Documentation/Calc Functions/TANH

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    Function name:

    TANH

    Category:

    Mathematical

    Summary:

    Calculates the hyperbolic tangent (tanh) of a hyperbolic angle expressed in radians.

    Syntax:

    TANH(Number)

    Returns:

    Returns a real number in the range (-1, 1) that is the hyperbolic tangent of the specified hyperbolic angle.

    Arguments:

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

    • If Number is non-numeric, then TANH reports a #VALUE! error.

    Additional details:

    The formula for the hyperbolic tangent of x is:

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

    The figure below illustrates the function TANH.

    TANH function

    Examples:

    Formula Description Returns
    =TANH(0) Hyperbolic tangent of 0. 0
    =TANH(D1) where cell D1 contains the number -2. Hyperbolic tangent of -2. −0.964027580075817
    =ATANH(TANH(3)) The hyperbolic tangent of 3 radians is taken and then the inverse hyperbolic tangent of that value is calculated. 3

    Related LibreOffice functions:

    ATANH

    COSH

    COTH

    CSCH

    FISHERINV

    SECH

    SINH

    ODF standard:

    Section 6.16.70, part 2

    Related (or similar) Excel functions:

    TANH