# Find the value of if $sin ^{-1} x=y$, then

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}\$.