In mathematics, hyperbolic functions are analogs of the ordinary
trigonometric, or circular, functions. The basic hyperbolic
functions are the hyperbolic sine "sinh" (typically pronounced
/ˈsɪntʃ/ or /ˈʃaɪn/), and the hyperbolic cosine "cosh"
(typically pronounced /ˈkɒʃ/), from which are derived the
hyperbolic tangent "tanh" (typically pronounced /ˈtæntʃ/ or
/ˈθæn/), etc., in analogy to the derived trigonometric
functions. The inverse hyperbolic functions are the area
hyperbolic sine "arsinh" (also called "asinh", or sometimes by
the misnomer of "arcsinh") and so on. 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 equilateral hyperbola.
Hyperbolic functions occur in the solutions of some important
linear differential equations, for example the equation defining
a catenary, and Laplace's equation in Cartesian coordinates. The
latter is important in many areas of physics, including
electromagnetic theory, heat transfer, fluid dynamics, a