# How do you find the exact value of arcsin1?

Dec 30, 2016

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

#### Explanation:

By general definition the $\arcsin$ function is defined as having a range $\left[0 , \pi\right)$

If we want a value $\theta = \arcsin \left(1\right)$
or, as an alternate view, $\sin \left(\theta\right) = 1$

Within the range $\left[0 , \pi\right)$ the only value for $\theta$ that satisfies this condition is $\theta = \frac{\pi}{2}$