# How do you evaluate arcsin (-1/2)?

Jun 9, 2015

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

#### Explanation:

$\sin x = - \frac{1}{2}$--> find x ?

Trig table gives:

$\sin x = - \frac{1}{2}$ = sin (-30) = sin (360 - 30) = sin 330 -> x = 330 deg

Trig unit circle gives another arc x that has the same sin value $\left(- \frac{1}{2}\right)$:

x = 180 + 30 = 210 deg

Within period (0, 360), there are 2 answers: 210 and 330 deg