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[plot qr]plot:asyimport math;import graph;size(0,400);real f(real t) {return 2*cos(t);}pair F(real x) {return (x,f(x));}draw(polargraph(f,0,pi,operator ..));defaultpen(fontsize(20pt));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);[/plot]
- [plot asy]plot:asyimport math;import graph;size(0,400);real f(real t) {return 2*cos(t);}pair F(real x) {return (x,f(x));}draw(polargraph(f,0,pi,operator ..));defaultpen(fontsize(20pt));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);[/plot]
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