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

The hyperbolic sine function, denoted sinh(x), is defined as:

sinh(x) = (e^x - e^(-x)) / 2

where e is the base of the natural logarithm.

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

Here's an example usage of the sinh function to calculate the hyperbolic sine of a given input:

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

int main() {
    double x = 1.5;
    double hyperbolic_sine = sinh(x);
    
    printf("The hyperbolic sine of %f is %f\n", x, hyperbolic_sine);
    
    return 0;
}

In this example, the sinh function is used to calculate the hyperbolic sine of 1.5, which is stored in the x variable. The calculated hyperbolic sine is then stored in the hyperbolic_sine variable, and printed to the console using the printf function.

Note that the sinh function is only defined for real values of x. Also note that the hyperbolic sine function grows very quickly for large positive or negative values of x, so it is important to be aware of potential overflow issues when working with large values.