# 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 More Math Problems, Questions and Online Self Tests.