Fichier f009.mp (figure 30) — Modifié le 12 Avril 2008 à 11 h 26

Source

input newcourbes;
input couleur;
input geometriesyr16;
input TEX;

verbatimtex
%&latex
\documentclass{article}
\usepackage[upright]{fourier}
\usepackage{color}
\def\E{\mathrm{e}}
\let\ve\vec
\def\DR{\mathcal{D}}
\def\CR{\mathcal{C}}
\def\HR{\mathcal{H}}
\newcommand{\Mathbold}[1]{\mbox{\boldmath$#1$\unboldmath}}
\definecolor{orange}{rgb}{1,0.8,0.2}
\newcommand{\ofr}[2]{%
\raisebox{0ex}{$#1$}\negthinspace\slash
\raisebox{-.5ex}{$#2$}}
\newcommand{\pa}[1]{\left({#1}\right)}
\newcommand{\cro}[1]{\left[{#1}\right]}
\newcommand{\ab}[1]{\left|{#1}\right|}
\newcommand{\ac}[1]{\left\{{#1}\right\}}
\def\bbr{\mathbb{R}}%
\newcommand{\fr}{\displaystyle\frac}
\begin{document}
etex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
% T R I G O  N O M É T R I E
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

beginfig(22)

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 withpen pencircle scaled 1.3bp withcolor red;
drawoptions(dashed evenly);
path t[] ;
t[1]=(u,0)--(cosd(60)*u,sind(60)*u)--(0,0);
draw t[1] withcolor rose;
for k=2 upto 6 : t[k]=t[1] rotatedaround ((0,0),60*(k-1));
draw t[k] withcolor rose;
endfor;
path c[] ;
c1 =(cosd(60)*u,-sind(60)*u)--(cosd(60)*u,sind(60)*u) ;
draw c1 dashed evenly withcolor rose;
c2 = c1 shifted (-u,0) ;
draw c2 dashed evenly withcolor rose;
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))withcolor rose;
label.lrt(btex $- {1 \over 2}$ etex,(-u/2,0))withcolor rose;
dotlabel.llft(btex $\pi$ etex,(-u,0));

label.urt(btex {${\pi \over 3}$} etex, z[2])withcolor rose;
label.ulft(btex {${2\pi \over 3}$} etex,z[3])withcolor rose;
label.llft(btex {$-{2\pi \over 3}$} etex,z[5])withcolor rose;
label.lrt(btex {$-{\pi \over 3}$} etex,z[6])withcolor rose;
label.llft(btex ${\sqrt{3} \over 2}$ etex,(0,sqrt(3)*u/2))withcolor rose;
label.ulft(btex $-{\sqrt{3} \over 2}$ etex,(0,-sqrt(3)*u/2))withcolor rose;

%  drawoptions(dashed evenly);
%  path p[] ;
%  p[1]=(0,u)--(cosd(30)*u,sind(30)*u)--(0,0);
%  draw p[1] withcolor  orange;
%  for k=2 upto 6 : p[k]=p[1] rotatedaround ((0,0),60*(k-1));
%    draw p[k] withcolor orange;
%  endfor;
%  path s[] ;
%  s1 =(-cosd(30)*u,sind(30)*u)--(cosd(30)*u,sind(30)*u) ;
%  draw s1 dashed evenly withcolor  orange;
%  s2 = s1 shifted (0,-u) ;
%  draw s2 dashed evenly withcolor orange;

%  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();
%  label.urt(btex ${\pi \over 6}$ etex,y[1])withcolor orange;
%  dotlabel.urt(btex ${\pi \over 2}$ etex, y[2]);
%  label.ulft(btex ${5\pi \over 6}$ etex,y[3])withcolor orange;
%  label.llft(btex $-{5\pi \over 6}$ etex,y[4])withcolor orange;
%  label.llft(btex $-{\pi \over 2}$ etex,y[5])withcolor orange;
%  label.lrt(btex $-{\pi \over 6}$ etex,y[6])withcolor orange;
%  label.llft(btex ${\sqrt{3} \over 2}$ etex,(sqrt(3)*u/2,0))withcolor orange;
%  label.lrt(btex $-{\sqrt{3} \over 2}$ etex,(-sqrt(3)*u/2,0))withcolor orange;
%  label.llft(btex ${1 \over 2}$ etex,(0,u/2))withcolor orange;
%  label.llft(btex $-{1 \over 2}$ etex,(0,-u/2))withcolor orange;

%  drawoptions(dashed evenly);

%  path r[] ;
%  r[1]=(cosd(45)*u,-sind(45)*u)--(cosd(45)*u,sind(45)*u)--(0,0);
%  draw r[1] withcolor blue;
%  for k=2 upto 4 : r[k]=r[1] rotatedaround ((0,0),90*(k-1));
%    draw r[k] withcolor blue;
%  endfor;

