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 (e^x + 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.

See Also

The C99 inverse hyperbolic cosine function acosh( ); the hyperbolic cosine and inverse hyperbolic cosine functions for complex numbers: ccosh( ), cacosh( ); the example for sinh( )