# Library Function atanh in Math Class

## Library Function atanh of math.h Header File in C

On this page we will discuss about library function atanh in math class which is used in C.
The C header file math.h contains the standard math library functions that can be used for performing various mathematical operations. The acosh function returns the arc hyperbolic tangent of x in radians.

## Library Function atanh in Math Class used in C

In C programming language the atanh function is included in math.h header file. The acosh function takes input argument in the range of $-1\leq x\leq 1$ and returns the inverse hyperbolic tangent of parameter x in radians.

### Declaration of atanh function

double atanh(double x)


We can find the inverse hyperbolic tangent of different data types like int, float or long double by using the cast operator which explicitly converts the data type to double as given below:

int x = 0;
double result;
result = atanh(double(x));

In C, two new functions atanhf() and atanhl() were added to work with data types float and long double respectively.
float atanhf(float x);
long double atanhl(long double x);


### Parameters of atanh function

The atanh function accepts a single input value which is greater than or equal to -1 and less than or equal to 1.

ParameterDescription
double valueThis value of double function is greater than or equal to 1($-1\leq x\leq 1$).

### Return value of atanh function

The atanh function returns inverse hyperbolic tangent when an input parameter is passed to it. The function returns NaN if the parameter passed is less than -1 or greater than 1.

ParameterReturn Value
x=1It returns infinite value($\infty$).
x=-1It returns a negative infinite value($-\infty$).
x>1 or x<-1NaN (not a number)
-1 < x < 1It returns a finite value.

### Implementation of Library Function math.h atanh

The following code shows the use of atanh function with different parameters passed to the function.

Run
#include <stdio.h>
#include <math.h>

int main()
{
// constant PI is defined
const double PI =  3.1415926;

// Declaring temporary variables
double y, return_value;

// Assigning values to variable
y =  -0.8;

// Calculating arc hyperbolic tangent of parameter y
return_value = atanh(y);

// Displaying the result of calculation
printf("The value of atanh(%.2f) function = %.2lf in radians\n", y, return_value);

return_value = atanh(y)*180/PI;

// Displaying the result of calculation
printf("The value of atanh(%.2f) function = %.2lf  in degrees\n", y, return_value);

// parameter not in range
y = 5;

// Calculating arc hyperbolic tangent of parameter y
return_value = atanh(y);

// Displaying the result of calculation
printf("The value of atanh(%.2f) function = %.2lf", y, return_value);

return 0;
}


#### Output:

The value of atanh(-0.80) function = -1.10 in radians
The value of atanh(-0.80) function = -62.95  in degrees
The value of atanh(5.00) function = -nan


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