# How do you evaluate the equation arcsin(sin ((5pi)/6))?

$\arcsin \left(\sin \left(\frac{5 \pi}{6}\right)\right) = \frac{\pi}{6}$
$\arcsin$ is only defined as having a range $\left[- \frac{\pi}{2} , + \frac{\pi}{2}\right]$
$\sin \left(\frac{5 \pi}{6}\right) = \frac{1}{2} = \sin \left(\frac{\pi}{6}\right)$
$\arcsin \left(\sin \left(\frac{5 \pi}{6}\right)\right) = \arcsin \left(\frac{1}{2}\right) = \frac{\pi}{6}$