The principal value of sin ^{-1}left(-frac{1} | vedclass

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Question

(D) Let $y = \sin ^{-1}\left(-\frac{1}{2}\right)$.Then,$\sin y = -\frac{1}{2}$.We know that the range of the principal value branch of $\sin ^{-1} x$

Vedclass · Accepted Answer

$-\frac{\pi}{6}$

Vedclass · Answer

(D) Let $y = \sin ^{-1}\left(-\frac{1}{2}\right)$.Then,$\sin y = -\frac{1}{2}$.We know that the range of the principal value branch of $\sin ^{-1} x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.Since $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$,we have $\sin\left(-\frac{\pi}{6}\right) = -\frac{1}{2}$.Thus,the principal value is $-\frac{\pi}{6}$.

The principal value of $\sin ^{-1}\left(-\frac{1}{2}\right)$ is

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