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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.
For each inverse hyperbolic integration formula below there is a corresponding formula in the list of integrals of inverse trigonometric functions. The ISO 80000-2 standard uses the prefix "ar-" rather than "arc-" for the inverse hyperbolic functions; we do that here.
The hyperbolic sine and the hyperbolic cosine are entire functions. As a result, the other hyperbolic functions are meromorphic in the whole complex plane. By Lindemann–Weierstrass theorem , the hyperbolic functions have a transcendental value for every non-zero algebraic value of the argument.
There are three common notations for inverse trigonometric functions. The arcsine function, for instance, could be written as sin −1, asin, or, as is used on this page, arcsin. For each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions.
Trigonometric functions of inverse trigonometric functions are tabulated below. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1 and another side of length x , {\displaystyle x,} then applying the Pythagorean theorem and definitions of the trigonometric ratios.
The Gudermannian and its inverse were used to make trigonometric tables of circular functions also function as tables of hyperbolic functions. Given a hyperbolic angle , hyperbolic functions could be found by first looking up = in a Gudermannian table and then looking up the appropriate circular function of , or by directly locating in an ...
where is the inverse hyperbolic sine function. If one desires to use the initial condition () ... is the hyperbolic tangent function, is the carrying ...
Pages in category "Inverse hyperbolic functions" The following 27 pages are in this category, out of 27 total. ... Inverse hyperbolic sine; Inverse hyperbolic tangent