Write the value

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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