Sharp EL-9900 User manual

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
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1
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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

2
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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
×
+–
÷
π
3
π
3
π
3

3
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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
π
4
×
+–
÷
▼

4
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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

5
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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

6
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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
2

7
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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
×
+–
÷

8
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
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
×
+–
÷

9
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
To solve a trigonometric equation graphically using the
zoom feature:
1. Turn the calculator on and press Y= CL to access and clear Y1 of an old
expression. Set the calculator to degree mode by pressing 2ndF SET UP
B(DRG) and 1 (Deg). Press 2ndF QUIT to exit the menu.
2. To find the solutions of 3sin2x– 4sin x+ 1 = 0, press 3 ( sin X/θ/T/n
) ab2 – 4 sin X/θ/T/n+ 1 ENTER .
3. Set your viewing window to the principal values for sine by pressing
WINDOW (–) 9 0 ENTER 9 0 ENTER 1 0 ENTER (–) 1
ENTER 1 ENTER 1 ENTER . Press GRAPH to view the graph.
4. To save this original graph and viewing window, press ZOOM G (STO) and
1(StoWin).
5. Set the zoom factors by pressing ZOOM B (FACTOR) ENTER 5
ENTER 5 ENTER . Press GRAPH to exit the menu.
6. To find the left intercept press TRACE and move the cursor near this
intercept by continuing to press the key.
7. Now, press ZOOM A (ZOOM) and 3 (In) to zoom in on
the left intercept and solution of this equation. Press TRACE and to
trace near and approximate the intercept.
8. Return to the original screen by pressing ZOOM H (RCL) and
1 (RclWin). Trace to find the right intercept.
SOLVING TRIGONOMETRIC EQUATIONS
▼
▼
▼

10
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
To solve a trigonometric equation graphically using the
CALC feature:
1. Press Y= CL to access and clear Y1. Set the calculator to radian mode
by pressing 2ndF SET UP B (DRG) and 2 (Rad).
Press 2ndF QUIT to exit the menu.
2. To find the solutions of 2sin2x– cos x– 1 = 0, press 2 ( sin X/θ/T/n)
ab2 – cos X/θ/T/n– 1 ENTER .
3. Set your viewing window by pressing WINDOW (–) 2ndF π÷2
ENTER 2ndF πENTER 2ndF π÷ 4 ENTER (–) 1 ENTER
1 ENTER 1 ENTER . Press GRAPH to view the graph.
4. To "calculate" an intercept (solution), press 2ndF CALC 5 (X_Incpt).
You can calculate the other two intercepts by pressing 2ndF CALC 5
(X_Incpt) again.
To solve an equation with functions on both the left and right sides:
1. Press Y= CL to access and clear Y1 of an old expression. To find the
solutions of 2tan xsin x+ 2sin x= tan x+ 1, you will enter the left side as Y1,
by pressing 2 tan X/θ/T/nsin X/θ/T/n+ 2 sin X/θ/T/nENTER .
2. Enter the right side as Y2, by pressing tan X/θ/T/n+ 1 ENTER .
3. Set your viewing window by pressing WINDOW (–) 2ndF π÷2
ENTER 2ndF πENTER 2ndF π÷ 4 ENTER (–) 2 ENTER
2 ENTER 1 ENTER . Press GRAPH to view the graph.
4. There appears to be four solutions to the equation. To "calculate" the
intersections (solutions), press TRACE , move the tracer right until it
appears on the screen. Next, press 2ndF CALC 2 (Intsct).
Do this several times.
SOLVING TRIGONOMETRIC EQUATIONS
▼

11
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
Steps for using the calculator to solving applications with
right triangles
1. Turn the calculator on and set it to degree mode by pressing 2ndF SET UP ,
B(DRG) 1(Deg). Press 2ndF QUIT to exit the set up menu.
2. Given a right triangle with A = 3 and C = 6, find B and θusing the SOLVER.
To access the SOLVER, press 2ndF SOLVER , and press CL to delete any
equation that may appear on the screen.
3. Type in the equation sin θ= with the keystrokes sin ALPHA θ
ALPHA = a/b ALPHA A ALPHA C .
4. Press 2ndF SOLVER A (METHOD) 1(Equation) to choose the
Equation solver. Press ENTER and see the list of variables.
5. Press ▼to move the blinking cursor over the A and press 3 ENTER .
Type in the value of C by pressing 6 ENTER . Solve for θby pressing
▲▲2nd EXE .
6. To use the SOLVER to find B, edit the current equation to the new equation
cos θ= . Do this by pressing CL CL to display the current equation
sin θ= . With the cursor over the s in sin, press cos to insert cos.
Press DEL to delete sin. Press to move the cursor over the A in
the numerator of the fraction. Press ALPHA B to insert B. Press DEL to
delete A.
7. Press ENTER to see the variable list. The value for θand C will remain as
before. Press ▼to position the cursor over the B and press 2ndF EXE
to find B.
APPLICATIONS WITH RIGHT TRIANGLES
A
C
B
C
A
C
▼
▼
▼
▼

