Sharp EL-9600 - Page 66

62 Blackline Masters/TRIGONOMETRY USING THE SHARP EL-9600
Copyright © 1998, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
Verify the half angle formula cos ( ) = ± ( ) :
1. To verify the formula, you will graph Y1 = cos and Y2 = ± ( )
and show that they are in fact th same graph.
2. In this problem you will need to limit your domain or x values to intervals
where cosine is either negative or positive and enter the appropriate radical
for Y2.
3. To do this you will turn the calculator on and press Y= . Press CL to clear
Y1 of an old expression.
4. Now, enter the cos for Y1 by pressing cos X/θ/T/n a/b 2 ENTER
and the
( )
for Y2 (limiting to where cosine is positive) by
pressing CL 2ndF a/b 1 + cos X/θ/T/n ▼ 2 ENTER .
5. Cos ( ) will be positive for a viewing window of 0 < x < π . Enter this
viewing window by pressing WINDOW 0 ENTER 2ndF π ENTER
2ndF π ÷ 2 ENTER (–) 3 ENTER 3 ENTER 1 ENTER .
6. Press GRAPH to view the graphs. Notice they appear as one graph.
7. To verify the formula for where cosine is negative, press Y= ▼ to access
the Y2 prompt and press (–) to insert a negative in front of the radical.
Cos ( ) will be negative for a viewing window of π< x < 3π. Enter this
viewing window by pressing WINDOW 2ndF π ENTER 3 2ndF π
ENTER . Press GRAPH to view the graphs.
GRAPHICAL VERIFICATION OF FORMULAS AND IDENTITIES
3.2
NAME _____________________________________________________ CLASS __________ DATE __________
θ
2
(1 + cos
θ)
2
(1 + cos x)
2
x
2
(1 + cos
x)
2
x
2
x
2
x
2
√
√
√
√