Solve Trigonometric Equations - Problems

10 problems, with their answers, on solving trigonometric equations are presented here and more in the applet below. This may be used as a self test on solving trigonometric equations and ,indirectly, on properties of trigonometric functions and identities.

Make use of the
unit circle as it helps in locating the solutions once you have the reference angle.

Solve Trigonometric Equations, problesm with answers

Select the correct answer.

Problem 1: Solve the trigonometric equation and find ALL solutions.

2 cos x + 1 = 0


a: Pi / 3 + 2n*Pi , 5Pi / 3 + 2n*Pi

b: -1/2

c: no solutions

d: 2Pi / 3 + 2n*Pi , 4Pi / 3 + 2n*Pi

e: Pi / 2 + n*Pi



Problem 2: Solve the trigonometric equation and find ALL solutions.

3 sec 2 x - 4 = 0


a: sqrt(3) , -sqrt(3)

b: Pi / 3 + 2n*Pi , 5Pi / 3 + 2n*Pi

c: Pi / 6 + 2n*Pi , 11 Pi / 6 + 2n*Pi

d: Pi / 3 + n*Pi , 5Pi / 3 + n*Pi

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


a: no solutions

b: 7Pi / 6 + 2n*Pi , 11Pi / 6 + 2n*Pi

c: Pi / 3 + 2n*Pi , 2Pi / 3 + 2n*Pi

d: 7Pi / 6 + n*Pi , 11Pi / 6 + n*Pi

e: -7 / 3 , -1 / 2

Problem 4: Solve the trigonometric equation and find ALL solutions.

(6 tan 2 x - 2) (2 tan 2 x - 6) = 0


a: Pi / 6 + n*Pi , 5Pi / 6 + 2n*Pi , Pi / 3 + n*Pi , 2Pi / 3 + n*Pi

b: no solutions

c: Pi / 6 , 5Pi / 6

d: -sqrt(3) , sqrt(3)

e: 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

b: no solutions

c: Pi

d: -1 , 2

e: Pi / 6 , 5Pi / 6 , 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)


a: 0 , Pi

b: 0 , Pi , 3Pi / 4 , 7Pi / 4

c: 3Pi / 4 , 7Pi / 4

d: 0 , Pi / 2

e: Pi / 6 , 4Pi / 3

Problem 7: Solve the trigonometric equation and find ALL solutions in the interval [0 , 2Pi).

sin 2x = -sin (-x)


a: no solutions

b: 0

c: 0 , Pi / 3 , Pi , 5Pi / 3

d: 0 , Pi

e: Pi / 3 , Pi

Problem 8: Which of these equations does not have a solution?

a: sin(100x) = 0.1

b: tan(x) = 10000

c: 2sin x = -3

d: cos
2 x - 1 / 4 = 0

e: csc x = -2000



Problem 9: Which of these equations does not have a solution?

a: 5sin(x) = 4.9

b: 4cot(x) = 400

c: 3tan x = 0

d: sec x = -1/2

e: cos x = -0.001

Problem 10: Solve the trigonometric equation and find ALL solutions in the interval [0 , 2Pi).

sin 2x + sin x = 6


a: 2 , -3

b: 0

c: 0 , Pi / 3 , Pi / 2

d: 2

e: no solutions

More Trigonometric Equations Problems - Using Applet

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1 - click on the button above "click here to start" to start the test and MAXIMIZE the window obtained.

2 - click on "start" on the main menu.

3 - answer the question by checking a,b,c,d or e in the lower part of the window.

You can review your answers and change them by checking the desired letter. Once you have finished, press "finish" and you get a table with your answers and the right answers to compare with.

To start the test with another set of questions, press "reset".

More references on trigonometric equations

Trigonometric Equations and The Unit Circle.

Math Problems, Questions and Online Self Tests.

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