Documentation/Calc Functions/COTH

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    Function name:

    COTH

    Category:

    Mathematical

    Summary:

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

    Syntax:

    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.

    Additional details:

    The formula for the hyperbolic cotangent of x is:

    [math]\displaystyle{ \coth(x)~=~\frac{\cosh(x)}{\sinh(x)}~=~\frac{e^x+e^{-x}}{e^x-e^{-x}} }[/math]

    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

    Related LibreOffice functions:

    ACOTH

    COSH

    CSCH

    SECH

    SINH

    TANH

    ODF standard:

    Section 6.16.22, part 2

    Related (or similar) Excel functions:

    COTH since v.2013.