Find the principal value of sin ^{-1}left(fra | vedclass

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Question

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

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(A) Let $\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right) = y$. Then,$\sin y = \frac{1}{\sqrt{2}}$. We know that the range of the principal value branch of $\sin ^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. Since $\sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$ and $\frac{\pi}{4} \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,the principal value is $\frac{\pi}{4}$.

Find the principal value of $\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)$.

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