Answer
$\theta=\dfrac{\pi}{12}+n\pi$ and $\theta=\dfrac{5\pi}{12}+n\pi$
Work Step by Step
We are given the equation:
$\sin (2\theta)=0.5$
$\sin (2\theta)=\dfrac{1}{2}$
The angles $2\theta$ in $[0,2\pi)$ matching the equation are:
$2\theta=\dfrac{\pi}{6}$ and $2\theta=\dfrac{5\pi}{6}$
Given the fact that the function has a period of $2\pi$, the solutions are:
$2\theta=\dfrac{\pi}{6}+2n\pi$ and $2\theta=\dfrac{5\pi}{6}+2n\pi$
We determine $\theta$:
$\theta=\dfrac{\pi}{12}+n\pi$ and $\theta=\dfrac{5\pi}{12}+n\pi$
