# Documentation

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# 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

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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

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

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

## Output Arguments

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

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### 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

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