Find the principal values of: ^ -1 (-1 2 )

Question

Find the principal values of: $\sin ^{-1}\left(\frac{-1}{2}\right)$

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Answer

(d) : Let $\sin ^{-1}\left(\frac{-1}{2}\right)=\theta \Rightarrow \sin \theta=\frac{-1}{2}=-\sin \frac{\pi}{6}=\sin \left(\frac{-\pi}{6}\right)$
$\Rightarrow \theta=\frac{-\pi}{6} \in\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
$\therefore$ Principal value of $\sin ^{-1}\left(\frac{-1}{2}\right)$ is $\left(\frac{-\pi}{6}\right)$.

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