If sin-1 x = y, then - Vidyadip

Question

If sin^-1 x = y, then

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Answer

sin^-1 x = y $\Rightarrow$ siny = x
We know that range of the principle value branch of $sin^{-1}x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
Because, we know that
$-1\le siny\le 1$
$\Rightarrow $ $sin(-\frac {\pi}{2})\le siny \le sin(\frac{\pi}{2})$
Therefore, $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$

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