Equation using the double-angle formula

Statement

Solve for $0^\circ\le\theta\le 360^\circ$: $\sin 2\theta=\cos\theta.$

Solution

With $\sin 2\theta=2\sin\theta\cos\theta$: $2\sin\theta\cos\theta-\cos\theta=0\Rightarrow \cos\theta\,(2\sin\theta-1)=0$.

$\cos\theta=0\Rightarrow \theta=90^\circ,\ 270^\circ$.

$\sin\theta=\dfrac12\Rightarrow \theta=30^\circ,\ 150^\circ$.

$\boxed{\theta=30^\circ,\ 90^\circ,\ 150^\circ,\ 270^\circ}$