# Documentation

### This is machine translation

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

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

# csc

Cosecant of input angle in radians

## Syntax

``Y = csc(X)``

## Description

example

````Y = csc(X)` returns the cosecant of the elements of `X`. The `csc` function operates element-wise on arrays. The function accepts both real and complex inputs. For real values of `X` in the interval [-Inf, Inf], `csc` returns real values in the interval [-Inf ,-1] and [1,Inf]. For complex values of `X`, `csc` returns complex values. All angles are in radians.```

## Examples

collapse all

Plot the cosecant function over the domain and as shown.

```x1 = -pi+0.01:0.01:-0.01; x2 = 0.01:0.01:pi-0.01; plot(x1,csc(x1),x2,csc(x2)), grid on```

Calculate the cosecant of the complex angles in vector `x`.

```x = [-i pi+i*pi/2 -1+i*4]; y = csc(x)```
```y = 0.0000 + 0.8509i 0.0000 + 0.4345i -0.0308 - 0.0198i ```

## Input Arguments

collapse all

Input angle in radians, specified as a scalar, vector, matrix, or multidimensional array.

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

## Output Arguments

collapse all

Cosecant of input angle, returned as a real-valued or complex-valued scalar, vector, matrix or multidimensional array.

## More About

collapse all

### Cosecant Function

The cosecant of an angle, α, defined with reference to a right angled triangle is

The cosecant of a complex angle, α, is

`$\text{csc}\left(\alpha \right)=\frac{2i}{{e}^{i\alpha }-{e}^{-i\alpha }}\text{\hspace{0.17em}}.$`

## See Also

#### Introduced before R2006a

Was this topic helpful?

#### Beyond Excel: The Manager's Guide to Solving the Big Data Conundrum

Download white paper