# How do you find the exact value of arcsin (-1/2)?

Sep 9, 2016

$- \frac{\pi}{6}$

#### Explanation:

Arcsin can be thought of as the ANGLE with the specified value of sin.

The range of $\arcsin$ or ${\sin}^{-} 1$ is $\frac{\pi}{2}$ to $- \frac{\pi}{2}$.

Arcsin of a positive value is found in QI or zero to $\frac{\pi}{2}$.
Arcsin of a negative value is found in QIV or zero to $- \frac{\pi}{2}$

In this case, $\arcsin \left(- \frac{1}{2}\right)$ is found in QIV. The angle with a sin of $- \frac{1}{2}$ in QIV is $- \frac{\pi}{6}$.