Write the value

We know that $\sin ^{-1}(\sin x)=x$.

Now,

$\sin ^{-1}\left\{\sin \left(-600^{\circ}\right)\right\}=\sin ^{-1}\left\{\sin \left(720^{\circ}-600^{\circ}\right)\right\}$

$=\sin ^{-1}\left\{\sin \left(120^{\circ}\right)\right\}$

$=\sin ^{-1}\left\{\sin \left(180^{\circ}-120^{\circ}\right)\right\} \quad[\because \sin x=\sin (\pi-x)]$

$=\sin ^{-1}\left(\sin 60^{\circ}\right)$

$=60^{\circ}$

$\therefore \sin ^{-1}\left\{\sin \left(-600^{\circ}\right)\right\}=60^{\circ}$