Answers to Trigonometric Equation Problems

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 2x + sin x = 6


ANSWER e: no solutions



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Updated: 2 April 2013

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