# Documentation

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# asin

## Syntax

`y = asin(x)`

## Description

`y = asin(x)` returns the Inverse Sine (sin-1) of the elements of `x`. The `asin` function operates element-wise on arrays. For real elements of `x` in the interval `[-1,1]`, `asin(x)` returns values in the interval `[-pi/2,pi/2]`. For real elements of `x` outside the interval `[-1,1]` and for complex values of `x`, `asin(x)` returns complex values. All angles are in radians.

## Examples

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### Inverse Sine of a Value

```asin(0.5) ```
```ans = 0.5236 ```

### Inverse Sine of a Vector of Complex Values

Find the inverse sine of the elements of vector `x`. The `asin` function acts on `x` element-wise.

```x = [0.5i 1+3i -2.2+i]; y = asin(x) ```
```y = 0.0000 + 0.4812i 0.3076 + 1.8642i -1.1091 + 1.5480i ```

### Graph of the Inverse Sine Function

Graph the inverse sine over the domain .

```x = -1:.01:1; plot(x,asin(x)) grid on ```

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### Inverse Sine

The inverse sine is defined as

`${\mathrm{sin}}^{-1}\left(z\right)=-i\mathrm{log}\left[iz+{\left(1-{z}^{2}\right)}^{1/2}\right].$`