The hyperbolic arccotangent is the inverse of the hyperbolic cotangent. Therefore,
The equation used to calculate the hyperbolic arccotangent is:
Further information on the inverse hyperbolic functions is provided on Wikipedia.The Excel Acoth function calculates the hyperbolic arccotangent (coth) of a supplied value.
Note: the Acoth function was only introduced in Excel 2013 and so is not available in earlier versions of Excel.
The syntax of the function is:
Where the number argument is the value that you want to calculate the hyperbolic arccotangent of. This must be less than 1 or greater than +1.
The following spreadsheet shows the Excel Acoth Function used to calculate the hyperbolic arccotangent of three different values:
Formulas:
 Results:

Further details and examples of the Excel Acoth function are provided on the Microsoft Office website.
If you get an error from the Excel Acoth function, this is likely to be one of the following:
#NUM!    Occurs if the supplied number is between 1 and +1 (inclusive). 
#VALUE!    Occurs if the supplied number argument is not recognized as a numeric value. 