Concept preview

What you will be able to do

1. 01Solve basic trig equations on a given interval using reference angles and quadrants
2. 02Write general solutions using the period of each function
3. 03Solve equations that require factoring, identities, or double angles

Because trig functions repeat, a trig equation usually has infinitely many solutions. To solve $\sin x = \tfrac12$, first find the reference angle ($\tfrac{\pi}{6}$, where $\sin$ is $\tfrac12$), then use the quadrants where the function has the right sign. Sine is positive in quadrants I and II, giving $x = \tfrac{\pi}{6}$ and $x = \pi - \tfrac{\pi}{6} = \tfrac{5\pi}{6}$ on $[0, 2\pi)$. The interval you are given decides how many of these repeats to list.