5/2/2013
Chapter 5 Review Material
VERSUS!!!!
My Own Mental Checklist
• I can use the fundamental identities.
• Given 1 trigonometric function of an angle, I can find
the remaining 5 trigonometric function exact values.
• I understand the meaning of “verify the identity.”
• I can verify identities using the fundamental
identities.
• I can verify identities using the sum and difference,
and double angle identities.
• I know how to identify positive and negative values
of the trigonometric functions.
1
5/2/2013
What do I need to do?
• Given csc x = -12 find the five remaining exact
trigonometric function values. X terminates in
QIV.
1
12
143
cos x 
12
143
tan x  
143
12 143
sec x 
143
cot x   143
sin x  
2
5/2/2013
What do I need to do?
• Given cot s = 15, s terminates in quadrant III,
find the five remaining trigonometric function
values.
tan s 
1
15
sin s  
226
226
15 226
226
csc s   226
cos s  
sec s  
226
15
3
5/2/2013
What do I need to do?
• Find cos (x – y) given sin x = ¼ and cos y = 3/5
both x and y terminate in quadrant I.
3 15  4
20
4
5/2/2013
What do I need to know?
• Simplify to a single trigonometric function value
or number:
tan 22.50
1  tan 2 22.50
2 tan 22.50
1 2 tan 22.50
(
) (
)
2 1  tan 2 22.50
2 1  tan 2 22.50
1
1
1
 (tan(2* 22.50 )  (tan 450 ) 
2
2
2
5
5/2/2013
What do I need to do?
• Find sin (z + q) given tan z = 15 and sin q = -2/3
both z and q terminate in QIII.
15 1130  2 226
678
6
5/2/2013
What do I need to do?
• Find sin 2x, cos 2x and tan 2x given cot x = 2/9
and x terminates in QI.
36
85
77
cos 2 x  
85
36
tan 2 x  
77
sin 2 x 
7
5/2/2013
What do I need to know?
• Simplify to a single trigonometric function value,
or number:
1
1 2 0
2
0
cos 15  sin 15
2
2
2 1
1
( cos 2 15  sin 2 15)
2 2
2
1 2 1
1
( ( cos 2 15  sin 2 15))
2 1 2
2
1
(cos 2 15  sin 2 15)
2
1
1
1 3
3
cos(2 *15)  cos 30  ( ) 
2
2
2 2
4
8
5/2/2013
What do I need to do?
Verify : 2cos 2
x
tan x  tan x  sin x
2
9