Inverse Hyperbolic Cosine

On this page the angle to the hyperbolic cosine is calculated. To calculate, enter the value of the hyperbolic cosine to which the angle should be calculated, then click on the 'Calculate' button.

The unit of measurement for the result can be switched between degrees and radians

Description

The ACosh function calculates the angle to the hyperbolic cosine, which is given as a real number.

Input

The argument must be greater than or equal to 1. If the value is less than 1, the function returns the result \(\text{NaN}\) (not a valid number).

Result

The result is given in degrees (full circle = 360°) or radians (full circle = 2 · π). The unit of measurement used is set using the Degrees or Radians menu

Curve of the ACosh function

Definition

The inverse hyperbolic cosine is the inverse function of the hyperbolic cosine. This feature is often abbreviated as ACosh. It calculates the angle that corresponds to the value of the hyperbolic cosine.

In a mathematical formula this can be expressed as follows:

\(\displaystyle \text{ACosh}(x) = \ln(x+\sqrt{x^2-1})\)

Here \(x\) is the value of the hyperbolic cosine. If the hyperbolic cosine is used as an argument, the ACosh function returns the angle in radians.