cosh

Calculates the hyperbolic cosine of a number

```#include <math.h>
double cosh ( double x  );
float coshf ( float x  );         (C99)
long double coshl ( long double x  );         (C99)
```

The hyperbolic cosine of any number x equals (ex + e-x)/2 and is always greater than or equal to 1. If the result of cosh( ) is too great for the double type, the function incurs a range error.

#### Example

```double x, sum = 1.0;
unsigned max_n;
printf("Cosh(x) is the sum as n goes from 0 to infinity "
"of x^(2*n) / (2*n)!\n");
// That's x raised to the power of 2*n, divided by 2*n factorial.
printf("Enter x and a maximum for n (separated by a space): ");
if (scanf(" %lf %u", &x, &max_n) < 2)
{
printf("Couldn't read two numbers.\n");
return -1;
}
printf("cosh(%.2f) = %.4f;\n", x, cosh(x));
for ( unsigned n = 1 ; n <= max_n ; n++ )
{
unsigned factor = 2 * n;         // Calculate (2*n)!
unsigned divisor = factor;
while ( factor > 1 )
{
factor--;
divisor *= factor;
}
sum += pow(x, 2 * n) / divisor;   // Accumulate the series
}
printf("Approximation by series of %u terms = %.4f.\n", max_n+1, sum);
```

With the numbers 1.72 and 3 as input, the program produces the following output:

```cosh(1.72) = 2.8818;
Approximation by series of 4 terms = 2.8798.
```