# Documentation/Calc Functions/CSCH

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## Function name:

CSCH

## Category:

Mathematical

## Summary:

Calculates the hyperbolic cosecant (csch) of a hyperbolic angle expressed in radians.

## Syntax:

CSCH(**Number**)

## Returns:

Returns a non-zero real number that is the hyperbolic cosecant of the specified hyperbolic angle.

## Arguments:

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

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

- If
**Number**is equal to 0, then CSCH reports a #NUM! error.

## Additional details:

The formula for the hyperbolic cosecant of x is:

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

The figure below illustrates the function CSCH.

## Examples:

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

=CSCH(1) | Hyperbolic cosecant of 1. | 0.850918128239321 |

=CSCH(D1) where cell D1 contains the number -2. | Hyperbolic cosecant of -2. | -0.275720564771783 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

CSCH