C in a Nutshell

Name

sinh

Synopsis

Calculates the hyperbolic sine of a number

#include <math.h>
doublesinh( double x );
float sinhf( float x );        (C99)
long double sinhl( long double x );        (C99)

The sinh() function returns the hyperbolic sine of its argument x. If the result of sinh() is too great for the double type, a range error occurs.

Example

// A chain hanging from two points forms a curve called a catenary.
// A catenary is an segment of the graph of the function
// cosh(k*x)/k, for some constant k.
// The length along the catenary over a certain span, bounded by the
// two vertical lines at x=a and x=b, is equal to sinh(k*b)/k − sinh(k*a)/k.

double x, k;
puts("Catenary f(x) = cosh(k*x)/k\n"
     "Length along the catenary from a to b: sinh(k*b)/k − sinh(k*a)/k)\n");

puts("           f(-1.0)   f(0.0)   f(1.0)   f(2.0)   Length(-1.0 to 2.0)\n"

     "-------------------------------------------------------------------");
for ( k = 0.5; k < 5; k *= 2)
{
  printf("k = %.1f: ", k);
  for (  x = -1.0; x < 2.1; x += 1.0)
    printf("%8.2f ", cosh(k*x)/k );

  printf("  %12.2f\n", (sinh(2*k) − sinh(−1*k))/ k);
}

This code produces the following output:

Catenary f(x) = cosh(k*x)/k
Length along the catenary from a to b:  sinh(k*b)/k − sinh(k*a)/k)

           f(-1.0)   f(0.0)   f(1.0)   f(2.0)    Length(-1.0 to 2.0)
---------------------------------------------------------------------
k = 0.5:     2.26     2.00     2.26     3.09           3.39
k = 1.0:     1.54     1.00     1.54     3.76           4.80
k = 2.0:     1.88     0.50     1.88    13.65          15.46
k = 4.0:     6.83     0.25     6.83   372.62         379.44

See Also

cosh(), tanh(), asinh(), csinh(), casinh() ...