# Documentation

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# tan

## Syntax

``Y = tan(X)``

## Description

example

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

## Examples

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Plot the tangent function over the domain .

```x = (-pi/2)+0.01:0.01:(pi/2)-0.01; plot(x,tan(x)), grid on```

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

```x = [-i pi+i*pi/2 -1+i*4]; y = tan(x)```
```y = 0.0000 - 0.7616i -0.0000 + 0.9172i -0.0006 + 1.0003i ```

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

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### Tangent Function

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

.

The tangent of a complex angle, α, is

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