%  pair w[];
%  w[1]=(u,0);
%  for n=2 upto 8:
%    w[n]=w[1] rotatedaround ((0,0),45(n-1));
%  endfor;
%  drawoptions();
%  label.urt(btex ${\pi \over 4}$ etex, w[2])withcolor blue;
%  dotlabel.urt(btex ${\pi \over 2}$ etex,w[3]);
%  label.ulft(btex ${3\pi \over 4}$ etex,w[4])withcolor blue;
% dotlabel.llft(btex ${\pi}$ etex,w[5]);
%  label.llft(btex $-{3\pi \over 4}$ etex,w[6])withcolor blue;
%  label.llft(btex $-{\pi \over 2}$ etex,w[7]);
%  label.lrt(btex $-{\pi \over 4}$ etex,w[8])withcolor blue;
%  label.ulft(btex ${\sqrt{2} \over 2}$ etex,(sqrt(2)*u/2,0))withcolor blue;
%  label.urt(btex $-{\sqrt{2} \over 2}$ etex,(-sqrt(2)*u/2,0))withcolor blue;
%  label.lrt(btex ${\sqrt{2} \over 2}$ etex,(0,sqrt(2)*u/2))withcolor blue ;
%  label.urt(btex $-{\sqrt{2} \over 2}$ etex,(0,-sqrt(2)*u/2))withcolor blue;

endfig;

beginfig(23)

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 withpen pencircle scaled 1.3bp withcolor red;
drawoptions(dashed evenly);
% path t[] ;
%  t[1]=(u,0)--(cosd(60)*u,sind(60)*u)--(0,0);
%  draw t[1] withcolor rose;
%  for k=2 upto 6 : t[k]=t[1] rotatedaround ((0,0),60*(k-1));
%    draw t[k] withcolor rose;
%  endfor;
% path c[] ;
%  c1 =(cosd(60)*u,-sind(60)*u)--(cosd(60)*u,sind(60)*u) ;
%  draw c1 dashed evenly withcolor rose;
%  c2 = c1 shifted (-u,0) ;
%  draw c2 dashed evenly withcolor rose;
%  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))withcolor rose;
%  label.lrt(btex $- {1 \over 2}$ etex,(-u/2,0))withcolor rose;
%  dotlabel.llft(btex $\pi$ etex,(-u,0));

%  label.urt(btex {${\pi \over 3}$} etex, z[2])withcolor rose;
%  label.ulft(btex {${2\pi \over 3}$} etex,z[3])withcolor rose;
%  label.llft(btex {$-{2\pi \over 3}$} etex,z[5])withcolor rose;
%  label.lrt(btex {$-{\pi \over 3}$} etex,z[6])withcolor rose;
%  label.llft(btex ${\sqrt{3} \over 2}$ etex,(0,sqrt(3)*u/2))withcolor rose;
%  label.ulft(btex $-{\sqrt{3} \over 2}$ etex,(0,-sqrt(3)*u/2))withcolor rose;

drawoptions(dashed evenly);
path p[] ;
p[1]=(0,u)--(cosd(30)*u,sind(30)*u)--(0,0);
draw p[1] withcolor  orange;
for k=2 upto 6 : p[k]=p[1] rotatedaround ((0,0),60*(k-1));
draw p[k] withcolor orange;
endfor;
path s[] ;
s1 =(-cosd(30)*u,sind(30)*u)--(cosd(30)*u,sind(30)*u) ;
draw s1 dashed evenly withcolor  orange;
s2 = s1 shifted (0,-u) ;
draw s2 dashed evenly withcolor orange;

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();
label.urt(btex ${\pi \over 6}$ etex,y[1])withcolor orange;
dotlabel.urt(btex ${\pi \over 2}$ etex, y[2]);
label.ulft(btex ${5\pi \over 6}$ etex,y[3])withcolor orange;
label.llft(btex $-{5\pi \over 6}$ etex,y[4])withcolor orange;
label.llft(btex $-{\pi \over 2}$ etex,y[5])withcolor orange;
label.lrt(btex $-{\pi \over 6}$ etex,y[6])withcolor orange;
label.llft(btex ${\sqrt{3} \over 2}$ etex,(sqrt(3)*u/2,0))withcolor orange;
label.lrt(btex $-{\sqrt{3} \over 2}$ etex,(-sqrt(3)*u/2,0))withcolor orange;
label.llft(btex ${1 \over 2}$ etex,(0,u/2))withcolor orange;
label.llft(btex $-{1 \over 2}$ etex,(0,-u/2))withcolor orange;

%  drawoptions(dashed evenly);

