Fichier f010.mp (figure 3) — Modifié le 14 Avril 2008 à 15 h 06

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}}
% %%% Fraction en exposant
\newcommand{\efr}[2]{%
\raisebox{.3ex}{\scriptsize{$#1$}}\negmedspace\slash
\negthinspace\raisebox{-.2ex}{\scriptsize{$#2$}}}

% %%% Fraction en oblique
\newcommand{\ofr}[2]{%
\raisebox{0ex}{$#1$}\negthinspace\slash
\raisebox{-.5ex}{$#2$}}
\begin{document}
etex

%parite
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(-3u,-2u,3u,2u);
numeric u;
u=2cm ;

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
t*t*t*t-2*t*t -1                  % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-2,2,-2,2,3cm,2cm);

fillcolor:=jaune;
transparence r_p(-3,-3)--r_p(0,-3)--r_p(0,3)--r_p(-3,3)--cycle;

r_axes;
r_origine;

r_labelxy;

draw f_courbe(fx,fy,0,2,500)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-2,0,500)withpen pencircle scaled 1.5bp withcolor red dashed withdots scaled 0.5;

pair X,mX,fX,fmX,Y;
numeric a;
a:=.5;
mX=r_p(-a,0); X=r_p(a,0); fX=f_point(fx,fy,a); fmX=r_p(fx(-a),fy(-a)); Y=r_p(0,fy(a));

drawarrow mX--fmX; drawarrow fmX--Y; drawarrow fX--Y; drawarrow X--fX;

dotlabel.top(btex $-x$ etex,mX );
dotlabel.top(btex $x$ etex,X );
dotlabel.llft(btex $f(-x)$ etex,Y );
dotlabel.lrt(btex $f(x)$ etex,Y );

r_fin;
endfig;

%  imparite
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(-3u,-2u,3u,2u);
numeric u;
u=2cm ;

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
0.25*t*t*t                  % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-2,2,-2,2,3cm,2cm);

fillcolor:=jaune;
transparence r_p(-3,-3)--r_p(0,-3)--r_p(0,3)--r_p(-3,3)--cycle;

r_axes;
%r_origine;

r_labelxy;

draw f_courbe(fx,fy,0,2,500)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-2,0,500)withpen pencircle scaled 1.5bp withcolor red dashed withdots scaled 0.5;

pair X,mX,fX,fmX,Y,mY;
numeric a;
a:=1.5;
mX=r_p(-a,0); X=r_p(a,0); fX=f_point(fx,fy,a); fmX=r_p(fx(-a),fy(-a)); Y=r_p(0,fy(a)); mY=r_p(0,fy(-a));

drawarrow mX--fmX; drawarrow fmX--mY; drawarrow fX--Y; drawarrow X--fX;

trace segment(fX,fmX);
trace codesegments(fmX,r_p(0,0),r_p(0,0),fX,2);

dotlabel.top(btex $-x$ etex,mX );
dotlabel.bot(btex $x$ etex,X );
dotlabel.lrt(btex $f(-x)$ etex,mY );
dotlabel.llft(btex $f(x)$ etex,Y );
label.lrt(btex O etex,origin );

r_fin;
endfig;

% fig 35
%cosinus
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
numeric u;
u=2cm ;
figure(-3.5u,-1.25u,3.5u,1.25u);

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
cos(t)                  % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-3.5,3.5,-1.25,1.25,2cm,2cm);

fillcolor:=jaune;
transparence r_p(-4,-3)--r_p(0,-3)--r_p(0,3)--r_p(-4,3)--cycle;

r_axes;
r_origine;
%r_unites;
r_labelxy;

draw f_courbe(fx,fy,0,Pi,500)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-Pi,0,500)withpen pencircle scaled 1.5bp withcolor red dashed withdots scaled 0.5;

pair X,mX,fX,fmX,Y;
numeric a;
a:=Pi;
mX:=r_p(-Pi,0); X:=r_p(a,0); fX:=f_point(fx,fy,a); fmX:=r_p(-a,fy(-a)); Y:=r_p(0,fy(a)); mY:=r_p(0,fy(-a));

drawarrow mX--fmX; drawarrow fmX--Y; drawarrow fX--Y; drawarrow X--fX;

dotlabel.top(btex $-\pi$ etex,mX );
dotlabel.top(btex $\pi$ etex,X );
dotlabel.llft(btex $-1$ etex,mY );
dotlabel.urt(btex $1$ etex,r_p(0,1) );
label.urt(btex $\ofr{\pi}{2}$ etex,r_p(Pi/2,0) );
label.ulft(btex $-\ofr{\pi}{2}$ etex,r_p(-Pi/2,0) );

r_fin;
endfig;

%sinus
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
numeric u;
u=2cm ;
figure(-3.5u,-1.25u,3.5u,1.25u);

