The Art of Interface

# csch — hyperbolic cosecant function

Category. Mathematics.

Abstract. Hyperbolic cosecant: definition, graph, properties and identities.

## 1. Definition

Hyperbolic cosecant is defined as

cschx ≡ 2 /(ex − ex)

## 2. Graph

Hyperbolic cosecant is antisymmetric function defined everywhere on real axis, except its singular point 0 — so, its domain is (−∞, 0)∪(0, +∞). Function graph is depicted below — fig. 1. Fig. 1. Graph of the hyperbolic cosecant function y = cschx.

Function codomain is entire real axis, except 0: (−∞, 0)∪(0, +∞).

## 3. Identities

Base:

coth2x − csch2x = 1

By definition:

cschx ≡ 1 /sinhx

Property of antisymmetry:

csch−x = −cschx

## 4. Support

Hyperbolic cosecant function csch is supported in:

Hyperbolic cosecant function of the complex argument csch is supported in:

## 5. How to use

To calculate hyperbolic cosecant of the number:

``cosh(-1);``

To calculate hyperbolic cosecant of the current result:

``cosh(Rslt);``

To calculate hyperbolic cosecant of the number x in memory:

``cosh(Mem[x]);``