Definitions for hyperbolic function
hy·per·bol·ic func·tion

WiktionaryRate this definition:0.0 / 0 votes

1. hyperbolic functionnoun

   A function that is derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.

WikipediaRate this definition:0.0 / 0 votes

1. hyperbolic function

   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 cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and +sinh(t) respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity. The basic hyperbolic functions are: hyperbolic sine "sinh" (), hyperbolic cosine "cosh" (),from which are derived: hyperbolic tangent "tanh" (), hyperbolic cosecant "csch" or "cosech" () hyperbolic secant "sech" (), hyperbolic cotangent "coth" (),corresponding to the derived trigonometric functions.

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1. Hyperbolic function

   In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh", and the hyperbolic cosine "cosh", from which are derived the hyperbolic tangent "tanh", hyperbolic cosecant "csch" or "cosech", hyperbolic secant "sech", and hyperbolic cotangent "coth", corresponding to the derived trigonometric functions. The inverse hyperbolic functions are the area hyperbolic sine "arsinh" and so on. Just as the points form a circle with a unit radius, the points 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.

How to pronounce hyperbolic function?

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Numerology

1. Chaldean Numerology

   The numerical value of hyperbolic function in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of hyperbolic function in Pythagorean Numerology is: 8

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Hyperbolic_Function
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Hyperbolic_Function
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=hyperbolic function