12
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
A rectangle has a length 16 cm and a width 8.6 cm. Find the degree measure of
angle A. Determine the length of the diagonal of the rectangle.
1. Press 2ndF SOLVER to access the SOLVER, and press CL to delete
the equation that is on the screen.
2. Enter the equation tan θ= by pressing tan ALPHA θALPHA =
a/b ALPHA A ALPHA B .
3. Press ENTER to view the variable list.
4. Enter 8.6 for A and 16 for B. (The value of θwill be listed as the one that
was used in the previously entered equation.)
5. Position the cursor over θand press 2ndF EXE to find θ.
6. To determine the length of the diagonal of the rectangle, return to the
equation by pressing CL CL and edit the current equation to read
sin θ= A/C.
7. Press ENTER to see the variable list. The value of θshould be as before,
so enter 8.6 for A and solve for C.
APPLICATIONS WITH RIGHT TRIANGLES
(
A
8.6
16
A
B
▼
×
+–
÷

13
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
Use the Graphic Solver with the Law of Sines.
1. Set the calculator to degrees by pressing 2ndF SET UP B (DRG)
and 1 (Deg). Press 2ndF QUIT to exit the set up screen.
2. To access the SOLVER, press 2ndF SOLVER CL . Enter =
by pressing a/b sin ALPHA A ALPHA X ALPHA = a/b
sin ALPHA B ALPHA Y .
3. Store it into memory by pressing 2ndF SOLVER C (SAVE) pressing
ENTER , and typing in LAWSINES. Press ENTER to store the formula.
4. Press 2ndF SOLVER A (METHOD) 3 (Graphic) to choose the
Graphic Solver. Press ENTER for the list of variables.
5. With the blinking cursor over the A, type in 95 and press ENTER .
Next, type 15 for x, the length of the side opposite the 95°, and press
ENTER . Enter 48 for B in the same manner. Solve for yby positioning the
blinking cursor over the yand press 2ndF EXE .
6. You must enter the range values for the unknown (from BEGIN to END)
within which you expect to find the solution. Let the BEGIN = 5 by pressing
5 ENTER . Enter a value for END that you do not expect yto exceed,
say 25, by pressing 2 5 ENTER . Press 2ndF EXE and an autoscaled
plot will be drawn showing graphs of the left and right sides of the current
equation.
7. The calculator will now display a box in the center of the viewing screen
while it looks for the intersection of the two graphs. The solution is
displayed at the bottom of the screen.
LAW OF SINES
▼
▼
▼
sin A
X
sin B
Y

14
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
Use the Newton Solver with the Law of Cosines.
1. Access the SOLVER with 2ndF SOLVER (or press CL twice if you are still
in the SOLVER). Press CL to delete the current equation. Return to the
Equation Solver by pressing 2ndF SOLVER A (METHOD) and
1(Equation).
2. Next enter the Law of Cosines by pressing ALPHA Z x2ALPHA =
ALPHA X x2+ ALPHA Y x2– 2 ALPHA X ×ALPHA
Y ×cos ALPHA θ.
3. Store this equation in the calculator.
4. Given a triangle in which two sides of lengths 13 cm and 8 cm enclose a 50°
angle. Find the length of the third side.
5. Press ENTER to view the list of variables. Press ▼to position the cursor
on X and enter 13. Next, enter 8 for Y and 50 for θ. Press ▲to move the
cursor over Z and press 0 ENTER .
6. Press 2ndF EXE to solve for Z. Notice that the SOLVER has automatically
changed to the Newton Solver. You should supply an initial estimate of the
solution in the START position (0 is the default value) and a step size STEP
(.001 is the default value).
7. Press 2ndF EXE to find the solution. (If you receive an error message, try
changing the START value or increasing the STEP value.)
8. Notice the left and right sides of the equation are displayed as equal values,
and the L – R = 0.
LAW OF COSINES