%  path r[] ;
%  r[1]=(cosd(45)*u,-sind(45)*u)--(cosd(45)*u,sind(45)*u)--(0,0);
%  draw r[1] withcolor blue;
%  for k=2 upto 4 : r[k]=r[1] rotatedaround ((0,0),90*(k-1));
%    draw r[k] withcolor blue;
%  endfor;

%  pair w[];
%  w[1]=(u,0);
%  for n=2 upto 8:
%    w[n]=w[1] rotatedaround ((0,0),45(n-1));
%  endfor;
%  drawoptions();
%  label.urt(btex ${\pi \over 4}$ etex, w[2])withcolor blue;
%  dotlabel.urt(btex ${\pi \over 2}$ etex,w[3]);
%  label.ulft(btex ${3\pi \over 4}$ etex,w[4])withcolor blue;
% dotlabel.llft(btex ${\pi}$ etex,w[5]);
%  label.llft(btex $-{3\pi \over 4}$ etex,w[6])withcolor blue;
%  label.llft(btex $-{\pi \over 2}$ etex,w[7]);
%  label.lrt(btex $-{\pi \over 4}$ etex,w[8])withcolor blue;
%  label.ulft(btex ${\sqrt{2} \over 2}$ etex,(sqrt(2)*u/2,0))withcolor blue;
%  label.urt(btex $-{\sqrt{2} \over 2}$ etex,(-sqrt(2)*u/2,0))withcolor blue;
%  label.lrt(btex ${\sqrt{2} \over 2}$ etex,(0,sqrt(2)*u/2))withcolor blue ;
%  label.urt(btex $-{\sqrt{2} \over 2}$ etex,(0,-sqrt(2)*u/2))withcolor blue;

endfig;

beginfig(24)

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 withpen pencircle scaled 1.3bp withcolor red;
drawoptions(dashed evenly);
% path t[] ;
%  t[1]=(u,0)--(cosd(60)*u,sind(60)*u)--(0,0);
%  draw t[1] withcolor rose;
%  for k=2 upto 6 : t[k]=t[1] rotatedaround ((0,0),60*(k-1));
%    draw t[k] withcolor rose;
%  endfor;
% path c[] ;
%  c1 =(cosd(60)*u,-sind(60)*u)--(cosd(60)*u,sind(60)*u) ;
%  draw c1 dashed evenly withcolor rose;
%  c2 = c1 shifted (-u,0) ;
%  draw c2 dashed evenly withcolor rose;
%  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))withcolor rose;
%  label.lrt(btex $- {1 \over 2}$ etex,(-u/2,0))withcolor rose;
%  dotlabel.llft(btex $\pi$ etex,(-u,0));

%  label.urt(btex {${\pi \over 3}$} etex, z[2])withcolor rose;
%  label.ulft(btex {${2\pi \over 3}$} etex,z[3])withcolor rose;
%  label.llft(btex {$-{2\pi \over 3}$} etex,z[5])withcolor rose;
%  label.lrt(btex {$-{\pi \over 3}$} etex,z[6])withcolor rose;
%  label.llft(btex ${\sqrt{3} \over 2}$ etex,(0,sqrt(3)*u/2))withcolor rose;
%  label.ulft(btex $-{\sqrt{3} \over 2}$ etex,(0,-sqrt(3)*u/2))withcolor rose;

%   drawoptions(dashed evenly);
%   path p[] ;
%   p[1]=(0,u)--(cosd(30)*u,sind(30)*u)--(0,0);
%   draw p[1] withcolor  orange;
%   for k=2 upto 6 : p[k]=p[1] rotatedaround ((0,0),60*(k-1));
%     draw p[k] withcolor orange;
%   endfor;
%   path s[] ;
%   s1 =(-cosd(30)*u,sind(30)*u)--(cosd(30)*u,sind(30)*u) ;
%   draw s1 dashed evenly withcolor  orange;
%   s2 = s1 shifted (0,-u) ;
%   draw s2 dashed evenly withcolor orange;

%   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();
%   label.urt(btex ${\pi \over 6}$ etex,y[1])withcolor orange;
%   dotlabel.urt(btex ${\pi \over 2}$ etex, y[2])withcolor orange;
%   label.ulft(btex ${5\pi \over 6}$ etex,y[3])withcolor orange;
%   label.llft(btex $-{5\pi \over 6}$ etex,y[4])withcolor orange;
%   label.llft(btex $-{\pi \over 2}$ etex,y[5])withcolor orange;
%   label.lrt(btex $-{\pi \over 6}$ etex,y[6])withcolor orange;
%   label.llft(btex ${\sqrt{3} \over 2}$ etex,(sqrt(3)*u/2,0))withcolor orange;
%   label.lrt(btex $-{\sqrt{3} \over 2}$ etex,(-sqrt(3)*u/2,0))withcolor orange;
%   label.llft(btex ${1 \over 2}$ etex,(0,u/2))withcolor orange;
%   label.llft(btex $-{1 \over 2}$ etex,(0,-u/2))withcolor orange;

