Documentation/Calc Functions/ACOTH

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    Function name:

    ACOTH

    Category:

    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).

    Additional details:

    The formula for the inverse hyperbolic cotangent of x is:

    [math]\displaystyle{ \text{arcoth}(x)~=~\frac{1}{2}\ln\left(\frac{x+1}{x-1}\right) }[/math]

    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 LibreOffice functions:

    ACOSH

    ASINH

    ATANH

    COTH

    ODF standard:

    Section 6.16.6, part 2

    Related (or similar) Excel functions:

    ACOTH since v.2013.