1import math;
2import graph;
3
4size(0,150);
5
6real f(real t) {return 5+cos(10*t);}
7
8xaxis("$x$");
9yaxis("$y$");
10
11real theta1=pi/8;
12real theta2=pi/3;
13path k=graph(f,theta1,theta2,operator ..);
14real rmin=min(k).y;
15real rmax=max(k).y;
16draw((0,0)--rmax*expi(theta1),dotted);
17draw((0,0)--rmax*expi(theta2),dotted);
18
19path g=polargraph(f,theta1,theta2,operator ..);
20path h=(0,0)--g--cycle;
21fill(h,lightgray);
22draw(h);
23
24real thetamin=3*pi/10;
25real thetamax=2*pi/10;
26pair zmin=polar(f(thetamin),thetamin);
27pair zmax=polar(f(thetamax),thetamax);
28draw((0,0)--zmin,dotted+red);
29draw((0,0)--zmax,dotted+blue);
30
31draw("$\theta_*$",arc((0,0),0.5*rmin,0,degrees(thetamin)),red+fontsize(10pt),
32     PenMargins);
33draw("$\theta^*$",arc((0,0),0.5*rmax,0,degrees(thetamax)),blue+fontsize(10pt),
34     PenMargins);
35
36draw(arc((0,0),rmin,degrees(theta1),degrees(theta2)),red,PenMargins);
37draw(arc((0,0),rmax,degrees(theta1),degrees(theta2)),blue,PenMargins);
38
39