# How do you calculate arcsin -1?

Nov 5, 2015

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

#### Explanation:

So, archsin(-1), also written as ${\sin}^{-} 1 \left(- 1\right)$ is an inverse function and has restrictions.

Note: Inverse of sine is restricted to quadrants 1 and 4 ( $\frac{\pi}{2}$ through $- \frac{\pi}{2}$).

Okay, so we know the restrictions now and that we are looking for what $a r c h \sin \left(- 1\right)$ equals.

And that would be $- \frac{\pi}{2}$ because it sits inside the restrictions of the inverse sin.

Solving these questions involves an understanding of the Unit Circle, the restrictions for each inverse function, and understanding the quadrants and what is negate and positive.

Drawing for better understanding...