# Documentation/Calc Functions/ACOSH

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ACOSH

Mathematical

## Summary:

Returns the inverse hyperbolic cosine of a number.

ACOSH(Number)

## Returns:

This function returns the inverse hyperbolic cosine of Number, that is the value whose hyperbolic cosine is Number. The resultant value ranges from 0 and +∞, i.e. [0,+∞).

## Arguments:

Number is the real number, or a reference to a cell containing that number, which must be greater than or equal to 1 whose inverse hyperbolic cosine value is to be calculated.

If the Number is less than +1, the function returns an error value because it is out of domain.

• The formula for inverse hyperbolic cosine is:

where N is the Number

The GIF below illustrates the function ACOSH.

## 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(1.5) Inverse hyperbolic cosine of 1.5. 0.962423650119207
=ACOSH(0.5) Inverse hyperbolic cosine of 0.5 will return an error because 0.5 is out of its domain. Err:502

COSH

ACOS

ASINH

ATANH

## ODF standard:

Section 6.16.4, part 2

ACOSH