# Documentation/Calc Functions/ACOTH

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## Function name:

ACOTH

## Category:

Mathematical

## Summary:

Returns the inverse hyperbolic cotangent of the given number.

## Syntax:

ACOTH(**Number**)

## Returns:

This function returns the inverse hyperbolic cotangent of **Number**, that is the number whose hyperbolic cotangent is **Number**.

## Arguments:

**Number** is the real number, or a reference to a cell containing that number whose inverse hyperbolic cotangent value is to be calculated.
**Number** should not be between -1 and 1 inclusive.

If **Number** is less than equal to 1 and greater than equal to -1, ACOTH returns the error value. Alternatively, if the absolute value of **Number** is less than 1, ACOTH returns the error value.

## Additional details:

- The hyperbolic arccotangent is an analog of the ordinary (circular) arccotangent.
- The formula for inverse hyperbolic cotangent is:

where x is the **Number**

The image 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. | 4 |

=ACOTH(-1.5) | Inverse hyperbolic cotangent of -1.5. | -0.80471895621705 |

=ACOTH(0.5) | Inverse hyperbolic cotangent of 0.5 will return an error because 0.5 is out of its domain. | Err:502 |

=ACOTH(1) | Inverse hyperbolic cotangent of 1 will return an error because 1 is out of its domain. | Err:502 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

ACOTH