All solutions in a stated interval

First isolate the trigonometric ratio. Find a reference angle, use signs or a graph to locate all matching angles, then keep only those in the stated interval.

Example

For \(2\sin x=1\), \(\sin x=1/2\). The reference angle is \(30^\circ\). Sine is positive in quadrants I and II, so for \(0^\circ\le x\le360^\circ\), \(x=30^\circ,150^\circ\).

For \(\cos x=-1/2\), the reference angle is \(60^\circ\), giving \(x=120^\circ,240^\circ\). For \(\tan x=1\), the solutions are \(45^\circ,225^\circ\).

Check endpoints separately: \(\sin x=0\) on the closed interval includes \(0^\circ,180^\circ,360^\circ\). Do not automatically give exactly two answers.