The value of sin^{-1}left(sin frac{7 pi}{6}ri | vedclass

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Question

(C) We know that the range of the principal value branch of $\sin^{-1} x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.Given expression is $\sin^{-

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) We know that the range of the principal value branch of $\sin^{-1} x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.Given expression is $\sin^{-1}\left(\sin \frac{7 \pi}{6}\right)$.Since $\frac{7 \pi}{6}$ does not lie in the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,we simplify the expression.$\sin \frac{7 \pi}{6} = \sin\left(\pi + \frac{\pi}{6}\right) = -\sin \frac{\pi}{6} = \sin\left(-\frac{\pi}{6}\right)$.Now,$\sin^{-1}\left(\sin \frac{7 \pi}{6}\right) = \sin^{-1}\left(\sin\left(-\frac{\pi}{6}\right)\right)$.Since $-\frac{\pi}{6} \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,the value is $-\frac{\pi}{6}$.Therefore,the correct option is $C$.

The value of $\sin^{-1}\left(\sin \frac{7 \pi}{6}\right)$ is equal to . . . . . . .

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