# 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 $-\pi\leq x\leq \pi$:

$\cos(2x)=1$