Sharp EL-9900 Manuale utente

Sharp EL-9900

Graphing Calculator

Basic Keyboard Activities

General Mathematics

Algebra

Programming

Advanced Keyboard Activities

Algebra

Calculus

Statistics

Trigonometry

Programming

Sharp EL-9900

Graphing Calculator

Advanced Keypad

EL-9900

SUB SPLIT TBLSET DRAW FORMAT CALC

OPTION LIST CLIP

OFF A-LOCK

STAT

PLOT

SLIDE

SHOW

2ndF

ALPHA

GRAPH

TABLE

WINDOW

ZOOM

TRACE

789 ()

456

–

0(–)

ENTER

+–

–

MATH

STAT

PRGM

sin

STO

DEL BS

X/0/T/n

x–1

log

abc

cos tan

INS

SOLVER

MATRIX

TOOL

RCL VARS

SET UP QUIT

sin cos tan

–1 –1 –1

BCDEF

GH I J K

uvw

L4 L5 L6

L1 L2 L3

MN O

{}

QRST

CATALOG

FINANCE

SPACE ENTRY

ANS

EXE

=

Y Z

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

Steps for graphing the sine function

1. Turn the calculator on and press Y= .

2. Press CL to remove an old Y1 expression.

3. Press ▼CL to clear additional expressions.

4. To set up the calculator press 2ndF SET UP B (DRG) 2(Rad)

E (COORD) 1(Rect) G (EDITOR) and 1 (Equation).

5. Press 2ndF QUIT again to return to the Y prompts.

6. Enter the sine function ( y= sin x) for Y1, by pressing sin X/θ/T/n.

7. Enter the viewing window range by pressing ZOOM E (TRIG) and

1(sin x).

Steps for graphing the cosecant function.

1. Press Y= CL to remove an old Y1 expression.

2. Enter the cosecant function for Y1 by pressing MATH A (CALC)

1 0 (csc) and press X/θ/T/n.

3. Continue to use the sine function's built-in viewing range.

4. Press GRAPH to view the graph.

GRAPHS OF TRIGONOMETRIC FUNCTIONS

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

Steps for evaluating sin 45° directly

1. Turn the calculator on and press to access the computation screen.

2. Press CL to clear the viewing window of any old expressions.

3. Set the calculator to operate in degrees by pressing 2ndF SET UP

B(DRG) 1 (Deg). Press 2ndF QUIT to exit the menu.

4. Enter and evaluate the expression by pressing sin 4 5 ENTER .

Steps for approximating sin ( ) graphically

1. Press Y= followed by CL to clear an old expression for Y1.

2. Enter the function sin xby pressing sin X/θ/T/n. Set the calculator to

radian mode by pressing 2nd F SET UP B (DRG) and 2 (Rad). Press

2nd F QUIT to exit the menu.

3. View the graph by pressing ZOOM E (TRIG) 1sin x.

4. Now, engage the trace by pressing TRACE and tracing near x= = 1.047.

5. With the cursor located near x= 1.047, you can zoom in to find a better

approximation for the yvalue. Press ZOOM A (ZOOM) 3 (In) to zoom

in on the cursor.

6. Once again, trace over near x= 1.047. Zoom in one more time to see an even

better approximation. The y value of .866 approximates sin ( )..

EVALUATING TRIGONOMETRIC FUNCTIONS

+–

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

Steps for evaluating sec ( ) directly in degree mode

1. Press to enter computation mode.

2. Press 2ndF SET UP to verify the calculator is in degree mode. If it is not,

change it to degree mode. Press 2ndF QUIT to exit the menu.

3. Enter and evaluate the expression by pressing MATH A (CALC)

0 9 (sec) 2ndF πa/b 4 MATH E (ANGLE) 4 (r) and

pressing ENTER .

Steps for approximating tan 20° graphically

1. Press Y= and press CL to remove an old expression for Y1.

2. Press 2ndF SET UP to verify the calculator is in degree mode. If it is not,

change it. Press 2ndF QUIT to exit the menu.

3. Enter the function tan xfor Y1 by pressing tan X/θ/T/n.

4. Instead of graphing the function in the default viewing window for tangent,

press WINDOW adjust the Xmin and Xmax to 10° and 30° (value of interest

± 10° ) respectively to start out closer to the value of interest. Set the Xscl =

1. Press ZOOM A (ZOOM) and 1 (Auto) to view the graph.

5. Now, engage the trace by pressing TRACE . Notice the tracer appears at

x= 20° since it is the middle of the xvalues. The approximate for tan 20°

is .36397.

