# How do you find the exact values of sin^-1(1/2)?

##### 1 Answer
Oct 15, 2016

${\sin}^{-} 1 \left(\frac{1}{2}\right) = \frac{\pi}{6}$

#### Explanation:

Find ${\sin}^{-} 1 \left(\frac{1}{2}\right)$

This problem is asking for the ANGLE with a sine of $\frac{1}{2}$.

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

If you are finding ${\sin}^{-} 1$ of a positive value, the answer will be between 0 and $\frac{\pi}{2}$, or the first quadrant in the unit circle. Do NOT use the second quadrant angle with a sine of $\frac{1}{2}$, because it does not fall within the range of ${\sin}^{-} 1$.

Using the unit circle, the angle with a sine of $\frac{1}{2}$ in the first quadrant is $\frac{\pi}{6}$.