beginfig(1); numeric u ; u=4.5cm; drawarrow (-1.2*u,0)--(1.2*u,0); drawarrow (0,-1.2*u)--(0,1.2*u); draw fullcircle scaled 9cm ; drawoptions(dashed evenly); path t[] ; t[1]=(u,0)--(cosd(60)*u,sind(60)*u)--(0,0); draw t[1]; for k=2 upto 6 : t[k]=t[1] rotatedaround ((0,0),60*(k-1)); draw t[k]; endfor; path c[] ; c1 =(cosd(60)*u,-sind(60)*u)--(cosd(60)*u,sind(60)*u) ; draw c1 dashed evenly; c2 = c1 shifted (-u,0) ; draw c2 dashed evenly; z[1]=(u,0); for l=2 upto 6: z[l]=z[1] rotatedaround ((0,0),60(l-1)); endfor; drawoptions(); dotlabel.lrt(btex $0$ etex,(u,0)); label.lrt(btex $1 \over2$ etex,(u/2,0)); label.lrt(btex $- {1 \over 2}$ etex,(-u/2,0)); dotlabel.llft(btex $\pi$ etex,(-u,0)); dotlabel.urt(btex ${\pi \over 3}$ etex, z[2]); dotlabel.ulft(btex ${2\pi \over 3}$ etex,z[3]); dotlabel.llft(btex $-{2\pi \over 3}$ etex,z[5]); dotlabel.lrt(btex $-{\pi \over 3}$ etex,z[6]); label.llft(btex ${\sqrt{3} \over 2}$ etex,(0,sqrt(3)*u/2)); label.ulft(btex $-{\sqrt{3} \over 2}$ etex,(0,-sqrt(3)*u/2)); drawoptions(dashed evenly); path p[] ; p[1]=(0,u)--(cosd(30)*u,sind(30)*u)--(0,0); draw p[1]; for k=2 upto 6 : p[k]=p[1] rotatedaround ((0,0),60*(k-1)); draw p[k]; endfor; path s[] ; s1 =(-cosd(30)*u,sind(30)*u)--(cosd(30)*u,sind(30)*u) ; draw s1 dashed evenly; s2 = s1 shifted (0,-u) ; draw s2 dashed evenly; pair y[]; y[1]=(cosd(30)*u,sind(30)*u); for l=2 upto 6: y[l]=y[1] rotatedaround ((0,0),60(l-1)); endfor; drawoptions(); dotlabel.urt(btex ${\pi \over 6}$ etex,y[1]); dotlabel.urt(btex ${\pi \over 2}$ etex, y[2]); dotlabel.ulft(btex ${5\pi \over 6}$ etex,y[3]); dotlabel.llft(btex $-{5\pi \over 6}$ etex,y[4]); dotlabel.llft(btex $-{\pi \over 2}$ etex,y[5]); dotlabel.lrt(btex $-{\pi \over 6}$ etex,y[6]); label.llft(btex ${\sqrt{3} \over 2}$ etex,(sqrt(3)*u/2,0)); label.lrt(btex $-{\sqrt{3} \over 2}$ etex,(-sqrt(3)*u/2,0)); label.llft(btex ${1 \over 2}$ etex,(0,u/2)); label.llft(btex $-{1 \over 2}$ etex,(0,-u/2)); drawoptions(dashed evenly); path r[] ; r[1]=(cosd(45)*u,-sind(45)*u)--(cosd(45)*u,sind(45)*u)--(0,0); draw r[1]; for k=2 upto 4 : r[k]=r[1] rotatedaround ((0,0),90*(k-1)); draw r[k]; endfor; pair w[]; w[1]=(u,0); for n=2 upto 8: w[n]=w[1] rotatedaround ((0,0),45(n-1)); endfor; drawoptions(); dotlabel.urt(btex ${\pi \over 4}$ etex, w[2]); dotlabel.urt(btex ${\pi \over 2}$ etex,w[3]); dotlabel.ulft(btex ${3\pi \over 4}$ etex,w[4]); dotlabel.llft(btex ${\pi}$ etex,w[5]); dotlabel.llft(btex $-{3\pi \over 4}$ etex,w[6]); dotlabel.llft(btex $-{\pi \over 2}$ etex,w[7]); dotlabel.lrt(btex $-{\pi \over 4}$ etex,w[8]); label.ulft(btex ${\sqrt{2} \over 2}$ etex,(sqrt(2)*u/2,0)); label.urt(btex $-{\sqrt{2} \over 2}$ etex,(-sqrt(2)*u/2,0)); label.lrt(btex ${\sqrt{2} \over 2}$ etex,(0,sqrt(2)*u/2)); label.urt(btex $-{\sqrt{2} \over 2}$ etex,(0,-sqrt(2)*u/2)); endfig; end