![]() hyperbolic cosecant " csch" or " cosech" ( / ˈ k oʊ s ɛ tʃ, ˈ k oʊ ʃ ɛ k/ ).hyperbolic tangent " tanh" ( / ˈ t æ ŋ, ˈ t æ n tʃ, ˈ θ æ n/),. ![]() hyperbolic cosine " cosh" ( / ˈ k ɒ ʃ, ˈ k oʊ ʃ/),.hyperbolic sine " sinh" ( / ˈ s ɪ ŋ, ˈ s ɪ n tʃ, ˈ ʃ aɪ n/),.Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and 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. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. 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. 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. In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle.
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