Constructing Inverse Trigonometric Functions Practice Test

Because restricting the domain makes $\sin(x)$ one-to-one (it passes the horizontal line test) on $[-\pi/2,\pi/2]$.

Because $\sin(x)$ still fails the horizontal line test on $[-\pi/2,\pi/2]$ unless we also restrict the range.

Because $\sin(x)$ is periodic, it is automatically one-to-one on all real numbers.

Because the range of $\sin(x)$ becomes $[-\pi/2,\pi/2]$ after restriction.