# How do you calculate the arcsin (-1/ sqrt 2)?

Nov 27, 2015

Calculate $\arcsin \left(- \frac{1}{\sqrt{2}}\right)$

Ans: $\frac{5 \pi}{4} \mathmr{and} \frac{7 \pi}{4}$

#### Explanation:

Unit circle and trig table of special arcs -->
$\sin x = - \frac{1}{\sqrt{2}} = - \frac{\sqrt{2}}{2}$ --> $a r c x = - \frac{\pi}{4}$
Unit circle gives another arc x that has the same sine value:
$x = \pi + \frac{\pi}{4} = 5 \frac{\pi}{4.}$
Ans: $x = \frac{5 \pi}{4}$, and $x = \frac{7 \pi}{4}$ (or -pi/4)