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

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)

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

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

2

005091•2

ENTER

Enter the value of the angle

5

of obliquity.

(Display of involute value)

14 1

ENTER

•

5

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

2

r

i

cos θ

i =

l cos θ

2

r

l =

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

FLOWCHART

Start

A

Selection of type

Y

S = 1

S = 2

CANDELA

To subroutine To subroutine

Entry of

illuminance

Calculation of

luminous intensity

Display of

luminous intensity

Subroutine

Entry of distance and angle

Return

start

N

A

Entry of

luminous intensity

Calculation of

illuminance

Display of

illuminance

End

DISTANCE

LUX

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.

Entry.

Returns to calling program.

Luminous Intensity l

θ

r

Illuminance i

PROGRAMME LIST(REAL MODE)

Title : CAND LUX

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

2

R

I/cos θ C Print "CANDELA Print C End Label LUX Gosub DISTANCE Print "Input CANDELA Input C C K K cos θ /R Print "LUX Print L End Label DISTANCE Print "Input DISTANCE Input D D R Print "Input ANGLE Input A A θ Return

2

L

Name of parameter I K R S

6

PARAMETERS

Content illuminance of illuminated side luminous intensity of luminous source distance

selecting calculation type

calculation of luminous intensity

(S=1: (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

EL-9900 Graphing Calculator

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.

2nd F

SET UP

CL

1C

Specify the programme mode.

1

Select the title CAND LUX.

Select calculation of luminous

2

intensity.

Enter the values of distance,

3

angle, and illuminance.

(Display of luminous intensity)

Key Operation

A

PRGM

ENTER

1

10 2

0

ENTER

60

DisplayStep

ENTER

Select calculation of illuminance.

4

Enter the values of distance, angle, and luminous intensity.

(Display of illuminance)

ENTER ENTER

10 6 4

2

ENTER

0

000

ENTER

7

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

angular velocity : ω = acceleration : a = -ω

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

FLOWCHART

Start

Entry of period

and amplitude

CALC

Entry of time

Calculation of

angular velocity, etc.

Display of

calculation result.

Calculation of

range and scale

Graph display

Display clear

2π

T

2

x velocity : v = A ω cos (ω t)

+

displacement : x = A sin (ω t)

0

+

Ax

2π

ωt

+

A

PROGRAMME LIST

Title : OSCILLAT

Rad Print "Input PERIOD Input P P F Print "Input AMPLITUDE Input A A D Label 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.

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

...

Xmin

0, Xmax

...

Ymin

-D, Ymax

Text and graph display cleared.

...

E, Xscl

...

D, Yscl

...

E/10

...

D/5

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

ωt

v

0

v ax

(REAL MODE)

8

PARAMETERS

EL-9900 Graphing Calculator

Name of parameter B E V W H Xscl Yscl

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

Name of parameter A P T D F X

Exercise

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.

2nd F

SET UP

E

1

C

CL

1

Key Operation

PRGM

A

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

DisplayStep

Enter the values of period,

2

amplitude, and time.

3

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

4

(Display of graph of simple harmonic oscillation)

5

2nd F

ENTER

π

ENTER

1

ENTER

3

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

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

R

•

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

0: change in amount of voltage with time

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

V

I

FLOWCHART

Start

Data entry

Calculation of power

Calculation of range

Display of power

Display of graph

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

PROGRAMME LIST

Title : AC POWER

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)) End

2

(REAL MODE)

Name of parameter S I T D W N M Xmax

10

PARAMETERS

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

EL-9900 Graphing Calculator

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.

SET UP

2nd F

1

C

1

E

CL

Specify the programme mode.

1

Select the title AC POWER.

Enter the resistance value,

2

voltage effective value, and frequency.

(Display of value power)

3

(Display of graph)

Key Operation

PRGM

A

15 10

0

5

ENTER

0 0

ENTER

DisplayStep

11

A

EL-9900 Graphing Calculator

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

←

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

←←

a• b

θ = cos

-1

←←

| a | | b |

←←←

End

FLOWCHART

Start

Entry of number

of vectors

Definition of arrays

Vector data entry

K = K + 1

Y

component of vector

K

≤

M

N

Entry of standard

vector data

Calculation of

component of

standard vector

Calculation of inner product

I = I + 1

I > M

N

Calculation of

PROGRAMME LIST

Title : VECTOR

Print " Input NUMBER

Enter no. of vectors for which angles are calculated.

