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 ^{ 2}x + 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
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.

