#include "library.h"

/*
   sin(x) =  x/1 - x^3/6 + x^5/120 - x^7/5040 .....

   factorial(0) = 1   
   factorial(N) = N * factorial(N-1),    where N > 0
*/
  
double factorial(const int N)
{ if (N == 0)
    return 1.0;       
  else
    return N * factorial(N-1); }

double sine(const double x)
{ const double t1 = x/1.0;
  const double t2 = t1 - x*x*x/6.0;
  const double t3 = t2 + pow(x, 5) / 120.0;
  const double t4 = t3 - pow(x, 7) / 5040.0;
  const double t5 = t4 + pow(x, 9) / factorial(9);
  const double t6 = t5 - pow(x, 11) / factorial(11);
  return t6; }
  
void plot(const double x, const double maxx)
{ const double y = sine(x);
  if (x == 0.0)
    move_to(x * 90, 300 - 300 * y);
  else
    draw_to(x * 90, 300 - 300 * y);
  if (x < maxx)
    plot(x+0.01, maxx); }
           
void plot2(const double x, const double maxx)
{ const double y = sin(x); 
  if (x == 0.0)
    move_to(x * 90, 300 - 300 * y);
  else     
    draw_to(x * 90, 300 - 300 * y);
  if (x < maxx)    
    plot2(x+0.01, maxx); }

void main()
{ make_window(600, 600);
  const double pi = acos(-1.0);
  plot(0.0, 2 * pi);
  plot2(0.0, 2 * pi); }