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import math;
import graph;
size(0,100);
real f(real t) {return 2*cos(t);}
pair F(real x) {return (x,f(x));}
draw(polargraph(f,0,pi,operator ..));
defaultpen(fontsize(10));
xaxis("$x$");
yaxis("$y$");
real theta=radians(50);
real r=f(theta);
draw("$\theta$",arc((0,0),0.5,0,degrees(theta)),red,Arrow,PenMargins);
pair z=polar(r,theta);
draw(z--(z.x,0),dotted+red);
draw((0,0)--(z.x,0),dotted+red);
label("$r\cos\theta$",(0.5*z.x,0),0.5*S,red);
label("$r\sin\theta$",(z.x,0.5*z.y),0.5*E,red);
dot("$(x,y)$",z,N);
draw("r",(0,0)--z,0.5*unit(z)*I,blue,Arrow,DotMargin);
dot("$(a,0)$",(1,0),NE);
dot("$(2a,0)$",(2,0),NE);
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