If $\theta=\sin ^{-1}\left\{\sin \left(-600^{\circ}\right)\right\}$, then one of the possible values of $\theta$ is
(a) $\frac{\pi}{3}$
(b) $\frac{\pi}{2}$
(c) $\frac{2 \pi}{3}$
(d) $-\frac{2 \pi}{3}$
(a) $\frac{\pi}{3}$
We know
$\sin ^{-1}(\sin x)=x$
Now,
$\theta=\sin ^{-1}\left\{\sin \left(-600^{\circ}\right)\right\}$
$=\sin ^{-1}\left\{\sin \left(720^{\circ}-600^{\circ}\right)\right\}$
$=\sin ^{-1}\left\{\sin \left(120^{\circ}\right)\right\}$ $[\because \sin x=\sin (\pi-x)]$
$=\sin ^{-1}\left\{\sin \left(180^{\circ}-120^{\circ}\right)\right\}$
$=\sin ^{-1}\left(\sin 60^{\circ}\right)$
$=60^{\circ}$
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