drawoptions(dashed evenly);

path r[] ;
r[1]=(cosd(45)*u,-sind(45)*u)--(cosd(45)*u,sind(45)*u)--(0,0);
draw r[1] withcolor blue;
for k=2 upto 4 : r[k]=r[1] rotatedaround ((0,0),90*(k-1));
draw r[k] withcolor blue;
endfor;

pair w[];
w[1]=(u,0);
for n=2 upto 8:
w[n]=w[1] rotatedaround ((0,0),45(n-1));
endfor;
drawoptions();
label.urt(btex ${\pi \over 4}$ etex, w[2])withcolor blue;
dotlabel.urt(btex ${\pi \over 2}$ etex,w[3]);
label.ulft(btex ${3\pi \over 4}$ etex,w[4])withcolor blue;
dotlabel.llft(btex ${\pi}$ etex,w[5]);
label.llft(btex $-{3\pi \over 4}$ etex,w[6])withcolor blue;
label.llft(btex $-{\pi \over 2}$ etex,w[7]);
label.lrt(btex $-{\pi \over 4}$ etex,w[8])withcolor blue;
label.ulft(btex ${\sqrt{2} \over 2}$ etex,(sqrt(2)*u/2,0))withcolor blue;
label.urt(btex $-{\sqrt{2} \over 2}$ etex,(-sqrt(2)*u/2,0))withcolor blue;
label.lrt(btex ${\sqrt{2} \over 2}$ etex,(0,sqrt(2)*u/2))withcolor blue ;
label.urt(btex $-{\sqrt{2} \over 2}$ etex,(0,-sqrt(2)*u/2))withcolor blue;

endfig;

beginfig(25)

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 withpen pencircle scaled 1.3bp withcolor red;
drawoptions(dashed evenly);
path t[] ;
t[1]=(u,0)--(cosd(60)*u,sind(60)*u)--(0,0);
draw t[1] withcolor rose;
for k=2 upto 6 : t[k]=t[1] rotatedaround ((0,0),60*(k-1));
draw t[k] withcolor rose;
endfor;
path c[] ;
c1 =(cosd(60)*u,-sind(60)*u)--(cosd(60)*u,sind(60)*u) ;
draw c1 dashed evenly withcolor rose;
c2 = c1 shifted (-u,0) ;
draw c2 dashed evenly withcolor rose;
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))withcolor rose;
label.lrt(btex $- {1 \over 2}$ etex,(-u/2,0))withcolor rose;
dotlabel.llft(btex $\pi$ etex,(-u,0));

label.urt(btex {${\pi \over 3}$} etex, z[2])withcolor rose;
label.ulft(btex {${2\pi \over 3}$} etex,z[3])withcolor rose;
label.llft(btex {$-{2\pi \over 3}$} etex,z[5])withcolor rose;
label.lrt(btex {$-{\pi \over 3}$} etex,z[6])withcolor rose;
label.llft(btex ${\sqrt{3} \over 2}$ etex,(0,sqrt(3)*u/2))withcolor rose;
label.ulft(btex $-{\sqrt{3} \over 2}$ etex,(0,-sqrt(3)*u/2))withcolor rose;

drawoptions(dashed evenly);
path p[] ;
p[1]=(0,u)--(cosd(30)*u,sind(30)*u)--(0,0);
draw p[1] withcolor  orange;
for k=2 upto 6 : p[k]=p[1] rotatedaround ((0,0),60*(k-1));
draw p[k] withcolor orange;
endfor;
path s[] ;
s1 =(-cosd(30)*u,sind(30)*u)--(cosd(30)*u,sind(30)*u) ;
draw s1 dashed evenly withcolor  orange;
s2 = s1 shifted (0,-u) ;
draw s2 dashed evenly withcolor orange;

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();
label.urt(btex ${\pi \over 6}$ etex,y[1])withcolor orange;
dotlabel.urt(btex ${\pi \over 2}$ etex, y[2]);
label.ulft(btex ${5\pi \over 6}$ etex,y[3])withcolor orange;
label.llft(btex $-{5\pi \over 6}$ etex,y[4])withcolor orange;
label.llft(btex $-{\pi \over 2}$ etex,y[5])withcolor orange;
label.lrt(btex $-{\pi \over 6}$ etex,y[6])withcolor orange;
label.llft(btex ${\sqrt{3} \over 2}$ etex,(sqrt(3)*u/2,0))withcolor orange;
label.lrt(btex $-{\sqrt{3} \over 2}$ etex,(-sqrt(3)*u/2,0))withcolor orange;
label.llft(btex ${1 \over 2}$ etex,(0,u/2))withcolor orange;
label.llft(btex $-{1 \over 2}$ etex,(0,-u/2))withcolor orange;

