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Name: _______________________________________________ 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° Name: _______________________________________________ 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