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- Hyperbolic_function abstract "In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" (/ˈsɪntʃ/ or /ˈʃaɪn/), and the hyperbolic cosine "cosh" /ˈkɒʃ/, from which are derived the hyperbolic tangent "tanh" (/ˈtæntʃ/ or /ˈθæn/), hyperbolic cosecant "csch" or "cosech" /ˈkoʊʃɛk/ or /ˈkoʊsɛtʃ/, hyperbolic secant "sech" /ˈʃɛk/ or /ˈsɛtʃ/, and hyperbolic cotangent "coth" /ˈkoʊθ/ or /ˈkɒθ/, corresponding to the derived trigonometric functions. The inverse hyperbolic functions are the area hyperbolic sine "arsinh" (also called "asinh" or sometimes "arcsinh") and so on.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 equilateral hyperbola. Hyperbolic functions occur in the solutions of some important linear differential equations, for example the equation defining a catenary, of some cubic equations, and of Laplace's equation in Cartesian coordinates. The latter is important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity.The hyperbolic functions take real values for a real argument called a hyperbolic angle.The size of a hyperbolic angle is the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.In complex analysis, the hyperbolic functions arise as the imaginary parts of sine and cosine. When considered defined by a complex variable, the hyperbolic functions are rational functions of exponentials, and are hence meromorphic.Hyperbolic functions were introduced in the 1760s independently by Vincenzo Riccati and Johann Heinrich Lambert. Riccati used Sc. and Cc. ([co]sinus circulare) to refer to circular functions and Sh. and Ch. ([co]sinus hyperbolico) to refer to hyperbolic functions. Lambert adopted the names but altered the abbreviations to what they are today. The abbreviations sh and ch are still used in some other languages, like European French and Russian.".
- Hyperbolic_function thumbnail Hyperbolic_functions-2.svg?width=300.
- Hyperbolic_function wikiPageExternalLink glab.trixon.se.
- Hyperbolic_function wikiPageExternalLink HyperbolicFunctions.html.
- Hyperbolic_function wikiPageExternalLink HyperbolicFunctions.html.
- Hyperbolic_function wikiPageExternalLink hyperbolic.
- Hyperbolic_function wikiPageID "56567".
- Hyperbolic_function wikiPageRevisionID "605776486".
- Hyperbolic_function alt "cosh is the average of exand e−x".
- Hyperbolic_function alt "sinh is half the difference of ex and e−x".
- Hyperbolic_function caption "cosh is the average of exand e−x".
- Hyperbolic_function caption "sinh is half the difference of ex and e−x".
- Hyperbolic_function direction "vertical".
- Hyperbolic_function footer "Hyperbolic functions cosh and sinh obtained using exponential functions and".
- Hyperbolic_function hasPhotoCollection Hyperbolic_function.
- Hyperbolic_function id "p/h048250".
- Hyperbolic_function image "Hyperbolic and exponential; cosh.svg".
- Hyperbolic_function image "Hyperbolic and exponential; sinh.svg".
- Hyperbolic_function title "Hyperbolic functions".
- Hyperbolic_function width "225".
- Hyperbolic_function subject Category:Analytic_functions.
- Hyperbolic_function subject Category:Elementary_special_functions.
- Hyperbolic_function subject Category:Exponentials.
- Hyperbolic_function subject Category:Hyperbolic_geometry.
- Hyperbolic_function type Abstraction100002137.
- Hyperbolic_function type AnalyticFunctions.
- Hyperbolic_function type ElementarySpecialFunctions.
- Hyperbolic_function type Exponential113789462.
- Hyperbolic_function type Exponentials.
- Hyperbolic_function type Function113783816.
- Hyperbolic_function type MathematicalRelation113783581.
- Hyperbolic_function type Relation100031921.
- Hyperbolic_function comment "In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.".
- Hyperbolic_function label "Fonction hyperbolique".
- Hyperbolic_function label "Función hiperbólica".
- Hyperbolic_function label "Funkcje hiperboliczne".
- Hyperbolic_function label "Funzioni iperboliche".
- Hyperbolic_function label "Função hiperbólica".
- Hyperbolic_function label "Hyperbelfunktion".
- Hyperbolic_function label "Hyperbolic function".
- Hyperbolic_function label "Hyperbolische functie".
- Hyperbolic_function label "Гиперболические функции".
- Hyperbolic_function label "دالة زائدية".
- Hyperbolic_function label "双曲函数".
- Hyperbolic_function label "双曲線関数".
- Hyperbolic_function sameAs Hyperbolické_funkce.
- Hyperbolic_function sameAs Hyperbelfunktion.
- Hyperbolic_function sameAs Υπερβολικές_συναρτήσεις.
- Hyperbolic_function sameAs Función_hiperbólica.
- Hyperbolic_function sameAs Fonction_hyperbolique.
- Hyperbolic_function sameAs Funzioni_iperboliche.
- Hyperbolic_function sameAs 双曲線関数.
- Hyperbolic_function sameAs 쌍곡선함수.
- Hyperbolic_function sameAs Hyperbolische_functie.
- Hyperbolic_function sameAs Funkcje_hiperboliczne.
- Hyperbolic_function sameAs Função_hiperbólica.
- Hyperbolic_function sameAs m.0fmrx.
- Hyperbolic_function sameAs Q204034.
- Hyperbolic_function sameAs Q204034.
- Hyperbolic_function sameAs Hyperbolic_function.
- Hyperbolic_function wasDerivedFrom Hyperbolic_function?oldid=605776486.
- Hyperbolic_function depiction Hyperbolic_functions-2.svg.
- Hyperbolic_function isPrimaryTopicOf Hyperbolic_function.