

Angle for throwing entered.

Entered angle less than or equal to 0˚ or larger than 90˚?

Graph (parabola) calculated and plotted.

Elapsed time counted.

Range of graph set based on values for released angle 45˚.

Calculation and plotting repeated until D (time elapsed) reaches T (duration of flight).

Entered time less than or equal to 0 or more than T?

Altitude and distance after entered time elapses from throwing calculated and displayed.

Returns to entry of time.

Deg Print "V0 (M S),θ,T(S) Print "Input V0 Input V 2 V sin 45/9.8 A V

2

/9.8 B

V

2

/19.6 C Print "HMAX= Print C Print "LMAX= Print B Print "TMAX= Print A Wait Label THETA Input θ If θ ≤ 0 Goto THETA If θ > 90 Goto THETA V

2

(sin θ)2/19.6 H V

2

sin (2θ)/9.8 L 2 V sin θ/9.8 T Print "H= Print H Print "L= Print L Print "T= Print T Wait

X = V0

•

cos θ

•

T Y = V

0

•

sin θ

•

T - 1 gT

2

Calculation and

display from

released angle 45ß

Calculation and

display of values

for entered angle

Entry of released angle

Initial velocity V0 [m/s] Angle θ [˚ ] Gravitational acceleration g = 9.8 [m/s

2

]

Time T [s]

Range setting

D = (D + T/100)

Entry of time

Display of graph

Calculation and

plotting of graph

Calculation and

display of distance

and altitude after time Z.

θ≤ 0 or θ> 90

D ≤ T

N

TX

Y

LOOP1

Z ≤ 0 or Z > T

N

Y

THETA

2

y

x

V

0

θ

C/10 Yscl B/10 Xscl 0 Xmin 0 Ymin B Xmax C Ymax For D, 0, T, T/100 V cos θ D X V sin θ D-(0.5 9.8 D

2

) Y Pnt0N(X,Y) NEXT Wait Label TX Print "Input TX Input Z If Z≤0 Goto THETA If Z>T Goto THETA V cos θ Z X V sin θ Z-(0.5 9.8 Z

2

) Y Print "X= Print X Print "Y= Print Y Wait Line(0,Y,X,Y) Line(X,0,X,Y) Wait Goto TX

Title : PARABOLA

25

EL-9900 Graphing Calculator

PARAMETERS

Name of parameter H L T X Y D Yscl

Content highest altitude horizontal distance time distance (after time Z) altitude (after time Z) time elapsed scale of y-coordinate

Name of parameter Xscl Z V

θ

C B A

Content scale of x-coordinate input of time period initial velocity (V

0

) angle (released angle) highest altitude when released at 90˚ horizontal distance when released at 45˚ time period when released at 45˚

3

DisplayStep

Key Operation

1

2

Specify the programme mode. Select the title PARABOLA.

Exercise

Find the horizontal distance and altitude three seconds after an object is thrown, when the initial velocity is 25m/sec and the angle is 52˚.

Set up condition: angle unit in Deg mode, and decimal point in Float Pt

mode.

4

5

(Display of graph of parabola)

6

(Highest altitude when released at 90˚) (Distance when released at 45˚) (Time when released at 45˚)

(Display of highest altitude) (Display of horizontal distance) (Display of time until dropping of object)

7

(Display of distance after Z seconds) (Display of altitude after Z seconds)

8

(Altitude and distance after Z seconds are displayed on the parabola graph.)

Enter the value of the initial velocity.

Enter the angle value.

Enter the value of time period Z.

26

PRGM

CL

ENTER

SET UP

2nd F

A

1C

2

5

ENTER

5

2

ENTER

3

ENTER

1B1E

Key pad for the SHARP EL-9900 Calculator

Graphing keys Power supply ON/OFF key Secondary function specification key Alphabet specification key Display screen

Cursor movement keys Clear/Quit key Variable enter key Calculation execute key Communication port for peripheral devices

Advanced Keyboard

Key pad for the SHARP EL-9900 Calculator

Graphing keys Power supply ON/OFF key Secondary function specification key Alphabet specification key Display screen

Cursor movement keys Clear/Quit key Variable enter key Calculation execute key Communication port for peripheral devices

Basic Keyboard

Dear Sir/Madam

We would like to take this opportunity to invite you to create a mathematical problem which can be solved with the SHARP EL-9900 graphing calculator, including the necessary procedures and definitions as outlined in the form below.

For this purpose, we would be grateful if you could complete the form and return it to us by fax or mail. If your contribution is chosen, your name will be included in the next edition of The EL-9900 Graphing Calculator Handbook or on our homepage. We regret that we are unable to return contributions. Also, please note that the problems you send us might be opened to the public at Sharp’s home page.

We thank you for your cooperation in this project.

Name: ( Mr. Ms.

)

School/College/Univ.: Address:

Post Code: Country:

Phone: Fax: E-mail:

SUBJECT: Write either a title or about the subject matter.

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INTRODUCTION and CALCULATION:

Write a brief explanation of the subject, and the formula with definitions, including a diagram if relevant.

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Use this form to send us your contribution

SHARP Graphing Calculator

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SHARP CORPORATION Osaka, Japan

Fax:

PARAMETERS:

Define the parameters used in the programme.

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EXERCISE and SET UP CONDITION:

Include an example of a problem which can be solved with the formula. Write a step-by-step guide to solving the problem with an explanation. Detail any important conditions to be set up before solving the problem.

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SHARP Graphing Calculator

PROGRAMME LIST:

List the procedure of data to be entered.

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SHARP CORPORATION OSAKA,JAPAN