# What does arcsin(sin ((-pi)/2))  equal?

Jan 20, 2016

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

#### Explanation:

If you want to know how please follow.

$\sin \left(- \frac{\pi}{2}\right) = - \sin \left(\frac{\pi}{2}\right)$ since $\sin \left(x\right)$ is a odd function.

$\sin \left(- \frac{\pi}{2}\right) = - 1$ since $\sin \left(\frac{\pi}{2}\right) = 1$

$\arcsin \left(\sin \left(- \frac{\pi}{2}\right)\right) = \arcsin \left(- 1\right)$

Now comes the range of $\arcsin \left(x\right)$
The range of $\arcsin \left(x\right)$ is $\left[- \frac{\pi}{2} , \frac{\pi}{2}\right]$

So $\arcsin \left(- 1\right)$ would give $- \frac{\pi}{2}$

Therefore,

$\arcsin \left(\sin \left(- \frac{\pi}{2}\right)\right) = - \frac{\pi}{2}$