Download Chapt 15 Review

Chapt 15 Review
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Write an equivalent expression in simplest form using only sin and or cosine.
2) sec x  cot x
1) sin x  tan x  cos x
Verify the identity
3) sec4x – tan4x= sec2x + tan2x
5)
cos x
1  sin x

 2sec x
1  sin x
cos x
4)
tan 2 x
 sec x  cos x
sec x
6) sec2x + csc2x = sec2xcsc2x
Use sum and difference formulas to give exact answers ( no calculator)
 5 

7) cos 105
8) cos 9) cos(-195) 10) cos
12
12
Find the sinx and siny and use these values to find the value of cos(x-y) under given
conditions.
5
3
3
4
, III , cos y  , IV
IV
11) cos x 
12) cos  , I , cos y 
12
2
5
5
Find the sinx and siny and use these values to find the value of cos(x + y) under given
conditions.
13) cos x 
14) cos x
3
, 0
2
3
,
4
x
x

2
, cos y 
5 3
,
3 2
3
2 2
, cos y 
,0
2
3
y
y

2
2
Use formulas for sin and tangent of a sum or difference, then evaluate
7
13
15) sin 165
16) sin
17) tan
18) tan (-105)
12
12
Find the sin (x + y), where x and y satisfy the given conditions.
1
2 2
, II
19) sin x  , III , cos y 
2
3
Find the sin2x for angle in given quadrant.
 7
3
5
20) I, sin 
21)III,
22) IV, cos x 
5
12
4
Use the half angle formulas to find each function value.
23) tan 112.5
24) sin 22.5
25) cos 75
26) cos
7
12
Using Law of sines solve the triangles. Angles to nearest degree, lengths to nearest tenth.
27) A = 440, B = 250, a = 12
28) a = 20, b = 15, A = 400
29) a = 7, b = 2.9, A = 1420
30) B = 800, C = 100, a = 8
Using Law of Cosines, solve the triangle. Angles to nearest degree, lengths to nearest
tenth.
31) a = 5, b= 7, C = 420
32) a = 4, c = 7, B = 550
33) a = 63, b = 22, c = 50
34) a = 66, b = 25, c = 45
Prove the identity
35)
1  cos 2 x
 tan 2 x
1  cos 2 x
36)sin3x=3 sinx -4sin3x