# Documentation/Calc Functions/SECH

TDF LibreOffice Document Liberation Project Community Blogs Weblate Nextcloud Redmine Ask LibreOffice Donate

## Function name:

SECH

## Category:

Mathematical

## Summary:

Calculates the hyperbolic secant (sech) of a hyperbolic angle expressed in radians.

## Syntax:

SECH(**Number**)

## Returns:

Returns a real number in the range (0, 1] that is the hyperbolic secant of the specified hyperbolic angle.

## Arguments:

**Number** is a real number, or a reference to a cell containing that number, that is the hyperbolic angle in radians whose hyperbolic secant is to be calculated.

- If
**Number**is non-numeric, then SECH reports a #VALUE! error.

## Additional details:

The formula for the hyperbolic secant of x is:

[math]\displaystyle{ \text{sech}(x)~=~\frac{1}{\cosh(x)}~=~\frac{2}{e^x+e^{-x}} }[/math]

The figure below illustrates the function SECH.

## Examples:

Formula | Description | Returns |
---|---|---|

=SECH(1) | Hyperbolic secant of 1. | 0.648054273663885 |

=SECH(D1) where cell D1 contains the number -2. | Hyperbolic secant of -2. | 0.26580222883408 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

SECH since v.2013.