# Trigonometric Equations

Trigonometric equations can be solved by first manipulating them into the form $\sin(x)=a$, $\cos(x)=b$

or $\tan(x)=c$.

This could be very simple, a straight forward manipulation of a linear equation or it could be a more complicated manipulation of a quadratic equation. See Example 1. It may be that the argument of the trigonometric function could be a function of x, see Example 2. In these cases it is very important to extend the interval of solution values so that the full set of solutions are obtained.

## Example 1

Solve the following for $0\leq x\leq 2\pi$: $\sin^2(x)=\sin(x)$

## Example 2

Solve the following for $-\pi\leq x\leq \pi$: $\cos(2x)=1$

### Past Trigonometric Exam Questions

We have collated past exam questions on trigonometry so that you may focus your concentration on this particular subject (answers on the back pages). Alternatively, visit our Questions by Topic page to see which topics you can focus on.

### Pure Maths Practice Papers

Are you ready to test your knowledge on all of the Pure Maths topics so far? If so…