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:


Example 2

Solve the following for -\pi\leq x\leq \pi: