# Why is arcsin(sin(12pi)) = 0 and not 0 and 2pi?

## I thought it would be equal to 0 and $2 \pi$, but the answers said 0 only.

Dec 4, 2017

arcsine is a function so for each input there is only one output.

#### Explanation:

The range of arcsine is $- \frac{\pi}{2} \le y \le \frac{\pi}{2}$, each $x$-value in the domain is associated with only one $y$-value. The only value in the range of arcsine that is associated with $x = 0$, which is the value of $\sin \left(12 \pi\right)$, is $y = 0$.