The answers to Solve Trigonometric Equations  Problems are presented. In what follows n is any integer number and Pi is the radian measure of a straight angle.
Problem 1: Solve the trigonometric equation and find ALL solutions.
2 cos x + 1 = 0
ANSWER d: 2Pi / 3 + 2n*Pi , 4Pi / 3 + 2n*Pi
Problem 2: Solve the trigonometric equation and find ALL solutions.
3 sec^{ 2} x  4 = 0
ANSWER e: Pi / 6 + n*Pi , 11 Pi / 6 + n*Pi
Problem 3: Solve the trigonometric equation and find ALL solutions.
(3 cos x + 7) (2 sin x  1) = 0
ANSWER b: 7Pi / 6 + 2n*Pi , 11Pi / 6 + 2n*Pi
Problem 4: Solve the trigonometric equation and find ALL solutions.
(6 tan^{ 2} x  2) (2 tan^{ 2} x  6) = 0
ANSWER a: Pi / 6 + n*Pi , 5Pi / 6 + 2n*Pi , Pi / 3 + n*Pi , 2Pi / 3 + n*Pi
Problem 5: Solve the trigonometric equation and find ALL solutions in the interval [0 , 2Pi).
2 sec^{ 2} x + 4 = 2sec x
a: Pi / 3 , 5Pi / 3 , Pi
Problem 6: Solve the trigonometric equation and find ALL solutions in the interval [0 , 2Pi).
2sin (x) cos (x) = 2 sin (x) sin (x)
ANSWER b: 0 , Pi , 3Pi / 4 , 7Pi / 4
Problem 7: Solve the trigonometric equation and find ALL solutions in the interval [0 , 2Pi).
sin 2x = sin (x)
ANSWER c: 0 , Pi / 3 , Pi , 5Pi / 3
Problem 8: Which of these equations does not have a solution?
ANSWER c: 2sin x = 3
Problem 9: Which of these equations does not have a solution?
ANSWER d: sec x = 1/2
Problem 10: Solve the trigonometric equation and find ALL solutions in the interval [0 , 2Pi).
sin ^{ 2}x + sin x = 6
ANSWER e: no solutions
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