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Solving for X : Trigonometric Equations (13 Problems)

Use factoring, the quadratic formula, or identities to solve the equations. Find all solutions in the interval (0,2pi)

65. 3 sin²x - 8 sin x - 3 = 0

answer x=3.4814, 5.9433

67. 2 tan²x + 5 tan x + 3 = 0
answer x= 3pi/4, 7pi/4, 2.1588, 5.3004

69. cotxcosx=cosx
ans. x=pi/4, pi/2, 5pi/4, 3pi/2

71. cos x csc x =2 cos x
ans. x=pi/6,pi/2,5pi/6,3pi/2

73. 4 sin x tan x-3 tan x + 20 sin x - 15 =0
(Hints: One factor is x + 5)
answer x=.8481, 1.7682,2.2935,4.9098

75. sin²x + 2 sin x - 2 = 0
answer x=.8213, 2.3203

77. tan²x + 1 = 3 tan x
answer x=.3649, 1.2059, 3.5065, 4.3475

79. 2 tan²x - 1 = 3 tan x
answer x=1.0591, 2.8679, 4.2007, 6.0095

81. sin²x + 3 cos²x = 0
answer no solution

83. sin 2 x + cos x = 0
answer x= pi/2, 7pi/6, 3pi/2, 11pi/6

85. 9-12 sin x = 4 cos²x
answer x=pi/6, 5 pi/6

87. cos²x - sin²x + sin x = 0
answer x=pi/2, 7pi/6, 11pi/6

89. sin x/2 = 1 - cos x
answer x=0. pi/3, 5pi/3

Solution Summary

Thirteen trigonometric equations are solved. The solution is detailed and well presented.

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