Arrays defined. matA, matB, matC.

Counter for data entry.

Enter x component and Y component of each vector.

Entry repeated by no. of vectors.

Enter x component and Y component of standard vector.

Length component of standard vector (scalar) calculated.

Product of matrices A and B calculated.

Counter for calculation of angle.

Calculation repeated by no. of vectors.

Length component of vector (scalar) calculated.

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) mat A mat B mat C For I, 1, M, 1 √ (mat A(I,1) cos Print "ANGLE OF VECTOR Print I Print "θ= Print θ Wait NEXT End

2

+mat B(2,1)2) B

2

-1

(mat C(I,1) / (A B)) θ

+mat A(I,2)2) A

(MATRIX MODE)

12

Calculation of angle and display of angle

Angle calculated and displayed.

PARAMETERS

EL-9900 Graphing Calculator

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

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.

2nd F

SET UP

1

B

C

CL

1

Key Operation

DisplayStep

Specify the programme mode.

1

Select the title VECTOR.

Enter the number of vectors.

2

Enter the values of vector 1.

3

Enter the values of vectors

4

2 and 3.

Enter the value of standard

5

vector.

A

PRGM

3

ENTER

5

ENTER

7

ENTER

9

2

ENTER

8

ENTER

4

ENTER

2

3

ENTER

6

(Display of angle of vector 1)

ENTER

(Display of angle of vector 2)

ENTER

(Display of angle of vector 3)

13

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

PARAMETERS

EL-9900 Graphing Calculator

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

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.

Specify the programme mode.

1

Select the title LINE TRN.

2nd F

SET UP

1B

1C

CL

Key Operation

PRGM

A

DisplayStep

Enter the values of the point.

2

Select symmetric transformation

3

to x-axis (case 1).

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

Select transformation revolving

4

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

Enter the angle value.

5

3

ENTER

1

ENTER

4

ENTER

2

4

5

ENTER

5

ENTER

6

ENTER

15

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

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

Hi =

M

( I = 1 +

M-1

2 2 2

, 2 +

M-1

FLOWCHART

Start

MAIN

Entry of number of divisions

Y

Setting of calculation range

Gosub MOVINGSUM

Y

Gosub AVERAGE

Gosub MOVINGSUM

Y

Gosub AVERAGE

Y

M>=n

N

Calculation

Gosub count

LOOP1

M>=J

N

LOOP2

Substitution

Gosub COUNT

LOOP3

(I+M)>J

N

Display of line

K≠

(n-int(M/2))

N

End

Hi: moving average M : number of divisions X

i

, ... , n +

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. Jumps to

subroutine.

M-1

)

COUNT

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

Return

MOVINGSUM

Subroutine Setting of counter

Subroutine Calculation of moving sum

: data

n : number of data

Calculation of moving sum

Jumps to subroutine.

Line displayed.

Judgment of end.

Return

AVERAGE

Subroutine Calculation of average

Calculation of moving average

Return

PROGRAMME LIST

Title : MVIN AVG

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)) 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

Goto LOOP2

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

Aug.

450

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

2nd F

SET UP

1

C

CL

Key Operation

DisplayStep

Enter statistical data into L1.

1

Specify the programme mode.

2

Select the title MVIN AVG.

Enter the number of divisions(3).

3

STAT

ENTER

PRGM

3

ENTER

A

0

03623

43

93

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.)

Start

Graph plot

Setting of

coordinates

of line

Display of line

I = I + 1

Y

I < N

End

FLOWCHART

Enter statistical data using statistics feature before executing program.

Graph plotted using

DRAWLOOP

N

automatic scaling.

Counter

Data as coordinates (starting point and finishing point).

Line drawn between set coordinates.

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

PROGRAMME LIST

Title : XY GRAPH

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

Name of parameter I X Z

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

PARAMETERS

Name of parameter Y W

Content

y of line starting point

y of line finishing point

*n = number of statistical data

18

EL-9900 Graphing Calculator

Exercise

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

Temperature [˚C] Pressure [mmHg]04.581109.2052017.5323031.8264055.3395092.55860149.4770223.7980355.2990525.90

Set up condition: decimal point in Float Pt Mode.

