# Documentation/Calc Functions/CSCH

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CSCH

Mathematical

## Summary:

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

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.

The formula for the hyperbolic cosecant of x is:

$\displaystyle{ \text{csch}(x)~=~\frac{1}{\sinh(x)}~=~\frac{2}{e^x-e^{-x}} }$

The figure below illustrates the function CSCH.

CSCH function

## 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

CSCH