hyperbolic function

mathematical function related with trigonometric functions

AI overview

Hyperbolic functions are mathematical tools that work similarly to the trigonometric functions you might know from geometry, but they apply to hyperbolas instead of circles. They're useful in engineering and physics for describing things like the shape of hanging cables and the behavior of certain physical systems.

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Described at

6.4 Hyperbolic functions | Functions | Siyavula

Siyavula's open Mathematics Grade 10 textbook, chapter 6 on Functions covering 6.4 Hyperbolic functions

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We use this information to present the correct curriculum and to personalise content to better meet the needs of our users. Functions of the general form (y= dfrac{a}{x}+q ) are called hyperbolic functions.

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Image: Mplwp hyperbolic functions.svg

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Stack Exchange tag: math.stackexchange.com/tags/hyperbolic-functions
described at URL: www.siyavula.com/read/za/mathematics/grade-10/functions/06-functions-03
Commons category: Hyperbolic functions

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Article

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 are used to express the angle of parallelism in hyperbolic geometry. They are used to express Lorentz boosts as hyperbolic rotations in special relativity. 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, and fluid dynamics.