Question

Domain of sin^-1

Answer 1

The domain of $\sin^{-1}(x)$ is $[-1, 1]$.

Answer 2

Let $y = \sin^{-1}(x)$. By definition, this implies $x = \sin(y)$. The range of the sine function, $\sin(y)$, is $[-1, 1]$. Therefore, the possible values for $x$ must lie within this range. Thus, the domain of $\sin^{-1}(x)$ is $[-1, 1]$.