15
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
1. Set the calculator to operate in degrees with 2ndF SET UP B (DRG)
and 1 (Deg). Press 2ndF QUIT to exit the set up screen.
2. Access the SOLVER by pressing 2ndF SOLVER , and press CL to delete
any equation on the screen.
3. Type in the equation A = B•H with the keystrokes: ALPHA A ALPHA
= a/b 1 2 ALPHA B ×ALPHA H
4. Press 2ndF SOLVER A (METHOD) 1 (Equation) to choose the
Equation solver. Press ENTER to see the list of variables for your
equation.
5. Find the area of a triangle with base = 4 and height = 8.35. Use ▼to
move the blinking cursor over B and type in 4. Type in 8.35 for H
and press ENTER . Press ▲twice to move the prompt to the A variable.
Press 2ndF EXE to find the area of 16.7.
6. Save the formula by pressing 2ndF SOLVER C (SAVE). Enter a name
and press ENTER .
7. Enter A = B•C•sin θby pressing CL a couple times to return to and delete
the current equation. Type in the equation with the keystrokes: ALPHA A
ALPHA = a/b 1 2 ALPHA B ×ALPHA C ×sin
ALPHA θ.
8. Consider the triangle where sides of lengths 4.8 and 5.73 enclose a 47° angle.
Press ENTER to access the variable list, enter 5.73 for B, 4.8 for C (or
vice-versa), and 47 for θ. Move the cursor to the A variable. Press 2ndF
EXE to solve for the area.
AREA OF A TRIANGLE
1
2
1
2
▼ ▼
▼ ▼

16
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
9. Continue with the formula and press 2ndF SOLVER A (METHOD) and
3 (Graphic) to choose the Graphic solver.
10. To start the problem from the beginning, set A to 0. Move the cursor to
the A variable and press 2ndF EXE to see the Graphic solver variable
range screen.
11. Since area is always nonnegative, 0 could be used for BEGIN. Enter END
a value that you do not expect area to exceed, say 25. (A little bit of
estimation helps here! If your value for END is too small, increase it and
try again.)
12. Press 2ndF EXE and an autoscaled graph of the two sides of the equation
is drawn and the solution is obtained.
13. Enter Heron’s formula, A = [S(S-X)(S-Y)(S-Z)], press CL , and type the
following: ALPHA A ALPHA = 2ndF ALPHA S (ALPHA
S – ALPHA X ) ( ALPHA S – ALPHA Y )(ALPHA
S – ALPHA Z ).
14. Note that the square root symbol extends over the entire right hand side of
the equation, automatically grouping the expression under it.
15. You could enter the semiperimeter, S = (X + Y + Z), in a separate formula
in the SOLVER, but it is probably easier to find the value of S in the
computation mode and then use Heron’s formula in the SOLVER.
Press ENTER to view the variable list.
16. Use Heron's formula to find the area of a triangle with three sides of
length 7, 8, and 9. The value for S will be 12. Enter these into the solver
and press 2ndF EXE to find the area.
AREA OF A TRIANGLE (continued)
√
1
2
√

17
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
A lawn sprinkler is set so that the region of the lawn that is watered is
approximately a sector of a circle of radius 6 feet. If the central angle of the
sector is radians, find the area of the region that is watered by the sprinkler.
1. Set the calculator to radian mode by pressing 2ndF SET UP
B(DRG) and 2 (Rad). Press 2ndF QUIT to exit the set
up screen.
2. Access the SOLVER by pressing 2ndF SOLVER . Press CL to delete
any equation that appears on the screen.
3. Type in the equation A= R2θby pressing ALPHA A ALPHA = 1
a/b 2 ALPHA R x2ALPHA θ.
4. Use the Equation solver by pressing 2ndF SOLVER A (METHOD)
and 1 (Equation). Press ENTER and see the list of variables.
5. Use ▼to place the cursor over R, type in 6, and press ENTER . Type in θ
by pressing 2ndF π÷ 5 ENTER . Press ▲twice to place the cursor
on the A variable. Press 2ndF EXE to find the area in square feet.
6. Use the Newton solver by pressing 2ndF SOLVER A (METHOD) and
2 (Newton). Reset A to 0 to start the problem from the beginning.
The values of R and O are correct for this problem, so use ▲to place
the cursor over the A variable and press 2ndF EXE to view the Newton
solver screen.
7. Since area is never negative, you could set START = 0. Leave the STEP size
as .001 and remember that you should change it to a slightly larger value if
an error message results. Press 2ndF EXE to find the area in square feet.
AREA OF A CIRCULAR SECTOR
π
5
1
2
▼
×
+–
÷

18
Advanced Keyboard/TRIGONOMETRY USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
8. Continue the problem and find the area using the Graphic Solver.
9. Press 2ndF SOLVER A (METHOD) 3 (Graphic).
10. Reset A to 0 to start the problem from the beginning.
11. Place the cursor on the A variable and press 2ndF EXE .
12. Recall that BEGIN and END are the lower and upper values between which
you feel the solution will lie. Enter a 20 for END so that the intersection of
the two graphs is visible on the screen.
13. Press 2ndF EXE to find the area.
AREA OF A CIRCULAR SECTOR (continued)