If sin ^{-1} x=y, then | vedclass

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Question

(C) It is given that $\sin ^{-1} x=y$. We know that the range of the principal value branch of the inverse sine function,$\sin ^{-1} x$,is defined as

Vedclass · Accepted Answer

$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$

Vedclass · Answer

(C) It is given that $\sin ^{-1} x=y$. We know that the range of the principal value branch of the inverse sine function,$\sin ^{-1} x$,is defined as the closed interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. Therefore,for any $x$ in the domain $[-1, 1]$,the value of $y$ must lie within this range. Hence,$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$.

If $\sin ^{-1} x=y,$ then

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