# hyperbolic function

- /haɪpəˌbɒlɪk ˈfʌŋkʃən/ (
*say*huypuh.bolik 'fungkshuhn)*noun*

one of the six mathematical functions which express angles in terms of distances between points on a hyperbola; analogous to the trigonometrical ratios, they are written*sinh, cosh, tanh, cosech, sech, cotanh*(or*coth)*. Sinh*x*is defined as ½*(e*and cosh^{x}- e^{-x})*x*as ½*(e*+^{x}*e*. The remaining four functions are derived from sinh and cosh on the same basis as that by which the trigonometrical ratios are derived from sin and cos.^{-x})

*Australian English dictionary.
2014.*

### Look at other dictionaries:

**hyperbolic function**— noun : any of a set of six functions analogous to the trigonometric functions but related to the hyperbola in a way similar to that in which trigonometric functions are related to a circle * * * Math. a function of an angle expressed as a… … Useful english dictionary**hyperbolic function**— hiperbolinė funkcija statusas T sritis fizika atitikmenys: angl. hyperbolic function vok. hyperbolische Funktion, f rus. гиперболическая функция, f pranc. fonction hyperbolique, f … Fizikos terminų žodynas**Hyperbolic function**— A ray through the origin intercepts the hyperbola in the point , where is twice the area between the ray and the … Wikipedia**hyperbolic function**— noun A function that is derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function. See Also: hyperbolic sine, hyperbolic cosine,… … Wiktionary**hyperbolic function**— Math. a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine: often expressed as combinations of exponential functions … Universalium**hyperbolic function**— hy′perbol′ic func′tion n. math. a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine • Etymology: 1885–90 … From formal English to slang**hyperbolic function**— noun Date: circa 1890 any of a set of six functions analogous to the trigonometric functions but related to the hyperbola in a way similar to that in which the trigonometric functions are related to a circle … New Collegiate Dictionary**inverse hyperbolic function**— noun The inverse of a hyperbolic function Syn: antihyperbolic function, arc hyperbolic function … Wiktionary**arc-hyperbolic function**— noun An inverse hyperbolic function … Wiktionary**Inverse hyperbolic function**— The inverses of the hyperbolic functions are the area hyperbolic functions. The names hint at the fact that they compute the area of a sector of the unit hyperbola x^{2} y^{2} = 1 in the same way that the inverse trigonometric functions compute… … Wikipedia