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# asin

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

expand all

### 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
```

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