757 7.7 Equations Involving Inverse Trigonometric Functions Solve each equation for x, where x is restricted to the given interval. See Example 1. 7. y = 5 cos x, for x in 30, p4 8. y = 1 4 sinx, for x in c - p 2 , p 2 d 9. y = 3 tan2x, for x in ap 4 , p 4b 10. y = 3 sin x 2 , for x in 3-p, p4 11. y = 6 cos x 4 , for x in 30, 4p4 12. y = -sin x 3 , for x in c - 3p 2 , 3p 2 d 13. y = -2 cos 5x, for x in c 0, p 5 d 14. y = 3 cot 5x, for x in a0, p 5b 15. y = sinx - 2, for x in c - p 2 , p 2 d 16. y = cot x + 1, for x in 10, p2 17. y = -4 + 2 sinx, for x in c - p 2 , p 2 d 18. y = 4 + 3 cos x, for x in 30, p4 19. y = 1 2 cot 3x, for x in a0, p 3b 20. y = 1 12 sec x, for x in c 0, p 2b ´a p 2 , pd 21. y = cos1x + 32, for x in 3-3, p - 34 22. y = tan12x - 12, for x in a 1 2 - p 4 , 1 2 + p 4b 23. y = 22 + 3 sec 2x, for x in c 0, p 4b ´a p 4 , p 2 d 24. y = -23 + 2 csc x 2 , for x in 3-p, 02 ´10, p4 Solve each equation for exact solutions. See Examples 2 and 3. 25. -4 arcsinx = p 26. 6 arccos x = 5p 27. 4 3 cos-1 x 4 = p 28. -4sin-1 x 3 = p 29. 6sin-1 x = 5p 30. 4 tan-1 x = -3p 31. cos-1 x = sin-1 3 5 32. cot-1 x = tan-1 4 3 33. tan-1 x = cot-1 7 5 34. sin-1 x = csc-1 6 5 35. arcsinx = arctan 3 4 36. arctanx = arccos 5 13 37. 2 arccos a x 3 - p 3b = 2p 38. 6 arccos ax - p 3b = p Solve each equation for exact solutions. See Example 4. 39. sin-1 x - tan-1 1 = - p 4 40. sin-1 x + tan-1 23 = 2p 3 41. arccos x + 2 arcsin 23 2 = p 42. arccos x - arcsin 1 2 = p 6 43. sin-1 x - 4 tan-11-12 = 2p 44. arccos x + 2 arcsin 23 2 = p 3 45. arcsin2x + arccos x = p 6 46. arcsin2x + arcsinx = p 2
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