drawoptions(dashed evenly);

path r[] ;
r[1]=(cosd(45)*u,-sind(45)*u)--(cosd(45)*u,sind(45)*u)--(0,0);
draw r[1] withcolor blue;
for k=2 upto 4 : r[k]=r[1] rotatedaround ((0,0),90*(k-1));
draw r[k] withcolor blue;
endfor;

pair w[];
w[1]=(u,0);
for n=2 upto 8:
w[n]=w[1] rotatedaround ((0,0),45(n-1));
endfor;
drawoptions();
label.urt(btex ${\pi \over 4}$ etex, w[2])withcolor blue;
dotlabel.urt(btex ${\pi \over 2}$ etex,w[3]);
label.ulft(btex ${3\pi \over 4}$ etex,w[4])withcolor blue;
dotlabel.llft(btex ${\pi}$ etex,w[5]);
label.llft(btex $-{3\pi \over 4}$ etex,w[6])withcolor blue;
label.llft(btex $-{\pi \over 2}$ etex,w[7]);
label.lrt(btex $-{\pi \over 4}$ etex,w[8])withcolor blue;
label.ulft(btex ${\sqrt{2} \over 2}$ etex,(sqrt(2)*u/2,0))withcolor blue;
label.urt(btex $-{\sqrt{2} \over 2}$ etex,(-sqrt(2)*u/2,0))withcolor blue;
label.lrt(btex ${\sqrt{2} \over 2}$ etex,(0,sqrt(2)*u/2))withcolor blue ;
label.urt(btex $-{\sqrt{2} \over 2}$ etex,(0,-sqrt(2)*u/2))withcolor blue;

endfig;

beginfig(26 )

numeric u;
u:=0.5cm;
%%
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-3,3,-2.5,2.5,1cm,1cm);
r_axes;
r_origine;
%r_unites;
r_labelxy;

draw (2.05u,0)--(2.05u,4u) withpen pencircle scaled 1.5bp withcolor red;
drawarrow (2.05u,4u)--(2.05u,5u ) withpen pencircle scaled 1.5bp withcolor red dashed evenly;

draw (2.05u ,0)--(2.05u ,-3.75u ) withpen pencircle scaled 1.5bp withcolor blue;

draw (2.05u ,-3.75u )--(2.05u ,-5u ) withpen pencircle scaled 1.5bp withcolor blue dashed evenly;

%le cercle
draw fullcircle scaled 2.05cm;

label.urt(btex $0$ etex,(2.05u ,0) );
dotlabel.rt(btex $-1$ etex,(2.05u ,-2.05u ) );
dotlabel.rt(btex $1$ etex,(2.05u ,2.05u ) );
dotlabel.rt(btex $0,5$ etex,(2.05u,1.025u) );
dotlabel.rt(btex $\sqrt{2}$ etex,(2.05u,2.9u) );
label.lrt(btex $\bbr$ etex,(2.05u,4.75u) )withcolor red;
r_fin;

endfig;

beginfig(27 )

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t*cos(t)/(2*Pi)
enddef;

vardef fy(expr t)=
t*sin(t)/(2*Pi)                      % spirale passant par (1,0)
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-3,3,-2.5,2.5,2cm,2cm);
r_axes;
r_origine;
%r_unites;
r_labelxy;

%On se débrouille pour que le cercle unite soit le cercle osculateur de la spirale :
%On fait une translation de (0,-1/(2Pi)) suivi d'une rotation de -Arctan(1/(2*pi)) autour de  (0,1/(2Pi))
path s,ss,S,sp,Sp,ssp;
s:=(f_courbe(fx,fy,2*Pi,13*Pi/3,1000) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
draw s withpen pencircle scaled 1.5bp withcolor red;
sp:=(f_courbe(fx,fy,13*Pi/3,13*Pi/3+Pi/6,1000) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
drawarrow ((f_point(fx,fy,13*Pi/3+Pi/6-0.05)-- f_point(fx,fy,13*Pi/3+Pi/6)) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061)withcolor red dashed evenly;
label.top(btex $\bbr$ etex,(f_point(fx,fy,13*Pi/3+Pi/6) shifted r_p(0,-1/(2*Pi)))rotatedaround(r_p(0,1/(2*Pi)),9.043061))withcolor red;
draw sp withpen pencircle scaled 1.5bp withcolor red dashed evenly;
% vers les négatifs
ss:=(f_courbe(fx,fy,2*Pi,8*Pi/3,1000) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
draw S withpen pencircle scaled 1.5bp withcolor blue;
ssp:=(f_courbe(fx,fy,8*Pi/3,8*Pi/3+Pi/6,1000) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
draw Sp withpen pencircle scaled 1.5bp withcolor blue dashed evenly;
%le cercle
draw fullcircle scaled 4.1cm withcolor orange;

