# Documentation/Calc Functions/TAN

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## Function name:

TAN

## Category:

Mathematical

## Summary:

Returns the tangent of the given angle (in radians).

## Syntax:

TAN(**Number**)

## Returns:

Returns the (trigonometric) tangent of **Number**, the angle in radians. The resultant value ranges from -∞ and +∞, i.e. (-∞,+∞).

## Arguments:

**Number** is the real number, or a reference to a cell containing that number, which is the angle in radians whose tangent value is to be calculated.

## Additional details:

- Mathematically, tangent of odd multiples of π/2, i.e. {......-3π/2,-π/2,0,+π/2,+3π/2.....} is undefined but the PI() function uses an approximate value of π hence the function doesn't return any error value.
- The formula for the tangent of an angle is:

where x in the **Number**.

- Based on the above formula tangent is equivalent to 1 divided by the cotangent of that angle.
- To insert an angle in degrees, either multiply the angle by PI()/180 or use the RADIANS function to convert the angle to radians.

The figure below illustrates the function TAN.

## Examples:

Formula | Description | Returns |
---|---|---|

=TAN(1) | tangent of 1 radian | 1.5574077246549 |

=TAN(PI()/4) | tangent of PI/4 or π/4 radians | 1 |

=TAN(RADIANS(45)) | tangent of 45° by first converting angle in degrees to radians | 1 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

TAN