%% verbatimtex %&latex \documentclass{article} \usepackage[latin1]{inputenc} \usepackage[frenchb]{babel} \usepackage{amsmath} \begin{document} etex %% %prologues:=2; input courbescp11; vardef titre(expr pos,largeur,hauteur,texte)= save $; picture $; $=image( fill ((pos shifted(-largeur/2*x.u,-hauteur/2*y.u))--(pos shifted(largeur/2*x.u,-hauteur/2*y.u))--(pos shifted(largeur/2*x.u,hauteur/2*y.u))--(pos shifted(-largeur/2*x.u,hauteur/2*y.u))--cycle) withcolor jaune; draw ((pos shifted(-largeur/2*x.u,-hauteur/2*y.u))--(pos shifted(largeur/2*x.u,-hauteur/2*y.u))--(pos shifted(largeur/2*x.u,hauteur/2*y.u))--(pos shifted(-largeur/2*x.u,hauteur/2*y.u))--cycle); label(texte,pos); ); $ enddef; string marque_c; marque_c="non"; vardef representation[](expr a,b,nb)(text texte)= save $; path $; if marque_c="cartesienne": $=courbe@(a,b,nb,texte) elseif marque_c="polaire": $=polaire@(a,b,nb,texte) elseif marque_c="param": $=param@(a,b,nb,texte) elseif marque_c="polaireparam": $=polaireparam@(a,b,nb,texte) fi; $ enddef; beginfig(1);%arcsin depart((-3,-3.5),(2.5,3.5),(0,0),2,2); grille(0.5); axes; graduantx.llft; graduanty.lft; draw courbe1(-1,1,100,arcsin(x)) withcolor bleu; draw titre(placepoint(-0.85,1.5),1.25,0.25,btex $y=\arcsin(x)$ etex); endfig; beginfig(2);%puissances depart((-5,-5),(5,5),(0,0),4,4); grille(1); axes; graduantx.llft; graduanty.lft; draw courbe1(-5,5,100,x**2) withcolor bleu; draw courbe2(-5,5,100,x**3) withcolor vert; draw courbe3(-2,2,100,x**4) withcolor orange; draw courbe4(-2,2,100,x**5) withcolor jaune; endfig; beginfig(3);%cos depart((-6.5,-1.5),(6.5,1.5),(0,0),1,1); grille(0.1); axes; graduantx.bot; graduanty.ulft; draw courbe2(-10,10,100,cos(x)) withcolor bleu; draw titre(placepoint(-2,1),2,0.5,btex $y=\cos(x)$ etex); endfig; beginfig(4);%ln depart((-0.5,-3.5),(6.5,2),(0,0),2,1); grille(0.5); axes; graduantx.bot; graduanty.ulft; draw courbe2(0.025,10,100,ln(x)) withcolor bleu; draw titre(placepoint(0.75,1),1,0.5,btex $y=\ln x$ etex); endfig; beginfig(5);%Cardioide depart((0,0),(9,10),(1,5),3,3); grille(1); axes; graduantx.bot; graduanty.ulft; marque_c:="polaire"; draw representation2(0,2*pi,100,1+cos(theta)) withcolor orange; draw titre(placepoint(2,4/3),2/3,1/3,btex Cardioïde etex); endfig; beginfig(6);%Astroide depart((-5,-5),(5,5),(0,0),4,4); grille(1); axes; graduantx.bot; graduanty.ulft; marque_c:="param"; draw representation3(0,2*pi,100,((cos(t))**3,(sin(t))**3)) withcolor violet; draw titre(placepoint(3/4,1),1/2,1/4,btex Astroïde etex); endfig; beginfig(7); depart((-5,-5),(5,6),(0,0),2,2); grille(1); axes; graduantx.bot; graduanty.ulft; marque_c:="polaireparam"; draw representation4(0,2*pi,100,((pi/2)*cos(t),sin(t))) withcolor jaune; draw titre(placepoint(1,2.5),1.5,3/4,btex $\left\{\begin{array}{l} \theta(t)=\dfrac{\pi}{2}\cos t\\ \rho(t)=\sin t\\ \end{array} \right.