pair a[];

a[1/2]:=(f_point(fx,fy,2*Pi+0.48) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
dotlabel.rt(btex 0.5 etex,a[1/2] );

a[1.414]:=(f_point(fx,fy,2*Pi+1.27) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
dotlabel.top(btex $\sqrt{2}$ etex,a[1.414] );

a[1]:=(f_point(fx,fy,2*Pi+0.9) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
dotlabel.urt(btex $1$ etex,a[1] );

a[5/2]:=(f_point(fx,fy,2*Pi+2.15) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
dotlabel.ulft(btex $\fr{5}{2}$ etex,a[5/2] );

a[3.14]:=(f_point(fx,fy,2*Pi+2.6) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
dotlabel.ulft(btex $\pi$ etex,a[3.14] );

a[6.28]:=(f_point(fx,fy,2*Pi+4.6) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
dotlabel.lrt(btex $2\pi$ etex,a[6.28] );

a[7.28]:=(f_point(fx,fy,2*Pi+5.14) shifted r_p(0,-1/(2*Pi))) rotatedaround(r_p(0,1/(2*Pi)),9.043061);
dotlabel.lrt(btex $2\pi+1$ etex,a[7.28] );

drawarrow a[5/2]{dir -85}..(-1.61cm,1.203cm){dir -45} dashed evenly;

drawarrow a[3.14]{dir -85}..(-2.05cm,0){dir -25} dashed evenly;

drawarrow a[6.28]{dir 20}..(2.05cm,0){dir 135} dashed evenly;

drawarrow a[7.28]{dir 50}..a[1]{dir 185} dashed evenly;

label.urt(btex $0$ etex,(2.05cm,0) );
dotlabel.lrt(btex $-1$ etex,(1.086cm,-1.75cm) );

r_fin;
endfig;

beginfig(28)

numeric u ;
u=2.5cm;
drawarrow (-1.2*u,0)--(1.2*u,0);
drawarrow (0,-1.2*u)--(0,1.2*u);
draw fullcircle scaled 2u withpen pencircle scaled 1.3bp withcolor red;
drawoptions(dashed evenly);
path t[] ;
t[1]=(cosd(60)*u,sind(60)*u)--(0,0);
draw t[1] withcolor rose;
for k=2 upto 6 : t[k]=t[1] rotatedaround ((0,0),60*(k-1));
draw t[k] withcolor rose;
endfor;
path c[] ;
c1 =(cosd(60)*u,-sind(60)*u)--(cosd(60)*u,sind(60)*u) ;
%draw c1 dashed evenly withcolor rose;
c2 = c1 shifted (-u,0) ;
%draw c2 dashed evenly withcolor rose;
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))withcolor rose;
%label.lrt(btex $- {1 \over 2}$ etex,(-u/2,0))withcolor rose;
dotlabel.llft(btex $\pi$ etex,(-u,0));

label.urt(btex {${\pi \over 3}$} etex, z[2])withcolor rose;
label.ulft(btex {${2\pi \over 3}$} etex,z[3])withcolor rose;
label.llft(btex {$-{2\pi \over 3}$} etex,z[5])withcolor rose;
label.lrt(btex {$-{\pi \over 3}$} etex,z[6])withcolor rose;
%label.llft(btex ${\sqrt{3} \over 2}$ etex,(0,sqrt(3)*u/2))withcolor rose;
%label.ulft(btex $-{\sqrt{3} \over 2}$ etex,(0,-sqrt(3)*u/2))withcolor rose;

drawoptions(dashed evenly);
path p[] ;
p[1]=(cosd(30)*u,sind(30)*u)--(0,0);
draw p[1] withcolor  orange;
for k=2 upto 6 : p[k]=p[1] rotatedaround ((0,0),60*(k-1));
draw p[k] withcolor orange;
endfor;
path s[] ;
s1 =(-cosd(30)*u,sind(30)*u)--(cosd(30)*u,sind(30)*u) ;
%draw s1 dashed evenly withcolor  orange;
s2 = s1 shifted (0,-u) ;
%draw s2 dashed evenly withcolor orange;

