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.

5 days ago · The inverse hyperbolic tangent tanh^(-1)z (Zwillinger 1995, p. 481; Beyer 1987, p. 181), sometimes called the area hyperbolic tangent (Harris and Stocker 1998, p. 267), is the multivalued function that is the inverse function of the hyperbolic tangent.

Hyperbolic tangent of angle, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. The atanh operation is element-wise when X is nonscalar. For real values x in the domain − 1 <x <1, the inverse hyperbolic tangent satisfies. tanh − 1 (x) = 1 2 log (1 + x 1 − x).

Inverse tangent calculator.Enter the tangent value, select degrees (°) or radians (rad) and press the = button.

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ArcTanh[ z ] (3911 formulas) Visualizations (225 graphics, 1 animation) Plotting : Evaluation

The calculator will find the inverse hyperbolic tangent of the given value. The inverse hyperbolic tangent y=tanh^{-1}(x) or y=atanh(x) or y=arctanh(x) is such

ArcTanh [z] gives the inverse hyperbolic tangent tanh -1 (z) of the complex number z.

arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2] . For real-valued input data types, arctanh always returns real output.

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