# Documentation/Calc Functions/COTH

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## Function name:

COTH

## Category:

Mathematical

## Summary:

Calculates the hyperbolic cotangent (coth) of a hyperbolic angle expressed in radians.

## Syntax:

COTH(**Number**)

## Returns:

Returns a real number that lies outside the range [-1, 1] that is the hyperbolic cotangent of the specified hyperbolic angle.

## Arguments:

**Number** is a non-zero real number, or a reference to a cell containing that number, that is the hyperbolic angle in radians whose hyperbolic cotangent is to be calculated.

- If
**Number**is non-numeric, then COTH reports a #VALUE! error. - If
**Number**is equal to 0, then COTH reports a #NUM! error.

## Additional details:

The formula for the hyperbolic cotangent of x is:

[math]\displaystyle{ \coth(x)~=~\frac{\cosh(x)}{\sinh(x)}~=~\frac{e^x+e^{-x}}{e^x-e^{-x}} }[/math]

The figure below illustrates the function COTH.

## Examples:

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

=COTH(1) | Hyperbolic cotangent of 1. | 1.31303528549933 |

=COTH(D1) where cell D1 contains the number -2. | Hyperbolic cotangent of -2. | −1.03731472072755 |

=ACOTH(COTH(3)) | The hyperbolic cotangent of 3 radians is taken and then the inverse hyperbolic cotangent of that value is calculated. | 3 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

COTH since v.2013.