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();
label.urt(btex ${\pi \over 6}$ etex,y[1])withcolor orange;
dotlabel.urt(btex ${\pi \over 2}$ etex, y[2]);
label.ulft(btex ${5\pi \over 6}$ etex,y[3])withcolor orange;
label.llft(btex $-{5\pi \over 6}$ etex,y[4])withcolor orange;
label.llft(btex $-{\pi \over 2}$ etex,y[5])withcolor orange;
label.lrt(btex $-{\pi \over 6}$ etex,y[6])withcolor orange;
%label.llft(btex ${\sqrt{3} \over 2}$ etex,(sqrt(3)*u/2,0))withcolor orange;
%label.lrt(btex $-{\sqrt{3} \over 2}$ etex,(-sqrt(3)*u/2,0))withcolor orange;
%label.llft(btex ${1 \over 2}$ etex,(0,u/2))withcolor orange;
%label.llft(btex $-{1 \over 2}$ etex,(0,-u/2))withcolor orange;

drawoptions(dashed evenly);

path r[] ;
r[1]=(cosd(45)*u,sind(45)*u)--(0,0);
draw r[1] withcolor blue;
for k=2 upto 4 : r[k]=r[1] rotatedaround ((0,0),90*(k-1));
draw r[k] withcolor blue;
endfor;

pair w[];
w[1]=(u,0);
for n=2 upto 8:
w[n]=w[1] rotatedaround ((0,0),45(n-1));
endfor;
drawoptions();
label.urt(btex ${\pi \over 4}$ etex, w[2])withcolor blue;
dotlabel.urt(btex ${\pi \over 2}$ etex,w[3]);
label.ulft(btex ${3\pi \over 4}$ etex,w[4])withcolor blue;
dotlabel.llft(btex ${\pi}$ etex,w[5]);
label.llft(btex $-{3\pi \over 4}$ etex,w[6])withcolor blue;
label.llft(btex $-{\pi \over 2}$ etex,w[7]);
label.lrt(btex $-{\pi \over 4}$ etex,w[8])withcolor blue;
%label.ulft(btex ${\sqrt{2} \over 2}$ etex,(sqrt(2)*u/2,0))withcolor blue;
%label.urt(btex $-{\sqrt{2} \over 2}$ etex,(-sqrt(2)*u/2,0))withcolor blue;
%label.lrt(btex ${\sqrt{2} \over 2}$ etex,(0,sqrt(2)*u/2))withcolor blue ;
%label.urt(btex $-{\sqrt{2} \over 2}$ etex,(0,-sqrt(2)*u/2))withcolor blue;

endfig;

%% Sin, Cos, Tan

beginfig(29);
numeric u;
u=2.5cm ;
drawarrow (-1.2*u,0)--(1.2*u,0);
drawarrow (0,-1.2*u)--(0,1.2*u);
draw fullcircle scaled 5cm withcolor bleu;
draw (0,0)--(cosd(40)*u,sind(40)*u) withpen pencircle scaled 1.2bp;
draw (0,sind(40)*u)--(cosd(40)*u,sind(40)*u) dashed evenly withpen pencircle scaled 1.2bp withcolor red;
draw (cosd(40)*u,0)--(cosd(40)*u,sind(40)*u) dashed evenly withpen pencircle scaled 1.2bp withcolor orange;
%draw (u,-1.3*u)--(u,1.3*u)withpen pencircle scaled 1.2bp withcolor rose;
drawarrow (0.2*u,0){dir 90}..(0.2*cosd(40)*u,0.2*sind(40)*u);
dotlabel.llft(btex $0$ etex, (0,0));
dotlabel.lrt(btex $I$ etex, (u,0));
dotlabel.ulft(btex $J$ etex, (0,u));
label.lft(btex $\sin(x)$ etex, (0,sind(40)*u))withcolor red;
label.bot(btex $\cos(x)$ etex, (cosd(40)*u,0))withcolor  orange;
%label.rt(btex $\tan(x)$ etex , (u,(sind(40)/cosd(40))*u)) withcolor rose;
dotlabel.top(btex $x$ etex,(cosd(40)*u,sind(40)*u));
endfig;

%fig 30  lien triangle 3eme
_nfig:=29;
numeric u;
u=4cm ;
figure(-.25u,-.25u,1.5u,1.5u);
pair O,I,J,M,C;
drawarrow (-1.2*u,0)--(1.2*u,0)dashed evenly;
drawarrow (0,-1.2*u)--(0,1.2*u)dashed evenly;
draw cercle(origin,u) withcolor blue dashed evenly;
O=origin;
I=(u,0);
J=(0,u);
M=(cosd(40)*u,sind(40)*u);C=(cosd(40)*u,0);
trace segment(O,M)withpen pencircle scaled 1.2bp;
trace segment(M,C) withcolor orange withpen pencircle scaled 1.2bp;
trace segment(O,C) withcolor red withpen pencircle scaled 1.2bp;
%trace Codeangle(O,C,M,1,btex x etex );
drawarrow (0.2*u,0){dir 90}..(0.2*cosd(40)*u,0.2*sind(40)*u);
trace codeperp(O,C,M,5);

label.rt(btex $x$ etex,(0.2*cosd(40)*u,0.2*sind(20)*u) );
dotlabel.llft(btex $0$ etex, (0,0));
dotlabel.lrt(btex $I$ etex, (u,0));
dotlabel.ulft(btex $J$ etex, (0,u));
%label.lft(btex $\sin(x)$ etex, (0,sind(40)*u))withcolor red;
label.bot(btex $C$ etex, (cosd(40)*u,0))withcolor  red;

dotlabel.urt(btex $M$ etex,(cosd(40)*u,sind(40)*u));

trace appelation(O,C,-2mm,btex \footnotesize \color{red}$\cos(x)$ etex );

trace appelation(C,M,-2mm,btex \footnotesize \color{orange}$\sin(x)$ etex );

trace appelation(O,M,2mm,btex \small 1 etex );
fin;

