For which codomain is $f(x) = \sin x$, defined on $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, a bijection?

Explanation

1. 01

   On $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, $\sin x$ is strictly increasing, so it is one-one.

2. 02

   It runs from $-1$ to 1, so it is onto exactly when the codomain is $[-1, 1]$.