Definition of Hyperbolic Functions

Hyperbolic functions are commonly used to study fluid dynamics and electromagnetic theory, where integrals having a term occur. They can be used to simplify integration of a function, because hyperbolic functions are analogous to circular (standard) trigonometric functions, and are written as the circular function with an "h" added: sinh, cosh, and so on. The points for all z inscribe an equilateral hyperbola, where their circular counterparts inscribe a circle. Hyperbolic functions are found by removing the complex portion i of their circular counterparts. For example, is equal to the hyperbolic sine of z, . The six hyperbolic functions are:

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