% fig 31 triangle equi

numeric u;
u=4cm ;
figure(-.25u,-.25u,1.5u,1.5u);
pair O,I,J,M,C;
drawarrow (-1.2*u,0)--(1.2*u,0)dashed evenly;
drawarrow (0,-1.2*u)--(0,1.2*u)dashed evenly;
draw cercle(origin,u) withcolor blue dashed evenly;
O=origin;
I=(u,0);
J=(0,u);
M=(cosd(60)*u,sind(60)*u);C=(cosd(60)*u,0);
trace segment(O,M)withpen pencircle scaled 1.2bp;
trace segment(M,C) withcolor orange withpen pencircle scaled 1.2bp;
trace segment(O,C) withcolor red withpen pencircle scaled 1.2bp;
trace segment(M,I);
%trace Codeangle(O,C,M,1,btex x etex );
drawarrow (0.2*u,0){dir 90}..(0.2*cosd(60)*u,0.2*sind(60)*u);
trace codeperp(O,C,M,5);

label.rt(btex $\small\ofr{\pi}{3}$ etex,(0.3*cosd(60)*u,0.3*sind(30)*u) );
label.lft(btex $\small \alpha$ etex,(0.3*cosd(60)*u,0.3*sind(30)*u)  reflectedabout(M,C));
dotlabel.llft(btex $0$ etex, (0,0));
dotlabel.lrt(btex $I$ etex, (u,0));
dotlabel.ulft(btex $J$ etex, (0,u));
%label.lft(btex $\sin\pa{\ofr{\pi}{3}}$ etex, (0,sind(60)*u))withcolor red;
label.bot(btex $C$ etex, (cosd(60)*u,0))withcolor  red;

dotlabel.urt(btex $M$ etex,(cosd(60)*u,sind(60)*u));

trace appelation(O,C,-2mm,btex \footnotesize \color{red}$\cos\pa{\ofr{\pi}{3}}$ etex );

trace appelation(C,M,-2mm,btex \footnotesize \color{orange}$\sin\pa{\ofr{\pi}{3}}$ etex );

trace appelation(O,M,2mm,btex \small 1 etex );
fin;

figure(-1.25u,-1.25u,1.25u,1.25u);
numeric u;
u=3cm ;
drawarrow (-1.2*u,0)--(1.2*u,0);
drawarrow (0,-1.2*u)--(0,1.2*u);
draw fullcircle scaled 6cm withcolor blue;
draw (0,0)--(u,(cosd(45)/sind(45))*u) withcolor red;
draw (0,0)--(u,-(cosd(45)/sind(45))*u)withcolor vert_e;
draw (cosd(45)*u,-sind(45)*u)--(cosd(45)*u,sind(45)*u) dashed evenly;
draw (0,-sind(45)*u)--(cosd(45)*u,-sind(45)*u) dashed evenly;
draw (0,sind(45)*u)--(cosd(45)*u,sind(45)*u) dashed evenly;
%draw (u,-1.3*u)--(u,1.3*u);
drawarrow (0.2*u,0){dir 90}..(0.2*cosd(45)*u,0.2*sind(45)*u);
drawarrow (0.2*u,0){dir -90}..(0.2*cosd(45)*u,-0.2*sind(45)*u);
dotlabel.ulft(btex $0$ etex, (0,0));
dotlabel.lrt(btex $I$ etex, (u,0));
dotlabel.ulft(btex $J$ etex, (0,u));
dotlabel.lft(btex   \footnotesize $\sin(x)$ etex, (0,sind(45)*u));
dotlabel.lft(btex \footnotesize $-\sin(x)$ etex, (0,-sind(45)*u));
dotlabel.urt(btex  \footnotesize $\cos(x)$ etex, (cosd(45)*u,0));
%dotlabel.rt(btex $\tan(x)$ etex , (u,(sind(45)/cosd(45))*u));
%dotlabel.rt(btex $-\tan(x)$ etex , (u,-(sind(45)/cosd(45))*u));
label.top(btex $x$ etex,(cosd(45)*u,sind(45)*u));
label.bot(btex $-x$ etex,(cosd(45)*u,(-sind(45)-0.05)*u));
endfig;

end