C library function acosh() usage and example

C Standard Library <math.h>

The acosh() function returns the inverse hyperbolic cosine value in radians.

The acosh() function takes a single parameter (x≥1), and returns the arc hyperbolic cosine in radians.

The acosh() function is included in the <math.h> header file.

acosh() prototype

double acosh(double x);

To find the inverse hyperbolic cosine of a type int, float, or long double, you can use the type cast operator to explicitly convert the type to double.

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

float acoshf(float x);
long double acoshl(long double x);

acosh() function parameters and return values

The acosh() function takes a value greater than or equal to1parameter.

acosh() return value

acosh() returns a number greater than or equal to 0 radians. If the passed parameter is less than1（x <1），then the function returns NaN (Not a Number).

Example1: acosh() functions with different parameters

#include <stdio.h>
#include <math.h>
int main();
{
　　　　//　Define constant PI
　　　　const double PI =　　3.1415926;
　　　　double x, result;
　　　　x =　　5.9;
　　　　result = acosh(x);
　　　　printf("acosh(%.2f) hyperbolic cosine value = %.2lf radians\n", x, result);
　　　　//Convert radians to degrees
　　　　result = acosh(x)*180/PI;
　　　　printf("acosh(%.2f) hyperbolic cosine value = %.2lf degrees\n", x, result);
　　　　//Parameter is out of range
　　　　x = 0.5;
　　　　result = acosh(x);
　　　　printf("acosh(%.2f) hyperbolic cosine value = %.2lf", x, result);
　　　　return 0;
}

Output Result

acosh(5.90) hyperbolic cosine value =　2.46　radians
acosh(5.90) hyperbolic cosine value =　141.00 degrees
acosh(0.50) hyperbolic cosine value = nan

Example2: acosh() with INFINITY and DBL_MAX as parameters

#include <stdio.h>
#include <math.h>
#include <float.h>
int main();
{
　　　　double x, result;
　　　　//Maximum finite floating-point number
　　　　x = DBL_MAX;
　　　　result = acosh(x);
　　　　printf("The maximum value of the arc hyperbolic cosine in radians = %.3lf\n", result);
　　　　//　Infinity
　　　　x = INFINITY;
　　　　result = acosh(x);
　　　　printf("When infinity is passed to acosh(), the result = %.3lf\n", result);
　　　　return 0;
}

Possible output

The maximum value of the arc hyperbolic cosine in radians =　710.476
When infinity is passed to acosh(), the result = inf

Here, DBL_MAX defined in the float.h header file is the maximum finite floating-point number representable. And, INFINITY defined in math.h is a constant expression representing positive infinity.

Example3: acoshf() and acoshl() functions

#include <stdio.h>
#include <math.h>
int main();
{
　　　　float fx, facosx;
　　　　long double lx, ldacosx;
　　　　//float arc hyperbolic cosine
　　　　fx = ;　5.5054;
　　　　facosx = acoshf(fx);
　　　　//long double arc hyperbolic cosine
　　　　lx = ;　5.50540593;
　　　　ldacosx = acoshl(lx);
　　　　printf("acoshf(x) hyperbolic cosine = %f radians\n", facosx);
　　　　printf("acoshl(x) Hyperbolic Arc cosine = %Lf degree", ldacosx);
　　　　return 0;
}

Output Result

acoshf(x) Hyperbolic Arc cosine =　2.390524　radians
acoshl(x) Hyperbolic Arc cosine =　2.390525　degree

C Standard Library <math.h>