Documentation/Calc Functions/COSH

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    Function name:

    COSH

    Category:

    Mathematical

    Summary:

    Calculates the hyperbolic cosine (cosh) of a hyperbolic angle expressed in radians.

    Syntax:

    COSH(Number)

    Returns:

    Returns a real number in the range [1, ∞) that is the hyperbolic cosine 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 cosine is to be calculated.

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

    Additional details:

    The formula for the hyperbolic cosine of x is:

    [math]\displaystyle{ \cosh(x)~=~\frac{e^x+e^{-x}}{2} }[/math]

    The figure below illustrates the function COSH.

    COSH function

    Examples:

    Formula Description Returns
    =COSH(0) Hyperbolic cosine of 0. 1
    =COSH(D1) where cell D1 contains the number -2. Hyperbolic cosine of -2. 3.76219569108363
    =ACOSH(COSH(3)) The hyperbolic cosine of 3 radians is taken and then the inverse hyperbolic cosine of that value is calculated. Note that =ACOSH(COSH(-3)) also returns 3, because COSH is an even function. 3

    Related LibreOffice functions:

    ACOSH

    COTH

    CSCH

    SECH

    SINH

    TANH

    ODF standard:

    Section 6.16.20, part 2

    Related (or similar) Excel functions:

    COSH