# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

# acsc

Inverse cosecant in radians

## Syntax

``Y = acsc(X)``

## Description

example

````Y = acsc(X)` returns the Inverse Cosecant (csc-1) of the elements of `X`. The `acsc` function operates element-wise on arrays. For real elements of `X` in intervals `[-Inf,-1]` and `[1,Inf]`, `acsc` returns real values in the interval `[-pi/2,pi/2]`. For real values of `X` in the interval `[-1,1]` and for complex values of `X`, `acsc` returns complex values. All angles are in radians.```

## Examples

collapse all

`acsc(3)`
```ans = 0.3398 ```

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

```x = [0.5i 1+3i -2.2+i]; Y = acsc(x)```
```Y = 1×3 complex 0.0000 - 1.4436i 0.0959 - 0.2970i -0.3795 - 0.1833i ```

Plot the inverse cosecant function over the intervals and .

```x1 = -10:0.01:-1.01; x2 = 1.01:0.01:10; plot(x1,acsc(x1),'b') hold on plot(x2,acsc(x2),'b') grid on```

## Input Arguments

collapse all

Numeric input, specified as a number, vector, matrix, or multidimensional array.

Data Types: `single` | `double`
Complex Number Support: Yes

collapse all

### Inverse Cosecant

The inverse cosecant is defined as

`${\mathrm{csc}}^{-1}\left(z\right)={\mathrm{sin}}^{-1}\left(\frac{1}{z}\right).$`