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([number](/features/value-types#numbers), required). The value whose hyperbolic arccosine is to be calculated. The value must be greater than or equal to 1. -# ACOSH +### Additional guidance +The hyperbolic arccosine function is defined as: -::: warning -🚧 This function is implemented but currently lacks detailed documentation. For guidance, you may refer to the equivalent functionality in [Microsoft Excel documentation](https://support.microsoft.com/en-us/office/excel-functions-by-category-5f91f4e9-7b42-46d2-9bd1-63f26a86c0eb). -::: \ No newline at end of file +$$ +\text{acosh(x)} = \ln(x + \sqrt{x^2 - 1}) +$$ + +### Returned value +ACOSH returns a [number](/features/value-types#numbers) that is the hyperbolic arccosine of the specified value, expressed in radians. +### Error conditions +* In common with many other IronCalc functions, ACOSH propagates errors that are found in its argument. +* If no argument, or more than one argument, is supplied, then ACOSH returns the [`#ERROR!`](/features/error-types.md#error) error. +* If the value of the *number* argument is not (or cannot be converted to) a [number](/features/value-types#numbers), then ACOSH returns the [`#VALUE!`](/features/error-types.md#value) error. +* If the value of the *number* argument is less than 1, then ACOSH returns the [`#NUM!`](/features/error-types.md#num) error. + +## Details +* The ACOSH function utilizes the *acosh()* method provided by the [Rust Standard Library](https://doc.rust-lang.org/std/). +* The figure below illustrates the output of the ACOSH function for values $x \geq 1$ in the range [0, +∞). +
Graph showing acosh(x) for x ≥ 0.
+ +## Examples +[See some examples in IronCalc](https://app.ironcalc.com/?example=acosh). + +## Links +* For more information about inverse hyperbolic functions, visit Wikipedia's [Inverse hyperbolic functions](https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions) page. +* See also IronCalc's [COSH](/functions/math_and_trigonometry/cosh), [ASINH](/functions/math_and_trigonometry/asinh) and [ATANH](/functions/math_and_trigonometry/atanh) functions. +* Visit Microsoft Excel's [ACOSH function](https://support.microsoft.com/en-us/office/acosh-function-e3992cc1-103f-4e72-9f04-624b9ef5ebfe) page. +* Both [Google Sheets](https://support.google.com/docs/answer/3093391) and [LibreOffice Calc](https://wiki.documentfoundation.org/Documentation/Calc_Functions/ACOSH) provide versions of the ACOSH function. \ No newline at end of file