How do you evaluate arcsin 1?

Sep 7, 2015

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

Explanation:

$\arcsin$ is defined as having a range restricted to $\left[- \frac{\pi}{2} , + \frac{\pi}{2}\right]$

If $\arcsin \left(1\right) = \theta \textcolor{w h i t e}{\text{XX")rarrcolor(white)("XX}} \sin \left(\theta\right) = 1$

That is for $\theta \in \left[- \frac{\pi}{2} , + \frac{\pi}{2}\right]$ with a unit circle, the ratio of the opposite side (y-coordinate) to the hypotenuse must be $= 1$

The only angle meeting this requirement is $\theta = \frac{\pi}{2}$