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Calculates the hyperbolic arccosine of a value. Hyperbolic trigonometric functions are based on the hyperbola with the equation x^{2} – y^{2} = 1. These functions differ from those in standard trigonometry (also called circular trigonometry), whose functions are based on the unit circle with the equation x^{2} + y^{2} = 1. However, they share many similar identities, such as sinh^{2} x + cosh^{2} x = 1, where h represents hyperbolic.

## Syntax

ACSH(number)

For number, specify the value or the column of values.

## Example

Column |
Calculator expression |
Result |

C1 contains 25 |
ACSH(C1) |
3.911622765215 |

## Uses

Hyperbolic functions have many useful applications in engineering, such as electrical transportation (to calculate length, weight, and stress of cables and conducting wires), superstructure (to compute elastic curves and deflection of suspension bridges), and aerospace (to determine ideal surface coatings for aircraft). In statistics, the inverse hyperbolic sine is used in the Johnson transformation to transform the data so it follows a normal distribution. Normality is a necessary assumption for some capability analyses.

## Formula

For a specified value of x, cosh x = (e^{x} + e^{−x}) / 2, where h represents hyperbolic, and e is the constant equal to approximately 2.718.

The inverse of the function is acsh x (cosh^{−1} x).