769 CHAPTER 7 Test Work each problem. 13. (Modeling) Voltage The voltage in common household current is expressed as V = 163 sin vt, where v is the angular speed (in radians per second) of the generator at an electrical plant and t is time (in seconds). (a) Use an identity to express V in terms of cosine. (b) If v = 120p, what is the maximum voltage? Give the least positive value of t when the maximum voltage occurs. 14. Graph y = sin-1 x, and indicate the coordinates of three points on the graph. Give the domain and range. 15. Find the exact value of each real number y. Do not use a calculator. (a) y = arccos a- 1 2b (b) y = sin-1 ¢- 23 2 ≤ (c) y = tan-1 0 (d) y = arcsec1-22 16. Give the degree measure of u. Do not use a calculator. (a) u = arccos 23 2 (b) u = tan-11-12 (c) u = cot-11-12 (d) u = csc-1 ¢- 223 3 ≤ 17. Use a calculator to approximate each value in decimal degrees to the nearest hundredth. (a) sin-1 0.69431882 (b) sec-1 1.0840880 (c) cot-11-0.71255862 18. Evaluate each expression without using a calculator. (a) cos aarcsin 2 3b (b) sin a2 cos-1 1 3b 19. Write tan1arcsin u2 as an algebraic expression in u, for u 70. Solve each equation over the interval 30°, 360°2. Write solutions as exact values or to the nearest tenth of a degree, as appropriate. 20. -3 sec u + 223 = 0 21. sin2 u = cos2 u + 1 22. csc2 u - 2 cot u = 4 Solve each equation over the interval 30, 2p2. Write solutions as exact values or to four decimal places, as appropriate. 23. cos x = cos 2x 24. 22 cos 3x - 1 = 0 25. sin x cos x = 1 3 Solve each equation for all exact solutions in radians (for x) or in degrees (for u). Write answers using the least possible nonnegative angle measures. 26. sin2 u = -cos 2u 27. 223 sin x 2 = 3 Work each problem. 28. Solve each equation for x, where x is restricted to the given interval. (a) y = cos 3x, for x in c 0, p 3 d (b) y = 4 + 3 cot x, for x in 10, p2
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