# How do you evaluate arcsin(sqrt2/2) without a calculator?

Feb 13, 2017

$\frac{\pi}{4} + 2 k \pi$
$\frac{3 \pi}{4} + 2 k \pi$

#### Explanation:

Use trig table and unit circle:
$\sin x = \frac{\sqrt{2}}{2}$ --> trig table gives --> arc $x = \frac{\pi}{4}$.
Unit circle gives another arc x that has the same sin value:
$x = \left(\pi - \frac{\pi}{4}\right) = \frac{3 \pi}{4}$.
$x = \frac{\pi}{4} + 2 k \pi$
$x = \left(3 \pi\right) 4 + 2 k \pi$