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# The Excel TANH Function

Hyperbolic Functions

The basic hyperbolic functions, cosh, sinh and tanh are related to the equilateral hyperbola, x^{2}-y^{2}=1.

If the area between a line through the origin, the x-axis, and the hyperbola x^{2}-y^{2}=1 has area α/2, then:

- cosh α is the x coordinate of the intersection between the line through the origin and the hyperbola x
^{2}-y^{2}=1 - sinh α is the y coordinate of the intersection between the line through the origin and the hyperbola x
^{2}-y^{2}=1 - tanh α is equal to sinh α / cosh α

The equation used to calculate the hyperbolic tangent is therefore:

## Function Description

The Excel Tanh function calculates the hyperbolic tangent (tanh) of a supplied number.

The syntax of the function is:

TANH( number )

Where the number argument is the real number that you want to calculate the hyperbolic tangent of.

## Tanh Function Examples

The following spreadsheet below shows the Excel Tanh Function, used to calculate the hyperbolic tangent of three different values:

Formulas: | Results: |

For further details and examples of the Excel Tanh function, see the Microsoft Office website.

## Tanh Function Error

If you get an error from the Excel Tanh Function, this is likely to be the #VALUE! error:

Common Error

#VALUE! | - | Occurs if the supplied number argument is not recognized as a numeric value. |