# Documentation/Calc Functions/COTH

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COTH

Mathematical

## Summary:

Calculates the hyperbolic cotangent (coth) of a hyperbolic angle expressed in radians.

COTH(Number)

## Returns:

Returns a real number that lies outside the range [-1, 1] that is the hyperbolic cotangent of the specified hyperbolic angle.

## Arguments:

Number is a non-zero real number, or a reference to a cell containing that number, that is the hyperbolic angle in radians whose hyperbolic cotangent is to be calculated.

• If Number is non-numeric, then COTH reports a #VALUE! error.
• If Number is equal to 0, then COTH reports a #NUM! error.

The formula for the hyperbolic cotangent of x is:

$\displaystyle{ \coth(x)~=~\frac{\cosh(x)}{\sinh(x)}~=~\frac{e^x+e^{-x}}{e^x-e^{-x}} }$

The figure below illustrates the function COTH.

COTH function

## Examples:

Formula Description Returns
=COTH(1) Hyperbolic cotangent of 1. 1.31303528549933
=COTH(D1) where cell D1 contains the number -2. Hyperbolic cotangent of -2. −1.03731472072755
=ACOTH(COTH(3)) The hyperbolic cotangent of 3 radians is taken and then the inverse hyperbolic cotangent of that value is calculated. 3

COTH