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.

# tan

Tangent of argument in radians

## 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

collapse all

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 = 1×3 complex 0.0000 - 0.7616i -0.0000 + 0.9172i -0.0006 + 1.0003i ```

## 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

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

collapse all

### Tangent Function

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

.

The tangent of a complex argument, α, is

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

.