The acos function is a standard math function in C, defined in the math.h header file. It is used to calculate the arccosine of a given value x.

The arccosine function, denoted acos(x), is the inverse of the cosine function. It is defined as:

acos(x) = cos⁻¹(x)

where cos⁻¹ denotes the inverse cosine function.

The acos function takes a single argument of type double, which represents the value whose arccosine is to be calculated. The function returns a double value, which represents the calculated arccosine.

Here's an example usage of the acos function to calculate the arccosine of a given input:

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

int main() {
    double x = 0.5;
    double arccosine = acos(x);
    
    printf("The arccosine of %f is %f\n", x, arccosine);
    
    return 0;
}

In this example, the acos function is used to calculate the arccosine of 0.5, which is stored in the x variable. The calculated arccosine is then stored in the arccosine variable, and printed to the console using the printf function.

Note that the acos function is only defined for values of x between -1 and 1 inclusive. If the input value is outside this range, the function will return a domain error.