# How do you evaluate arcsin^-1(-1/2) without a calculator?

May 25, 2018

$\theta = \frac{11}{6} \pi = {330}^{\circ}$

#### Explanation:

Given: ${\arcsin}^{-} 1 \left(- \frac{1}{2}\right)$

I believe what you want is $\arcsin \left(- \frac{1}{2}\right) = {\sin}^{-} 1 \left(- \frac{1}{2}\right)$

$\arcsin \left(- \frac{1}{2}\right)$ says, find me the angle that has a sine $= - \frac{1}{2}$,

or what is the angle $\theta$ that yields $\sin \theta = - \frac{1}{2}$?

Since the $\arcsin$ function has a limited domain: $- \frac{\pi}{2} \le \theta \le \frac{\pi}{2}$, we will only need to look at the 4th quadrant due to the negative sign.

$\theta = \frac{11}{6} \pi = {330}^{\circ}$