The ACOSH function returns the inverse hyperbolic cosine of a number. The number must be greater than or equal to 1. The inverse hyperbolic cosine is the value whose hyperbolic cosine is number, so ACOSH(COSH(number)) equals number.

Syntax

=ACOSH(number)

Arguments

Argument Description
number Any real number ≥ 1

Examples

  A B C
1 Formula Result Notes
2 =ACOSH(1) 0 Inverse hyperbolic cosine of 1
3 =ACOSH(2.5) 1.5667992 Inverse hyperbolic cosine of 2.5
4 =ACOSH(10) 2.9932228 Inverse hyperbolic cosine of 10

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if the supplied number argument is not a numeric value
#NUM! Occurs if the supplied number argument is less than 1

The ACOSH function returns the inverse hyperbolic cosine. The equation to calculate the inverse hyperbolic cosine is:

 

    \[    acosh(z) = ln \left( z + \sqrt{z+1} \sqrt{z-1} \right)    \]

See Wikipedia for more information on Inverse Hyperbolic Function.