JavaScript | Math.atanh() function

The Math.atanh() function is an inbuit function in JavaScript which is used to get hyperbolic arctangent of a number.
The hyperbolic arctangent is known by many names such as hyperbolic inverse tangent and atanh.It is inverse of the hyperbolic tangent function i.e, The inverse hyperbolic tangent of any value say x is the value y for which the hyperbolic tangent of y is x.

if y = atanh(x)
then x = tanh(y)

we have,

 atanh(x) = \frac{1}{2} ln(\frac{1+x}{1-x})



Syntax:

Math.atanh(x)

Parameters:

  • Here x is a number whose hyperbolic arctangent is going to be calculated.
  • Return value:

  • It returns the hyperbolic arc-tangent of the given number.
  • Browser Support:

  • Here 2nd column contain int values which are the version of the corresponding browser.
    Feature Basic support
    Chrome 38
    Edge Yes
    Firefox 25
    Internet Explorer No
    Opera 25
    Safari 8
    Android webview Yes
    Chrome for Android Yes
    Edge mobile Yes
    Firefox for Android 25
    Opera Android Yes
    iOS Safari 8

Examples:

Input: Math.atanh(-1)
Output: -Infinity

Explaination:
Here output 0 is the hyperbolic arc-sine of a number 1.

Input: Math.atanh(0)
Output: 0
Input: Math.atanh(0.5)
Output: 0.5493061443340548
Input: Math.atanh(1)
Output: Infinity
Input: Math.atanh(1.2)
Output: NaN
Input: Math.atanh(-2.2)
Output: NaN

For values greater than 1 or less than -1, NaN i.e, not a number is returned.
Let’s see JavaScripts program:

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// Here different values is being used for
// getting hyperbolic tangent function's values.
console.log(Math.atanh(-1));
console.log(Math.atanh(0));
console.log(Math.atanh(0.5));
console.log(Math.atanh(1));
console.log(Math.atanh(1.2));
console.log(Math.atanh(-2.2));

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Output:

> 0
> 0.5493061443340548
> Infinity
> NaN
> NaN

Application:
Whenever we need to get a get hyperbolic arc-tangent of a number that time we can take help of Math.atanh() function in JavaScript.

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// Here different values is being used for getting
// hyperbolic cosine function's values.
console.log(Math.atanh(0.1));
console.log(Math.atanh(22));

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Output:

> 0.10033534773107558
> NaN


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