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Date: ________________
9-7: Angle Sum & Difference - Practice
4
1. If cos 𝑥 = 5, and x is a positive acute angle,
Period: _____
4
5
2. If sin 𝑥 = , find cos(2𝑥)
find sin(𝑥 + 90)
3. Find the exact value of cos 75°
4. Find the exact value of
sin 42° cos 12° − cos 42° sin 12°
5. Find all solutions of 2 cos 𝑥 + sin 2𝑥 = 0
6. Find the exact value of sin 105°
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Date: ________________
Period: _____
7. Prove the cofunction identity
8. If A and B are both positive acute angles,
3
5
𝜋
and sin 𝐴 = and sin 𝐵 =
cos ( 2 − 𝑥) = sin 𝑥
5
,
13
find
sin(𝐴 − 𝐵).
9. If sin 𝐴 =
√3
,
2
1
2
sin 𝐵 = − , A is in quadrant
10. If tan 𝑥 = 1, sin 𝑦 =
II, and B is in quadrant III, find sin(𝐴 + 𝐵).
√2
,
2
and x and y are
both positive, acute angles find cos(𝑥 + 𝑦).
11. Simplify the expression sin 2𝑥 cos 3𝑥 + cos 2𝑥 sin 3𝑥 into one trigonometric function.
Answer Key:
4
1. 5
7. (Use cos (A-B)
formula)
7
2. − 25
3.
8.
√6−√2
4
16
65
4.
1
2
1
9. − 2
5. {90°, 270°}
6.
10. 0
11. sin 5𝑥
√6+√2
4