# How do you find the exact value of sin^-1(-1)?

Sep 10, 2016

$- \frac{\pi}{2}$

#### Explanation:

The range of arcsin is defined as between $- \frac{\pi}{2}$ radians and $\frac{\pi}{2}$ radians.

arcsin(x) is the one angle within this range whose sine is x

The one angle between $- \frac{\pi}{2}$ and $\frac{\pi}{2}$ with a $\sin \left(x\right) = - 1$ is $x = - \frac{\pi}{2}$

On the unit circle, a sin of -1 falls on the negative x axis,
which is at $- \frac{\pi}{2}$