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Article 11 — Appendix A.26

sech — hyperbolic secant function

Category. Mathematics.

Abstract. Hyperbolic secant: 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 secant is defined as

sechx ≡ 2 /(ex + ex)

2. Graph

Hyperbolic secant is symmetric function defined everywhere on real axis. Its graph is depicted below — fig. 1.

Fig. 1. Graph of the hyperbolic secant function y = sech x Fig. 1. Graph of the hyperbolic secant function y = sechx.

Function codomain is limited to the range (0, 1].

3. Identities

Base:

sech2x + tanh2x = 1

By definition:

sechx ≡ 1 /coshx

Property of symmetry:

sech−x = sechx

4. Support

Hyperbolic secant function sech is supported in:

Hyperbolic secant function of the complex argument sech is supported in:

5. How to use

To calculate hyperbolic secant of the number:

sech(-1);

To calculate hyperbolic secant of the current result:

sech(Rslt);

To calculate hyperbolic secant of the number x in memory:

sech(Mem[x]);