If $\alpha=\frac38\pi$, and $\frac{\pi}{2}<\theta<2\pi$ with $\sin\alpha=\sin\theta$, then how do we find $\theta$?

Question

$\alpha=\frac38\pi$ rad. Angle $\theta$ is such that $\frac{\pi}{2}<\theta<2\pi$ and $\sin(\alpha)=sin(\theta)$.

How to find $\theta$?

Trigonometry has never been my strongest point in math, i know this should be an easy exercise.

Answer 1

If $\theta = \pi - \frac{3}{8}\pi$, we have the result. See here for more details.

Answer 2

Geometrically, you can see that $\theta = \pi - \alpha$. I let you the proof after having visualized this on the unit circle ;)