E32 Answer

bad cos( 0.050000 ) = 0.975000
bad sin( 0.050000 ) = 0.050000

good cos( 0.050000 ) = 0.998750
good sin( 0.050000 ) = 0.049979

Comments: Declaring a function static enables you to use a name that might otherwise conflict with the name of a function in another file.

In this case, the static functions are the ones that main() uses, and the external ones from the math library are the ones that goodMath uses.

* --- goodMath.c --- */
#include  <math.h>

void goodMath( double angle )
{
  printf("good cos( %lf ) = %lf\n", angle, cos(angle) );
  printf("good sin( %lf ) = %lf\n", angle, sin(angle) );
}


/* --- main.c --- */

static double sin( double x )
{
  return x;
}

static double cos( double x )
{
  return 1 - x/2.0;
}

void badMath( double angle )
{
  printf("bad cos( %lf ) = %lf\n",    angle, cos(angle) );
  printf("bad sin( %lf ) = %lf\n\n",  angle, sin(angle) );
}

main()
{
  double angle = .05  ;   /*  radians */

  badMath ( angle );
  goodMath( angle );
  system("pause");
}