# Documentation/Calc Functions/ACOTH

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ACOTH

Mathematical

## Summary:

Returns the inverse hyperbolic cotangent of the given number.

ACOTH(Number)

## Returns:

This function returns the inverse hyperbolic cotangent of Number, that is the number whose hyperbolic cotangent is Number.

## Arguments:

Number is the real number, or a reference to a cell containing that number whose inverse hyperbolic cotangent value is to be calculated. Number should not be between -1 and 1 inclusive.

If Number is less than equal to 1 and greater than equal to -1, ACOTH returns the error value. Alternatively, if the absolute value of Number is less than 1, ACOTH returns the error value.

• The hyperbolic arccotangent is an analog of the ordinary (circular) arccotangent.
• The formula for inverse hyperbolic cotangent is:

where x is the Number

The image below illustrates the function ACOTH.

## 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. 4
=ACOTH(-1.5) Inverse hyperbolic cotangent of -1.5. -0.80471895621705
=ACOTH(0.5) Inverse hyperbolic cotangent of 0.5 will return an error because 0.5 is out of its domain. Err:502
=ACOTH(1) Inverse hyperbolic cotangent of 1 will return an error because 1 is out of its domain. Err:502

COTH

ACOT

ATANH

## ODF standard:

Section 6.16.6, part 2

ACOTH