Question:
Write the value of $\sin ^{-1}\left(\sin 1550^{\circ}\right)$.
Solution:
We know that $\sin ^{-1}(\sin x)=x$.
Now,
$\sin ^{-1}\left(\sin 1550^{\circ}\right)=\sin ^{-1}\left\{\sin \left(1620^{\circ}-1550^{\circ}\right)\right\} \quad\left[\because \sin x=\sin \left(1620^{\circ}-x\right)\right]$
$=\sin ^{-1}\left(\sin 70^{\circ}\right)$
$=70^{\circ}$
$\therefore \sin ^{-1}\left(\sin 1550^{\circ}\right)=70^{\circ}$
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