Enter statistical data into

1

L1 and L2.

Enter the value for temperature.

2nd F

SET UP

CL1C

Key Operation

A

ENTER

01

ST A T

…

0

2

1

(Other numbers not shown)

00

ENTER

100

760.00

DisplayStep

Enter the value for pressure.

3

Specify the programme mode.

4

Select the title XY GRAPH.

(Drawing of graph)

▲

…

PRGM

• 0

6

7

A

854

ENTER

1

ENTER

19

EL-9900 Graphing Calculator

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

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

n + 1

and Y

n - 1

equation X

0

starting point X

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

.

from Xn and Yn. Input Qo = 0 at the

(1)

= Yn +R

1

Y

2. Q1 = Q0 + 3R1- (1/2)K K1 = Hf (Xn + H/2, Y

3. Q2 = Q1 + 3R2 - (1 - 1/2) K K2 = Hf (Xn + H/2, Y

4. Q3 = Q2 + 3R3- (1 + 1/2) K K3 = Hf (X Q4 = Q3 + 3R4 - (1/2)K

n+1

, Y

Start

Entry of data

Initial setting

MAIN

Gosub

Calculation of step 1.

Gosub

Calculation of step 2.

Gosub

Calculation of step 3.

Gosub

Calculation of step 4.

Z <= I

Y S = I

O = J

Z ≠ I Y

Processing

in case of inequality

SUB1

Display of result

Processing for

next calculation

0

(1)

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

1

(2)

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

(3)

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

N

2

3

Enter Data.

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

Data for calculation set. Calculation executed.

Jumps to subroutine.

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

Following calculation

SUB2

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

(Z - S) (J - O)

P =

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

(2)=Y(1)

+ R

2

(3)

(2)

= Y

+ R

(3)

n+1

= Y

+ R

4

FLOWCHART

M = Z

+ O,

H

N = P

3

Subroutine

FORMULA

Subroutine for

calculating

built-in function

Return

PROGRAMME LIST

Title : RUNGE

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

1+√(2

) A

-1

1- √(2

) 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 H F K B (K-Q) R J+R J Q+3 R-B K Q Rem 3 Gosub H F K A (K-Q) R J+R J Q+3 R - A K Q I+H/2 I Rem 4 Gosub H F K (K - 2 Q) /6 R J+R J Q+3 R - K/2 Q If Z≤I Goto I S J O

Y

3

Y

2

1

Y

h

0

X1X2X

Subroutine for calculating built-in function

(Another equation can be used.)

(REAL MODE)

FORMULA

3

f = -I J

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

20

PARAMETERS

EL-9900 Graphing Calculator

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 input of Y indicates Xn indicates Yn

0

Exercise

Initial settings: Y = 10 when X = 0. Find 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.

2nd F

SET UP

C

CL2B

1

Key Operation

DisplayStep

...

.

Specify the programme mode.

1

Select the title RUNGE.

Enter the values of X0, Y0,

2

H and T.

3

(Display of X1) (Display of Y1)

4

(Display of X2) (Display of Y2)

2nd F

A

PRGM

0

ENTER

0

ENTER

0

•

0

ENTER

1

1 30

5

(Display of X3) (Display of Y3)

Similar operation is performed hereafter.

ENTER

21

A

EL-9900 Graphing Calculator

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

Analysis of variance chart of one-way layout method

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 VE = SE ÷ θ

Variance ratio (F)

A

FA = VA ÷ V

E

[X] = (Σ Σ Xij)2 ÷ AN

2

[A] = Σi (Σj Xij) [AS] = Σi Σj (Xij)

÷ N

2

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

FLOWCHART PROGRAMME LIST

Start

LOOP2

Entry of number of levels

and repeat frequency

Declaration of one

variable statistic

LOOP1

Entry of data

Accumulation of data

Accumulation of

square of data

K = K + 1

Y

K ≤ N

N

Display of ΣX

(sum of levels)

Accumulation

of (ΣX)

2

S = S + 1

Y

S

≤

1 N

Calculation of X,Y and Z

Calculation and display

of sum of squares

Calculation and display

of degree of freedom

Calculation and display

of variance

Judgment of repeated frequency

Repeated frequency corresponding to no. of levels judged.

Title : VARIANCE

Rem INPUT

Enter no. of levels and repeated frequency.

