26 - 37 odds

394 Chapter 5 Analytic Trigonometry 5.3 EXERCISES See www.CalcChat.com for worked-out solutions to odd-numbered exercise In Exercises VOCABULARY: Fill in the blanks. the trigonometric solutions (t 1. When solving a trigonometric equation, the preliminary goal is to interval [0,2 function involved in the equation. 17 + 2nT and 0 = 117 + 2n7, which are 49. 2 sin x 2. The equation 2 sin 0 + 1 = 0 has the solutions 0 = 6 called 6 50. 4 sin - solutions. 1 + sir 3. The equation 2 tan? x - 3 tan x + 1 = 0 is a trigonometric equation that is of type. 51. 4. A solution of an equation that does not satisfy the original equation is called an solution. cos 53. x tan x SKILLS AND APPLICATIONS 55. sec2 x 56. csc2 In Exercises 5-10, verify that the x-values are solutions of the 27. 3 tan' x = tan x 28. 2 sin2 x = 2 + cos x 57. 2 tan equation. 29. sec2 x - sec x = 2 30. sec x csc x = 2 csc x 58. 6 sin 5. 2 cos x - 1 = 0 31. 2 sin x + csc x = 0 32. sec x + tan x = 1 A In Exerci (a) x = (b) x = ST 33. 2 cos2 x + cos x - 1 = 0 3 equation 3 34. 2 sin2 x + 3 sin x + 1 = 0 to approx 6. sec x - 2 = 0 35. 2 sec2 x + tan2 x - 3 = 0 59. 12 s (a) x = TT 36. cos x + sin x tan x = 2 3 ( b) x = 5 TT 60. 3 tan 3 37. csc x + cot x = 1 38. sin x - 2 = cos x - 2 7. 3 tan2 2x - 1 = 0 61. tan 62. 4 co (a) x =" 5 TT In Exercises 39-44, solve the multiple-angle equation. 12 (b) x= 12 8. 2 cos2 4x - 1 = 0 39. cos 2x = 40. sin 2x = 3 In Exerc find all (a) x = - TT 3 TT 41. tan 3x = 1 12. sec 4x = 2 63. tan 16 (b)x= 16 9. 2 sin2 x - sin x - 1 = 0 43. cos 44. sin 64. tan 65. tan (a) x = 2 (b) x = 7 TT 66. sec 6 In Exercises 45-48, find the x-intercepts of the graph 10. csc4x - 4 csc2 x = 0 67. 2 c 45. y = sin 12 + 1 68. 2 s (a) x = 6 ( b) x = 5 TT 46. y = sin TX + COS TX 6 69. cot 70. co In Exercises 11-24, solve the equation. NOW AAt 71. se 11. 2 cos x + 1 = 0 12. 2 sin x + 1 = 0 72. se 13. 3 csc x - 2 = 0 14. tan x + 3 = 0 73. cs 15. 3 sec2 x - 4 = 0 16. 3 cot2 x - 1 = 0 -2+ 74. cs 17. sin x(sin x + 1) = 0 18. (3 tan? x - 1)(tan2 x - 3) = 0 47. y = tan?" In Ex - 3 48. y = sect Tx_ 19. 4 cos2 x - 1 = 0 1- 4 soluti 20. sin2 x = 3 cos2 x given 21. 2 sin2 2x = 1 22. tan2 3x = 3 23. tan 3x(tan x - 1) = 0 24. cos 2x(2 cos x + 1) = 0 75. In Exercises 25-38, find all solutions of the equation in the 3 - 3 76. interval [0, 2 TT). 77. 25. cos' x = Cos x 26. sec2 x - 1 = 0 78