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In advanced analysis, the hyperbolic functions crop up as the imaginary parts of sine and cosine. When considered described by a posh variable, the hyperbolic capabilities are rational functions of exponentials, and are hence holomorphic.
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Hyperbolic functions take place from the solutions of many linear differential equations (one example is, the equation defining a catenary), of some cubic equations, in calculations of angles and distances in hyperbolic geometry, and of Laplace's equation in Cartesian review coordinates.
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