# asympt01

Jan 26th, 2015
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1. \begin{asy}
2. // file fod.asy
3. //
4. // to get fod.pdf, run `asy -f pdf fod.asy`
5. //
6. size(8cm);
7. import graph;
8. import fontsize;
9. defaultpen(fontsize(9pt));
10.
11. texpreamble("\usepackage{lmodern}");
12.
13. pen curvepen=darkblue+0.8bp;
14. pen linepen=darkred+0.8bp;
15. pen fillpen=orange+opacity(0.5);
16.
17. real
18. xmin=-20, xmax=-xmin,
19. ymin=-20, ymax=-ymin;
20.
21. xaxis(xmin,xmax,RightTicks(Step=10,step=5,OmitTick(0)));
22. yaxis(ymin,ymax, LeftTicks(Step=10,step=5,OmitTick(0)));
23.
24. real a=10;
25.
26. real r(real t){return 3*a*sin(t)*cos(t)/(sin(t)^3+cos(t)^3);};
27.
28. real tmin=-0.16pi, tmax=pi/2-tmin;
29.
30. guide
31. loop=polargraph(r,0,pi/2)--cycle,
32. curve=polargraph(r,tmin,tmax);
33.
34. fill(loop, fillpen);
35. draw(curve,curvepen);
36.
37. pair
38. p=point(curve,0),
39. q=point(curve,length(curve));
40.
41. draw((p.x,-p.x-a)--(-q.y-a,q.y),linepen);
42. \end{asy}