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Article 11 — Appendix A.17

csch — hyperbolic cosecant function

Category. Mathematics.

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

References. This article is a part of scientific calculator Li-L, scientific calculator Li-X, scientific calculator Li-Lc and scientific calculator Li-Xc products.

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 = csch x 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]);