# The Excel COTH Function

Hyperbolic Cotangent

The hyperbolic cotangent is the reciprocal of the hyperbolic tangent.

Therefore, the value of the hyperbolic cotangent is given by the equation:

For further information, see the Wikipedia Hyperbolic Functions page.

## Function Description

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:

COTH( number )

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.

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:

An example of this is provided below.

## Coth Function Examples

The following spreadsheet shows the Excel Coth Function, used to calculate the hyperbolic cotangent of three different angles:

Formulas:
A
1 =COTH( -3.14159265358979 )
2 =COTH( PI() / 2 )
3 =COTH( RADIANS( 120 ) )
Results:
A
1 -1.003741873
2 1.090331411
3 1.030796253

Note that, in the examples above:

• In cell A2, the Excel Pi function is used to provide the value π/2 to the Coth function;
• In cell A3, the Excel Radians function is used to convert the angle, 120 degrees, into radians before it is supplied to the Coth function.

For further details and examples of the Excel Coth function, see the Microsoft Office website.

## Coth Function Errors

If you get an error from the Excel Coth function, this is likely to be one of the following:

Common Errors
 #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.