Question

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

Answer 1

`-pi/2`

Explanation:

The range of arcsin is defined as between `-pi/2` radians and `pi/2` radians.

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

The one angle between `-pi/2` and `pi/2` with a `sin(x)=-1` is `x = -pi/2`

On the unit circle, a sin of -1 falls on the negative x axis,
which is at `-pi/2`