cosh

cosh

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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( )