Solve Trigonometric Equations

Tutorial, with detailed explanations, on how to solve trigonometric equations using different methods and strategies and the properties of trigonometric functions and identities. The unit circle helps in locating the solutions once you have the reference angle.
Many more examples on how to solve trigonomteric equations with detailed solutions - Grade 12, are presented in this site.

Examples with Solutions

Example 1

Solve the trigonometric equation.(find all solutions)
2 cos x + 2 = 3

Solution to example 1

conclusion: There is an infinite number of solutions which can be generated by giving different values to k.

Example 2

Find the solutions in the interval [0 , 2pi) for the trigonometric equation
-5 cos 2x + 9 sin x = -3

Solution to example 2

Example 3

Find all solutions for the trigonometric equation
cot x cos 2x = cot x

Solution to example 3

Note that many of the techniques used in solving algebraic equations are also used to solve trigonometric equations.