## Purpose

## Return value

## Arguments

*number*- The angle in radians for which you want the tangent.

## Syntax

## Usage notes

The TAN function returns the tangent of an angle provided in radians. In geometric terms, the tangent of an angle returns the ratio of a right-triangle's opposite side over its adjacent side. For example, the tangent of PI()/4 (45°) returns the ratio of 1.0.

```
=TAN(PI()/4) // Returns 1.0
```

### Using Degrees

To supply an angle to TAN in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians. For example, to get the TAN of 60 degrees, you can use either formula below:

```
=TAN(60*PI()/180)
=TAN(RADIANS(60))
```

### Explanation

The graph of the tangent function, shown above, visualizes the output of the function for angles from 0 to a full rotation corresponding to the range [0, 2π]. The function has two vertical asymptotes within the range [0, 2π] where the output diverges to infinity. The tangent function can be equivalently defined in terms of SIN and COS:

```
=TAN(θ) = SIN(θ)/COS(θ)
```