Hyperbolic function
In mathematics,
hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the
hyperbolic sine "sinh", and the
hyperbolic cosine "cosh" /ˈkɒʃ/, from which are derived the
hyperbolic tangent "tanh",
hyperbolic cosecant "csch" or "cosech" /ˈkoʊʃɛk/ or /ˈkoʊsɛtʃ/,
hyperbolic secant "sech" /ˈʃɛk/ or /ˈsɛtʃ/, and
hyperbolic cotangent "coth" /ˈkoʊθ/ or /ˈkɒθ/, corresponding to the derived trigonometric functions. The inverse hyperbolic functions are the
area hyperbolic sine "arsinh" and so on. Just as the points form a circle with a unit radius, the points form the right half of the equilateral hyperbola. The hyperbolic functions take a real argument called a hyperbolic angle. The size of a hyperbolic angle is the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.