Search results
Results from the WOW.Com Content Network
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 unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and +sinh(t) respectively.
Graphs of the inverse hyperbolic functions The hyperbolic functions sinh, cosh, and tanh with respect to a unit hyperbola are analogous to circular functions sin, cos, tan with respect to a unit circle. The argument to the hyperbolic functions is a hyperbolic angle measure.
العربية; Bosanski; Català; Чӑвашла; Čeština; Español; Euskara; فارسی; Français; Galego; 한국어; Հայերեն; Hrvatski; Bahasa Indonesia ...
Tanh-sinh quadrature is a method for numerical integration introduced by Hidetoshi Takahashi and Masatake Mori in 1974. [1] It is especially applied where singularities or infinite derivatives exist at one or both endpoints.
This formula can be derived from a power series expansion using the fact that cosh has only even powers while that for sinh has odd powers. [2] For all real values of the hyperbolic angle θ the split-complex number λ = exp(jθ) has norm 1 and lies on the right branch of the unit hyperbola. Numbers such as λ have been called hyperbolic versors.
Right triangles with legs proportional to sinh and cosh. The hyperbolic functions sinh, cosh, and tanh can be illustrated with hyperbolic coordinates. Let
The Poincaré half-plane model is closely related to a model of the hyperbolic plane in the quadrant Q = {(x,y): x > 0, y > 0}. For such a point the geometric mean = and the hyperbolic angle = / produce a point (u,v) in the upper half-plane.
The curve represents xy = 1. A hyperbolic angle has magnitude equal to the area of the corresponding hyperbolic sector, which is in standard position if a = 1. In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane.