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Inverse Hyperbolic Tangent Calculator arctanh(x)

Written by:
PK

On this page is an inverse hyperbolic tangent calculator (or atanh calculator), which calculates an angle from the result of the hyperbolic tangent function.

Inverse Hyperbolic Tangent Calculator

Using the Inverse Hyperbolic Tangent Calculator

To use the tool to find the angle from a hyperbolic tangent, enter the ratio and compute.

  • Hyperbolic tangent - computed result

Once you're happy with the inputs, click the "Compute Hyperbolic Angle" button.

  • Angle - the angle you'd input if you wanted to get the hyperbolic tangent you entered

What is the atanh or inverse hyperbolic tangent?

Inverse hyperbolic tangent is the inverse of the hyperbolic tangent, which is the hyperbolic sine over the hyperbolic cosine. It can also be written using the natural logarithm:

arctanh(x)=\frac{\ln(\frac{1+x}{1-x})}{2}
Inverse hyperbolic sine, cosine, tangent, cotangent, secant, and cosecant on a graph
Inverse hyperbolic sine, cosine, tangent, cotangent, secant, and cosecant (Wikimedia)

Arctanh as a formula

Inverse hyperbolic tangent is often written as arctanh, but usually abbreviated as "atanh" or "artanh", as in the following equation:

arctanh(y) = atanh(y) = artanh(y)

Where it is the inverse of hyperbolic tangent, or:

x=arctanh(y)\\y=tanh(x)

Next, see all inverse hyperbolic functions or hyperbolic functions in just two tools.

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