Download Trig. Review Sheet 2.4 and 2.5 Answer Sheet

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Trigonometry
2.4 and 2.5 Review
Verify the following identities.
Simplify the following trigonometric expressions.
13.
sin 2
cot 
1 – cos 2
14.
15.
16.
sin (π + )
-sin 
Evalute the following.
17.
-1
Given: sin  =
and  is in quadrant III.
3
Find: cos , tan , csc , sec , and cot.
2sin2 x + cos 2x
1
cos 160 cos 20 - sin 160 sin 20
-1
cos  = -22
3
tan  = 2
4
18.
π
π π
Find the exact value of cos
knowing that it is equal to cos ( - ).
12
3 4
sec  = -32
4
cot  = 22
csc  = -3
2 + 6
4
19.
8
Given: A is an angle in quadrant III and B is an angle in quadrant IV, tan A = and tan B = -5 .
15
12
Find: sin (A + B).
-21
221
20.
Given:  is an angle in quadrant II and sin  = 3 .
5
Find: cos 2.
7
25
Trigonometry
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21.
Given:  is an angle in quadrant IV and cos  = 5 .
13
-120
169
Find: sin 2.
Half Angle Identities:
u
sin = 
2
1 – cos u
2
2
cos
u
=
2
1 + cos u
2
2
tan
u 1 – cos u
=
sin u
2
13
or
sin u
1 + cos u
13
22.
Use the Half-Angle Identities to determine the exact value of sin 105.
2 + 3
2
23.
Use the Half-Angle Identities to determine the exact value of tan 22 1/2.
2 - 1
24.
Given: cos  = -4
5
Find: sin 
2
and
π
<  < π.
2
310
10
25. Use the Half-Angle Identities to verify the following:
sin 2  = 1 – cos 
2
2
Answers will vary
Trigonometry
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Product-to-Sum Identities:
Sum-to-Product Identities:
sin u sin v = 1 cos (u – v) – cos (u + v)
2
1
cos u cos v = cos (u – v) + cos (u + v)
2
sin u cos v = 1 sin (u + v) + sin (u – v)
2
1
cos u sin v = sin (u + v) – sin (u – v)
2
sin u + sin v = 2 sin
u+v
u-v
cos
2
2
u+v
sin u – sin v = 2 cos
sin u - v
2
2
u-v
u+v
cos u + cos v = 2 cos
cos
2
2
u+v
cos u – cos v = - 2 sin
sin u - v
2
2
Express the following products as sums or differences.
26.
27.
2 sin 41cos 25
sin 66 + sin 16
Express the following sums or differences as products.
28.
29.
sin 28 + sin 18
2sin 23 cos 5
2 cos  cos 3
cos 2 + cos 4
sin 4x – sin 6x
-2cos 5x sin x
Trigonometry
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