# What is the domain and range of y=Arc sin x?

##### 1 Answer
Oct 31, 2016

$D = \left\{x \epsilon R | - 1 \le x \le 1\right\}$
$R = \left\{y \epsilon R | - \frac{\pi}{2} \le y \le \frac{\pi}{2}\right\}$

The domain is restricted as $y = \sin x$ doesn't pass the horizontal line test.

#### Explanation:

graph{y=arcsinx [-10, 10, -5, 5]}

You can tell from the graph that this is the domain and range. You must note that $\pm \frac{\pi}{2}$ were memorized values or properties of the $y = \arcsin x$ function.