In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. PHP provides us with builtin functions for inverse hyperbolic calculations. The atanh() function in PHP is used to find the inverse hyperbolic tangent of a number passed to it as an argument.

Syntax:

float atanh($value)

Parameters: This function accepts a single parameter $value. It is the number whose inverse hyperbolic tangent value you want to find. The value of this parameter must be in radians.

Return Value: It returns a floating point number which is the inverse hyperbolic tangent value of a number passed to it as argument.

Examples:

Input : atanh(0.50)  
Output : 0.54930614433405

Input : atanh(-0.50) 
Output : -0.54930614433405

Input : atanh(1)
Output : INF

Input : atanh(M_PI_4) 
Output : 1.0593061708232

Below programs, taking different values of the parameter $value are used to illustrate the atanh() function in PHP:

• Passing 0.50 as a parameter:
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  <?php    echo (atanh(0.50));    ?>

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  Output:

  0.54930614433405

• Passing -0.50 as a parameter:
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  <?php    echo (atanh(-0.50));    ?>

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  Output:

  -0.54930614433405

• Passing 1 as a parameter:
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  <?php    echo (atanh(1));    ?>

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  Output:

  INF

• When (M_PI_4) is passed as a parameter, M_PI_4 is a constant in PHP and it’s value is 0.78539816339744830962:
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  <?php    echo (atanh(M_PI_4));    ?>

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  Output:

  1.0593061708232

Reference:
http://php.net/manual/en/function.atanh.php