EVALUATING TRIGONOMETRIC FUNCTIONS

+–

▼

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

1. Verify the double angle formula sin 2θ= 2 sin θcos θ, by graphing Y1 = sin

(2x) and Y2 = 2 sin xcos xand show that they are in fact the same graph.

2. Turn the calculator on and press Y= . Press CL to clear Y1 of an old

expression. Press ▼CL to clear additional expressions.

3. Make sure the calculator is in radian mode by pressing 2ndF SET UP ,

B(DRG) and 2 (Rad). Press 2ndF QUIT to exit the menu.

4. Now enter sin (2x) for Y1 by pressing sin ( 2 X/θ/T/n) ENTER

and the 2 sin xcos xfor Y2 by pressing 2 sin X/θ/T/ncos X/θ/T/n

ENTER .

5. Set your viewing window by pressing ZOOM E (TRIG) 1 (sin x).

6. They appear as one graph. An invalid formula or identity would result in

two graphs.

GRAPHICAL VERIFICATION OF FORMULAS

AND IDENTITIES

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

Investigate changes in amplitude.

1. Turn the calculator on and press Y= and CL to clear old expressions.

2. Enter y = sin x for Y1 by pressing sin X/θ/T/n.

3. Enter y = 3 sin x for Y2 by pressing 3 sin X/θ/T/n.

4. Press ZOOM A (ZOOM) 5 (Default) to view the graphs.

5. Notice that the 3 in front of the sine function makes the curve oscillate

between 3 and -3 instead of 1 and -1.

6. Press Y= ▼CL to clear Y2. Enter y= -2 sin x for Y2 by pressing

( - ) 2 sin X/θ/T/n.

7. Press GRAPH to view the graphs. Notice that the -2 in front of the sine

function makes the curve reflect on the x-axis and makes the curve oscillate

between -2 and 2.

AMPLITUDE

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

Investigate the change in a trigonometric function by multiplying

the argument θby 2.

1. Press Y= CL to access and clear Y1 of an old expression.

2. Make sure the calculator is in radian mode by pressing 2ndF SET UP ,

B(DRG) and 2 (Rad). Press 2ndF QUIT to exit the menu.

3. Now, enter sin x for Y1 by pressing sin X/θ/T/nENTER and the sin (2x)

for Y2 by pressing CL sin (2 X/θ/T/n)ENTER .

4. Set your viewing window by pressing ZOOM E (TRIG) and 1 (sin x).

Note the change in the second graph versus the first graph. Engage the

trace to show the period has changed from 2πto π.

Investigate the change in a trigonometric function by subtracting

to the argument θ.

1. Press Y= ▼CL and enter Y= sin (X - 3π/2) for Y2 by pressing

sin ( X/θ/T/n– 3 2ndF π÷ 2 ) ENTER .

2. Press GRAPH to view the graphs. Observe and note the changes in sin x

when you change the phase shift.

PERIOD AND PHASE SHIFT

3π

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

To compute the inverse sine function in degrees:

1. Turn the calculator on and press CL to enter computation mode.

2. Change to degree mode by pressing 2ndF SET UP B (DRG) and

1(Deg). Press 2ndF QUIT to exit the menu.

3. Find sin–1 (.5) by pressing 2ndF sin-1 • 5 ENTER . The answer of 30°

is shown below.

To graph the inverse sine function in degrees:

1. Press Y= CL to access and clear the Y1 expression.

2. Press ENTER CL to clear additional Y expressions.

3. Enter sin-1 xfor Y1 by pressing 2ndF sin-1 X/θ/T/nENTER .

4. Set your viewing window by pressing ZOOM E (TRIG) and

4(sin-1 x).

INVERSE TRIGONOMETRIC FUNCTIONS

+–

Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900

To compute the inverse sine function in radians:

1. Turn the calculator on and press CL to access and clear the

home screen.

2. Change to radian mode by pressing 2ndF SET UP B (DRG)

and 2 (Rad). Press 2ndF QUIT to exit the menu.

3. Find sin-1 (.4), press 2ndF sin-1 • 4 ENTER . The answer of .4115

radians is shown below. To find the result in terms of πpress ÷ 2ndF

πENTER .

To graph the inverse cosine function in radians:

1. Press Y= CL to access and clear the Y1 prompt.

2. Enter cos -1 xfor Y1 by pressing 2ndF cos-1 X/θ/T/nENTER .

3. Set your viewing window by pressing ZOOM E (TRIG) and

5 (cos-1 x).

INVERSE TRIGONOMETRIC FUNCTIONS

+–

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