Ad
related to: hyperbolic trig identities formula
Search results
Results from the WOW.Com Content Network
The hyperbolic functions represent an expansion of trigonometry beyond the circular functions. Both types depend on an argument , either circular angle or hyperbolic angle . Since the area of a circular sector with radius r and angle u (in radians) is r 2 u /2 , it will be equal to u when r = √ 2 .
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.
The argument to the hyperbolic functions is a hyperbolic angle measure. In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant ...
Plot of the hyperbolic sine integral function Shi(z) ... trigonometric integrals are a family of nonelementary integrals involving trigonometric functions.
Since cosh x + sinh x = e x, an analog to de Moivre's formula also applies to the hyperbolic trigonometry. For all integers n, ( + ) = + . If n is a rational number (but not necessarily an integer), then cosh nx + sinh nx will be one of the values of (cosh x + sinh x) n. [4]
The spherical triangle identities are written in terms of the ordinary trigonometric functions but differ from the plane triangle identities. Hyperbolic trigonometry: Study of hyperbolic triangles in hyperbolic geometry with hyperbolic functions. Hyperbolic functions in Euclidean geometry: The unit circle is parameterized by (cos t, sin t ...
In mathematics, hyperbolic trigonometry can mean: The study of hyperbolic triangles in hyperbolic geometry (traditional trigonometry is the study of triangles in plane geometry) The use of the hyperbolic functions; The use of gyrotrigonometry in hyperbolic geometry
Ad
related to: hyperbolic trig identities formula