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
sin(t)                  % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-3.5,3.5,-1.25,1.25,2cm,2cm);

fillcolor:=jaune;
transparence r_p(-4,-3)--r_p(0,-3)--r_p(0,3)--r_p(-4,3)--cycle;

r_axes;
%r_origine;

r_labelxy;

draw f_courbe(fx,fy,0,Pi,500)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-Pi,0,500)withpen pencircle scaled 1.5bp withcolor red dashed withdots scaled 0.5;

pair X,mX,fX,fmX,Y,mY;
numeric a;
a:=Pi/2;
mX=r_p(-a,0); X=r_p(a,0); fX=f_point(fx,fy,a); fmX=r_p(fx(-a),fy(-a)); Y=r_p(0,fy(a)); mY=r_p(0,fy(-a));

drawarrow mX--fmX; drawarrow fmX--mY; drawarrow fX--Y; drawarrow X--fX;

%trace segment(fX,fmX);
%trace codesegments(fmX,r_p(0,0),r_p(0,0),fX,2);

dotlabel.top(btex $-\ofr{\pi}{2}$ etex,mX );
dotlabel.bot(btex $\ofr{\pi}{2}$ etex,X );
dotlabel.lrt(btex $-1$ etex,mY );
dotlabel.llft(btex $1$ etex,Y );
label.lrt(btex O etex,origin );

dotlabel.top(btex $-\pi$ etex,r_p(-Pi,0) );
dotlabel.bot(btex $\pi$ etex,r_p(Pi,0) );

r_fin;
endfig;

numeric u;
u=2.75cm ;
figure(-3.5u,-1.25u,3.5u,1.25u);

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
sin(t)                  % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-14,14,-1.25,1.25,0.75cm,2.5cm);

fillcolor:=jaune;
transparence r_p(-Pi,-3)--r_p(Pi,-3)--r_p(Pi,3)--r_p(-Pi,3)--cycle;

r_axes;
%r_origine;

r_labelxy;

draw f_courbe(fx,fy,-Pi,Pi,500)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-3*Pi,-Pi,500)withpen pencircle scaled 1.5bp withcolor blue dashed withdots scaled 0.5;
draw f_courbe(fx,fy,Pi,3*Pi,500)withpen pencircle scaled 1.5bp withcolor 0.8white dashed evenly scaled 0.5;
draw f_courbe(fx,fy,-5*Pi,-3*Pi,500)withpen pencircle scaled 1.5bp withcolor vert_e dashed evenly;
draw f_courbe(fx,fy,3*Pi,5*Pi,500)withpen pencircle scaled 1.5bp withcolor orange dashed withdots scaled 0.25;

dotlabel.urt(btex $\pi$ etex,r_p(Pi,0) );
dotlabel.urt(btex $3\pi$ etex,r_p(3*Pi,0) );
dotlabel.urt(btex $-3\pi$ etex,r_p(-3*Pi,0) );
dotlabel.urt(btex $-\pi$ etex,r_p(-Pi,0) );
dotlabel.urt(btex $5\pi$ etex,r_p(5*Pi,0) );

drawarrow origin--r_p(1,0)withpen pencircle scaled 1.3bp;
drawarrow origin--r_p(0,1)withpen pencircle scaled 1.3bp;

label.lft(btex $\ve{j}$ etex,r_p(0,0.5) );

label.bot(btex $\ve{i}$ etex,r_p(0.5,0) );

drawarrow r_p(fx(Pi/4),fy(Pi/4))--r_p(fx(Pi/4+2*Pi),fy(Pi/4+2*Pi)) withcolor blue;
label.top(btex $2\pi\ve{i}$ etex, 0.5[r_p(fx(Pi/4),fy(Pi/4)),r_p(fx(Pi/4+2*Pi),fy(Pi/4+2*Pi))] ) withcolor blue;

drawarrow r_p(fx(-Pi/6),fy(-Pi/6))--r_p(fx(-Pi/6+2*Pi),fy(-Pi/6+2*Pi)) withcolor blue;
label.top(btex $2\pi\ve{i}$ etex, 0.5[r_p(fx(-Pi/6),fy(-Pi/6)),r_p(fx(-Pi/6+2*Pi),fy(-Pi/6+2*Pi))] ) withcolor blue;

drawarrow r_p(fx(-37*Pi/12),fy(-37*Pi/12))--r_p(fx(-37*Pi/12+2*Pi),fy(-37*Pi/12+2*Pi)) withcolor blue;
label.top(btex $2\pi\ve{i}$ etex, 0.5[r_p(fx(-37*Pi/12),fy(-37*Pi/12)),r_p(fx(-37*Pi/12+2*Pi),fy(-37*Pi/12+2*Pi))] ) withcolor blue;

drawarrow r_p(fx(-5*Pi/2),fy(-5*Pi/2))--r_p(fx(-5*Pi/2+2*Pi),fy(-5*Pi/2+2*Pi)) withcolor blue;
label.top(btex $2\pi\ve{i}$ etex, 0.5[r_p(fx(-5*Pi/2),fy(-5*Pi/2)),r_p(fx(-5*Pi/2+2*Pi),fy(-5*Pi/2+2*Pi))] ) withcolor blue;

fin;

end