Download Chapt 15 Review

Chapter 15 Review
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Questions 1-2: Write an equivalent expression in simplest form.
1.
sin x  tan x  cos x
2.
sec x  cot x
Questions 3-6: Verify the identity.
3.
cos x
1  sin x

 2sec x
1  sin x
cos x
4.
tan 2 x
 sec x  cos x
sec x
5.
cot x 
sin x
 csc x
1  cos x
6.
sec2 x  csc2 x  sec2 x csc2 x
Questions 7-10: Use sum and difference formulas to give exact answers (no calculator)
7.
cos105
8.
cos

12
9.
sin  195

10.
 13 
tan 

 12 
Questions 11-12: Find the sinx and siny and use these values to find the value of cos(x - y) under given
conditions.
11.
3
4
cos x   ,QIII; cos y  ,QIV
5
5
12.
cos 
5
3
, I , cos y 
IV
12
2
Questions 13-14: Find the sinx and siny and use these values to find the value of sin(x + y) under given
conditions.
3

,0 x ;
2
2
cos y 
5 3
,
 y  2
3 2
13.
cos x 
14.
3
3
2 2

cos x   ,   x 
, cos y 
,0  y 
4
2
3
2
Questions 15-17: Use half angle formulas to find each function value.
15.
16.
tan112.5
cos
7
12
17.
sin 75
Questions 18-19: Find the sin2x for angle in given quadrant. Question 20: Find cos2x.
18.
I, sin x 
3
5
19.
III, cos x  
7
4
20.
IV, cos x 
Questions 21-22: Prove the identity.
21.
1  cos 2 x
 tan 2 x
1  cos 2 x
22.
sin 3x  3sin x  4sin 3 x
5
12