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What is the value of $\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right) ?$
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The correct answer is:
$\frac{\pi}{3}$
$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=\sin ^{-1}\left[\sin \left(\pi-\frac{2 \pi}{3}\right)\right]=\sin ^{-1}\left(\sin \frac{\pi}{3}\right)$
$=\frac{\pi}{3} \quad\left[\right.$ Since, $\left.\sin \frac{2 \pi}{3}=\sin \left(\pi-\frac{\pi}{3}\right)\right]$
$=\frac{\pi}{3} \quad\left[\right.$ Since, $\left.\sin \frac{2 \pi}{3}=\sin \left(\pi-\frac{\pi}{3}\right)\right]$
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