One variable statistic (Stat X) declared.

Data and square of data accumulated.

ΣX (sum of levels) displayed. ΣX obtained with

statistics feature. Square of ΣX accumulated.

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

calculated and displayed. Sum of degree of freedom

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

2

C+I

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

2

B

/A/N X W/N Y C Z

(Q, R, D) calculated and displayed.

Variance (V, U) calculated and displayed.

2

W

(STAT MODE)

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

Calculation and display

of variance ratio

End

22

Variance ratio (F) calculated and displayed.

PARAMETERS

EL-9900 Graphing Calculator

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

2

/ a/ n

(ΣΣ xi) Σi Σj (xij) variance ratio factor sum of squares factor sum of squares error sum of squares total

2

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

Content variance factor variance error

2

Σi (Σ jxij) 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)

/ n

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.

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

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.

1

2

3

2nd F

SET UP

CL1C

Specify the programme mode. Select the title VARIANCE.

Enter the number of levels and the repeated frequency.

PRGM

3

ENTER

Key Operation

A

5

DisplayStep

23

EL-9900 Graphing Calculator

Enter the statistical data

4

in level 1.

(Display of total of hormone 10 g)

Enter the statistical data

5

in level 2.

(Display of total of hormone 20 g)

Enter the statistical data

6

in level 3.

(Display of total of hormone 30 g)

Key Operation

2

88

ENTER

88

ENTER

19

ENTER

39

ENTER

9

3

ENTER

39

ENTER

8

5

0

9

2

68

ENTER

29

ENTER

19

ENTER

39

ENTER

49

ENTER

4

3

2

3

0

ENTER

DisplayStep

198

588

329

529

7

8

9

10

11

ENTER

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

ENTER

(Display of sum of squares)

ENTER

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

ENTER

(Display of sum of degrees of freedom)

ENTER

(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.

24

ENTER

EL-9900 Graphing Calculator

w

Calculating Parabolic Motion

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

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

•

X = V0

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

Entry of initial velocity

Calculation and

display from

released angle 45ß

Entry of released angle

Y

θ≤ 0 or θ> 90

Calculation and

display of values

for entered angle

Range setting

LOOP1

Calculation and

plotting of graph

•

cos θ

T Y = V

FLOWCHART PROGRAMME LIST

Start

THETA

N

•

0

Enter velocity when thrown. Highest altitude, throwing

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

Angle for throwing entered.

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

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

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

Graph (parabola) calculated and plotted.

sin θ

2

]

•

T - 1 gT

2

y

0

V

θ

Title : PARABOLA

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

2

/9.8 B

V

2

V

/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

2

(sin θ)2/19.6 H

V

2

sin (2θ)/9.8 L

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

x

(REAL MODE)

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

2

) Y

2

) Y

D = (D + T/100)

Y

D ≤ T

N

Entry of time

Z ≤ 0 or Z > T

N

Calculation and

display of distance

and altitude after time Z.

Display of graph

Elapsed time counted. Calculation and plotting repeated

until D (time elapsed) reaches T (duration of flight).

TX

Entered time less than or equal

Y

to 0 or more than T?

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

Returns to entry of time.

25

PARAMETERS

EL-9900 Graphing Calculator

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

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.

2nd F

SET UP

Specify the programme mode.

1

Select the title PARABOLA.

1B1E

1

C

CL

Key Operation

PRGM

A

DisplayStep

0

)

Enter the value of the initial velocity.

2

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

3

Enter the angle value.

4

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

5

(Display of graph of parabola)

6

25

ENTER

2

5

ENTER

26

Enter the value of time period Z.

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

3

ENTER

Key pad for the SHARP EL-9900 Calculator

Advanced Keyboard

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

Key pad for the SHARP EL-9900 Calculator

Basic Keyboard

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

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Use this form to send us your contribution

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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SHARP Graphing Calculator

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PARAMETERS:

Define the parameters used in the programme.

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PROGRAMME LIST:

List the procedure of data to be entered.

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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 pr oblem with an explanation. Detail any important conditions to be set up before solving the problem.

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SHARP CORPORATION Osaka, Japan

Fax:

SHARP Graphing Calculator

SHARP CORPORATION OSAKA,JAPAN

Sharp EL-9900 User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual