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If $\theta=\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]$, then one of the possible value of $\theta$ is
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$\frac{\pi}{3}$
$\theta=\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]$
$\begin{aligned} & \Rightarrow \theta=\sin ^{-1}\left[-\left(\sin 240^{\circ}\right)\right]=\sin ^{-1}\left[-\sin \left(180^{\circ}+60^{\circ}\right)\right] \\ & \Rightarrow \theta=\sin ^{-1} \sin 60^{\circ}=\sin ^{-1}\left[\sin \left(\frac{\pi}{3}\right)\right]=\frac{\pi}{3}\end{aligned}$
$\begin{aligned} & \Rightarrow \theta=\sin ^{-1}\left[-\left(\sin 240^{\circ}\right)\right]=\sin ^{-1}\left[-\sin \left(180^{\circ}+60^{\circ}\right)\right] \\ & \Rightarrow \theta=\sin ^{-1} \sin 60^{\circ}=\sin ^{-1}\left[\sin \left(\frac{\pi}{3}\right)\right]=\frac{\pi}{3}\end{aligned}$
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