$\sin^{-1}\left(\sin frac{2\pi}{3} ight)$ equals

Question

$\sin^{-1}\left(\sin	frac{2\pi}{3}ight)$ equals

Accepted Answer

A. $	frac{\pi}{3}$

$\sin^{-1}$ must return a value in $[-	frac{\pi}{2},	frac{\pi}{2}]$ — and $	frac{2\pi}{3}$ is outside that. Use the supplement identity $\sin(\pi - 	heta) = \sin	heta$: $\sin	frac{2\pi}{3} = \sin\left(\pi - 	frac{2\pi}{3}ight) = \sin	frac{\pi}{3}$, and $	frac{\pi}{3}$ IS in range. So the inverse returns $	frac{\pi}{3}$.

Answer

$-	frac{\pi}{3}$

Answer

$	frac{2\pi}{3}$

Answer

$	frac{\pi}{6}$

$\sin^{-1}\left(\sin\tfrac{2\pi}{3}\right)$ equals