/* -*-ePiX-*- */
/* cosine.xp -- April 02. 2003 */
#include "epix.h"
using namespace ePiX;

double cos2(double t) { return 1-(1.0/2.0)*t*t; }
double cos4(double t) { return 1-(1.0/2.0)*t*t+(1.0/24.0)*pow(t,4); }

const double r1 = sqrt(2);
const double r2 = sqrt(6-sqrt(12));

main()
{
  unitlength("1pt");
  bounding_box(P(0,-0.25), P(2,1));
  picture(320,200);

  begin();
  crop();
  h_axis(x_size);
  v_axis(P(0, 0), P(0, y_max), y_max);

  // function graphs and labels
  green(0.5);
  pen(1);
  plot(Cos, x_min, x_max, 60);
  masklabel(P(1, 0.25), "$y=\\cos x$");

  plain();
  rgb(0.5, 0.5, 0.9);
  plot(cos2, x_min, x_max, 60);
  label(P(1, cos2(1)), P(0,0), "$\\displaystyle y = 1-\\frac{1}{2!}x^2$", bl);

  rgb(0.3, 0, 0.7);
  plot(cos4, x_min, x_max, 60);
  label(P(1, cos4(1)), P(0,0),
        "$\\displaystyle y = 1-\\frac{1}{2!}x^2+\\frac{1}{4!}x^4$", tr);

  black();
  // axis point labels
  arrow(P(M_PI_2, -0.15), P(M_PI_2, -0.025));
  masklabel(P(M_PI_2, -0.15), P(0, -2), "$\\displaystyle\\frac{\\pi}{2}$", b);

  arrow(P(r1, -0.15), P(r1, -0.025));
  label(P(r1, -0.15), P(0, -2), "$\\sqrt{2}$", b);

  arrow(P(r2, 0.15), P(r2, 0.025));
  label(P(r2, 0.15), P(0, 2), "$\\sqrt{6-\\sqrt{12}}$", t);

  h_axis_labels(x_size, P(0,-4), b);
  
  // diagram label
  label(P(x_max, y_max), P(0,0), 
	"Degree 2 and 4 Taylor polynomials of cosine", bl);

  end();
}