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Honors Advanced Algebra with Trigonometry Name:_______________________ Chapter 14 Date:________________________ Practice Test Period:______________________ **NO CALCULATORS!!!** Cosine of sum or difference cos (A + B) = cos A cos B - sin A sin B cos (A - B) = cos A cos B + sin A sin B Double-Angle Identities cos 2A = cos2 A - sin2 A cos 2A = 1 - 2 sin2 A Sine of sum or difference sin (A + B) = sin A cos B + cos A sin B sin (A - B) = sin A cos B - cos A sin B cos 2A = 2 cos2 A - 1 sin 2A = 2 sin A cos A 1. Write the fundamental identities that you have memorized below (three reciprocal identities, two quotient identities, three Pythagorean identities, and three negative angle identities). Simplify the following to a single trig function, a power of a single trig function, or a constant. 2. 1 - cos2 x 3. sin (x - 90°) 2. 3. 4. csc2 x - 1 5. cot2 x - csc2 x 4. 5. 6. cot x csc x 7. sec x csc x tan x 6. 7. 8. 1 - sin x csc x 9. tan x - sec x csc x 8. 9. Prove that each equation is an identity. 10. tan x = sec x csc x 1 − cos 2 x 12. 2 tan x csc 2x - tan2 x = 1 11. csc A sin 2A - sec A = cos 2A sec A 13. 1 + cos 2x = cot x sin 2x Use the sum and/or difference identities to find the exact value of the following. ⎛ 7π ⎞ 14. sin⎜ ⎟ ⎝ 12 ⎠ 15. cos255° 14. 15. Solve each equation for solutions in the interval [0, 2π) by first solving for the trig function. 16. 2 sin x + 1 = 0 17. 2 cos 2 x + cos x − 1 = 0 16. 17. 18. cos 2 x = 3 4 18. Solve each equation for solutions in the interval [0, 360°) by first solving for the trig function. 19. tan 2 x = 1 20. sin x + sin 2x = 0 19. 20. 21. cos ⎛ x⎞ 2 = ⎝ 2⎠ 2 21.