Documentation/Calc Functions/ACOSH

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    Function name:

    ACOSH

    Category:

    Mathematical

    Summary:

    Calculates the inverse hyperbolic cosine (arcosh) of a real number. The value returned is non-negative and expressed in radians.

    Syntax:

    ACOSH(Number)

    Returns:

    Returns a real number in the range [0, ∞) that is the inverse hyperbolic cosine of Number in radians.

    Arguments:

    Number is a real number in the range [1, ∞), or a reference to a cell containing that number, whose inverse hyperbolic cosine is to be calculated.

    • If Number is non-numeric, then ACOSH reports a #VALUE! error.
    • If Number lies outside the range [1, ∞), then ACOSH reports an invalid argument error (Err:502).

    Additional details:

    The formula for the inverse hyperbolic cosine of x is:

    [math]\displaystyle{ \operatorname{arcosh}(x) = \ln\left (x+\sqrt{(x^2-1)}\right ) }[/math]

    The figure below illustrates the function ACOSH.

    ACOSH function

    Examples:

    Formula Description Returns
    =ACOSH(1) Inverse hyperbolic cosine of 1. 0
    =ACOSH(COSH(4)) Inverse hyperbolic cosine of hyperbolic cosine of 4. 4
    =ACOSH(D1) where cell D1 contains the value 1.5. Inverse hyperbolic cosine of 1.5. 0.962423650119207

    Related LibreOffice functions:

    ACOTH

    ASINH

    ATANH

    COSH

    ODF standard:

    Section 6.16.4, part 2

    Related (or similar) Excel functions:

    ACOSH