# Documentation/Calc Functions/ACOTH

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## Function name:

ACOTH

## Category:

Mathematical

## Summary:

Calculates the inverse hyperbolic cotangent (arcoth) of a real number, in radians.

## Syntax:

ACOTH(**Number**)

## Returns:

Returns a non-zero real number that is the inverse hyperbolic cotangent of **Number** in radians.

## Arguments:

**Number** is a real number that lies outside the range [-1, 1], or a reference to a cell containing that number, whose inverse hyperbolic cotangent is to be calculated.

- If
**Number**is non-numeric, then ACOTH reports a #VALUE! error.

- If
**Number**lies in the range [-1, 1], then ACOTH reports an invalid argument error (Err:502).

## Additional details:

The formula for the inverse hyperbolic cotangent of x is:

[math]\displaystyle{ \text{arcoth}(x)~=~\frac{1}{2}\ln\left(\frac{x+1}{x-1}\right) }[/math]

The figure below illustrates the function ACOTH.

## Examples:

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

=ACOTH(1.1) | Inverse hyperbolic cotangent of 1.1. | 1.52226121886171 |

=ACOTH(COTH(4)) | Inverse hyperbolic cotangent of hyperbolic cotangent of 4. | 3.99999999999997 |

=ACOTH(D1) where cell D1 contains the value -1.5. | Inverse hyperbolic cotangent of -1.5. | −0.80471895621705 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

ACOTH since v.2013.