The hyperbolic cotangent is the reciprocal of the hyperbolic tangent.
Therefore, the value of the hyperbolic cotangent is given by the equation:
Further information is provided on the Wikipedia Hyperbolic Functions page.The Excel Coth function calculates the hyperbolic cotangent (coth) of a supplied angle.
Note: the Coth 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 angle (in radians) that you want to calculate the hyperbolic cotangent of. This must be between 2^27 and +2^27.
If the supplied number is equal to 0, the Coth function returns the #DIV/0! error.
Converting from Degrees to Radians
If your angle is in degrees, you will need to convert it into radians before supplying it to the Coth function. This can be done using the Excel Radians function:
The following spreadsheet shows the Excel Coth Function, used to calculate the hyperbolic cotangent of three different angles:
Formulas:
 Results:

Note that, in the examples above:
Further details and examples of the Excel Coth function are provided on the Microsoft Office website.
If you get an error from the Excel Coth function, this is likely to be one of the following:
#DIV/0!    Occurs if the supplied number is equal to 0. 
#NUM!    Occurs if the supplied number is less than 2^27 or is greater than 2^27. 
#VALUE!    Occurs if the supplied number argument is not recognized as a numeric value. 