# Documentation/Calc Functions/ACOTH

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ACOTH

Mathematical

## Summary:

Calculates the inverse hyperbolic cotangent (arcoth) of a real number, in radians.

## Syntax:

ACOTH(Number)

## Returns:

Returns a non-zero real number that is the inverse hyperbolic cotangent of Number in radians.

## Arguments:

Number is a real number that lies outside the range [-1, 1], or a reference to a cell containing that number, whose inverse hyperbolic cotangent is to be calculated.

• If Number is non-numeric, then ACOTH reports a #VALUE! error.
• If Number lies in the range [-1, 1], then ACOTH reports an invalid argument error (Err:502).

The formula for the inverse hyperbolic cotangent of x is:

$\displaystyle{ \text{arcoth}(x)~=~\frac{1}{2}\ln\left(\frac{x+1}{x-1}\right) }$

The figure below illustrates the function ACOTH.

ACOTH function

## 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. 3.99999999999997
=ACOTH(D1) where cell D1 contains the value -1.5. Inverse hyperbolic cotangent of -1.5. −0.80471895621705

## Related (or similar) Excel functions:

ACOTH since v.2013.