Implicit differentiation and inverse trigonometric functions practice question 3

Does $\arcsin(\sin\theta)$ always give back $\theta$? Think about which angles arcsin is allowed to return.

arcsin returns the one angle in $\left[-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right]$ with a given sine. Work out $\sin\tfrac{5\pi}{6}$ first, then find that angle.