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How do you use the cosh(x) function?

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The cosh(x) function is the mathematical hyperbolic cosine function, and it is used to describe the shape of a hanging cable and may sometimes appear as ch(x). The hyperbolic cosine function is a part of the hyperbolic function family which is based on standard trigonometric functions. The cosh(x) function, when combined with the sinh(t) function, describes the right half of a hyperbola.

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Cosh(x) and its related hyperbolic functions appear in the solutions to various linear differential equations. Often, these functions are used to measure things such as Laplace's equation. This equation has common applications in numerous fields within physics, including theories such as special relativity, heat transfer and fluid dynamics.

In certain types of complex analysis, the hyperbolic function serves as the imaginary counterparts of the basic trigonometric functions. They are further defined as meromorphic and serve as a rational function for exponentials, but this only occurs when they are considered in the context of a complex variable.

The cosh(x) function and other hyperbolic functions were independently introduced during the 1760s by two mathematicians from Italy and Switzerland. The Italian mathematician, Vincenzo Ricca, introduced the functions using the ch(x) and sh(x) terms, while the Swiss mathematician Johann Heinrich Lambert created the terms that are now used throughout the mathematical world.

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