Q.Range of $\sin^{-1}x$ is ________.

The range of $\sin^{-1}x$ is $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$.

The function $y=\sin x$ is not one-to-one over all of $\mathbb{R}$, so its inverse is defined by restricting the angle to the principal branch $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$, on which $\sin$ is one-to-one and takes every value in $[-1,1]$.

Hence:

• Domain of $\sin^{-1}x$: $[-1,1]$ …