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, inverse hyperbolic secant, and inverse hyperbolic cotangent.

artanhx = 1 2 ln 1 + x 1 x ; Domain=( 1;1), Range=(1 ;+1) (25) Remember that the domain of the inverse is the range of the original function, and the range of the inverse is the domain of the original function. To retrieve these formulas we rewrite the de nition of the hyperbolic function as a degree two polynomial in ex; then we solve for ex ...

Feb 3, 2020 · The first, blue, curve is the tanh function. The grey dashed line is the line y = x. The second, red, curve is the artanh function. As with any inverse function, it is identical to the original function reflected in the line y = x. There is a also a formula for finding artanh directly: artanh x = 1 2 ln (1 + x 1 − x)

4 days ago · The principal value of is implemented in the Wolfram Language as ArcTanh [z] and in the GNU C library as atanh (double x). The inverse hyperbolic tangent is a multivalued function and hence requires a branch cut in the complex plane, which the Wolfram Language 's convention places at the line segments and . This follows from the definition of as

Arc-hyperbolic tangent function artanh or arth: definition, graph, properties and identities.

Sep 19, 2018 · Notation arctanh(x) arctanh (x) means area tangent which is inverse of hyperbolic tangent. arctanh(x) = tanh−1(x) arctanh (x) = tanh − 1 (x) Trying to invert the tanh(x) tanh (x) we get:

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…

Use this inverse hyperbolic tangent or arctanh tool to find the hyperbolic angle when you know the hyperbolic tangent.

from $u = artanhx$ I know that: $tanhu = x$ $\therefore tanh^2u = x^2$ $\therefore 1- sech^2u = x^2 $ $\therefore cosh^2u = \dfrac{1}{1-x^2}$ $\therefore coshu = \dfrac{1}{\sqrt{1-x^2}}$ From …