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Hyperbolic functions

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are…

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Overview

History

Definitions

Characterizing properties

Useful relations

Second derivatives

Standard integrals

Taylor series expressions

Comparison with circular functions

Relationship to the exponential function

Hyperbolic functions for complex numbers

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Hyperbolic functions

Nodes94
Edges93
Triples35
Avg. degree1.98
Density0.021277
Components1

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Hyperbolic functions

Top relations

related to External links · 8
Hyperbolic functions → EMS Press, Encyclopedia, Hyperbolic, Java Web Start, Mathematics, PlanetMathGonioLab, Visualization, Web-based
related to history · 6
Hyperbolic functions → Gerardus Mercator, Isaac Newton, It, Mercator, Principia Mathematica, The
related to Comparison with circular functions · 5
Hyperbolic functions → Both, In, Similarly, Since, The
related to Definitions · 5
Hyperbolic functions → In, OA, OB, OC, With
related to Hyperbolic functions for complex numbers · 4
Hyperbolic functions → Euler's, Relationships, Since, The
related to Useful relations · 4
Hyperbolic functions → George Osborn, In, Osborn's, The
related to Complex trigonometric definitions · 1
Hyperbolic functions → Hyperbolic
related to Differential equation definitions · 1
Hyperbolic functions → The
see also · 1
Hyperbolic functions → Equal

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Important terminology

hyperbolic functions cosh sinh displaystyle frac complex tanh function cosine coth sech csch angle trigonometric sine right exponential operatorname tangent

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hyperbolic functionsrelated to Comparison with circular functionsThe0.60section
Hyperbolic functionsrelated to Comparison with circular functionsBoth0.60section
Hyperbolic functionsrelated to Comparison with circular functionsSince0.60section
Hyperbolic functionsrelated to Comparison with circular functionsIn0.60section
Hyperbolic functionsrelated to Comparison with circular functionsSimilarly0.60section
Hyperbolic functionsrelated to Complex trigonometric definitionsHyperbolic0.60section
Hyperbolic functionsrelated to DefinitionsWith0.60section
Hyperbolic functionsrelated to DefinitionsIn0.60section
Hyperbolic functionsrelated to DefinitionsOA0.60section
Hyperbolic functionsrelated to DefinitionsOB0.60section
Hyperbolic functionsrelated to DefinitionsOC0.60section
Hyperbolic functionsrelated to Differential equation definitionsThe0.60section

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