Question:
Find the value of if $\sin ^{-1} x=y$, then
(A) $0 \leq y \leq \pi$ (B) $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
(C) $0
Solution:
It is given that $\sin ^{-1} x=y$.
We know that the range of the principal value branch of $\sin ^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.
Therefore, $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$.
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