$ etex); endfig; beginfig(8); depart((0,0),(8,6),(1,3),2,2); grille(1); axes; graduantx.bot; graduanty.ulft; draw polaire1(-pi,pi,100,3*cos(theta)*cos(2*theta)) withcolor bleu; draw titre(placepoint(5/4,1),3/2,1/3,btex $\rho=3\cos\theta\cos(2\theta)$ etex); endfig; beginfig(9); depart((0,0),(14,16),(10,7),3,3); axes; grille(1); graduantx.bot; graduanty.ulft; draw polaire1(0,2*pi,200,(5/3)*cos(2*theta)-cos(theta)) dashed evenly withcolor bleu; pair I,A,O; O=z.origine*cm; A=point(0.5*length Cpo1) of Cpo1; I=1/2[z.origine*cm,A]; dotlabel.llft(btex A etex,A); dotlabel.top(btex I etex,I); pair m[],M[]; vues=100; for j=0 upto vues: m[j]=point(j*length Cpo1/vues) of Cpo1; M[j]=((distance(A,I)**2)/(distance(I,m[j])**2))*(m[j]-I); endfor; path courbeinv; courbeinv=M0 for j=1 upto vues: ..M[j] endfor; draw courbeinv shifted I withcolor rouge; draw titre(placepoint(-5/3,2.5),3,1/3,btex Le scarabée (en bleu) et sa courbe inverse (rouge) etex); endfig; beginfig(10); depart((0,0),(9,10),(1,5),1,1); axes; grille(1); graduantx.bot; graduanty.ulft; draw polaire1(-pi/2+0.01,pi/2-0.01,100,(2*(sin(theta))**2)/(cos(theta))) withcolor orange; draw titre(placepoint(5,4),3,1,btex Cissoïde droite etex); draw titre(placepoint(5,3),2,1,btex $\rho=2\dfrac{\sin^2\theta}{\cos\theta}$ etex); endfig; beginfig(11); depart((3,0),(12,10),(5,5),1,1); axes; grille(1); graduantx.bot; graduanty.ulft; draw polaire1(-pi/2+0.01,pi/2-0.01,100,(2*cos(2*theta))/(cos(theta))) withcolor orange; draw titre(placepoint(3.5,4),6,1,btex Strophoïde droite : $\rho=2\dfrac{\cos2\theta}{\cos\theta}$ etex); endfig; beginfig(12); depart((0,0),(9,10),(3,5),1,0.5); axes; grille(1); graduantx.bot; graduanty.ulft; draw polaire1(-pi/2+0.01,pi/2-0.01,100,(8*cos(theta))-2/(cos(theta))) withcolor orange; draw titre(placepoint(3,6),4,4,btex\begin{minipage}{3cm} Trisectrice de\\ Mac-Laurin\\$\rho=8\cos\theta-\dfrac{2}{\cos\theta}$\end{minipage} etex); endfig; beginfig(13); depart((0,0),(9,10),(4,5),1,2); axes; grille(1); graduantx.bot; graduanty.ulft; draw courbe1(-5,5,100,4*x/(x**2+1)) withcolor orange; draw titre(placepoint(-2,1.5),4,0.5,btex Anguinéa : $y=\dfrac{4x}{x^2+1}$ etex); endfig; beginfig(14); depart((0,0),(9,10),(1,5),2,1); axes; grille(1); graduantx.bot; graduanty.ulft; draw courbe1(0.001,1.9999,100,sqrt((4*(2-x))/x)) withcolor orange; draw courbe2(0.001,1.9999,100,-sqrt((4*(2-x))/x)) withcolor orange; draw titre(placepoint(2.5,3),3,0.5,btex Cubique d'Agnesi : $xy^2=4(2-x)$ etex); endfig; beginfig(15); depart((0,0),(9,10),(3,5),1.5,1.5); axes; grille(1); graduantx.bot; graduanty.ulft; draw param1(0,2*pi,100,(2*cos(t)+cos(2*t),2*sin(t)-sin(2*t))) withcolor orange; draw titre(placepoint(2,2),4,1,btex\begin{minipage}{6cm}Hypocycloïde à trois rebroussements\\$\left\{\begin{tabular}{l} $x(t)=2\cos t+\cos2t$\\ $y(t)=2\sin t-\sin2t$\\ \end{tabular} \right.$ \end{minipage} etex); endfig; beginfig(16); depart((0,2),(9,10),(1,5),2,2); axes; grille(1); graduantx.bot; graduanty.ulft; draw param1(0,2*pi,100,(2*(cos(t))**2,4*((cos(t))**3)*sin(t))) withcolor orange; draw titre(placepoint(1.5,2),2,1,btex\begin{minipage}{4cm} Quartique piriforme\\$\left\{\begin{tabular}{l} $x(t)=2\cos^2t$\\ $y(t)=4\cos^3t\sin t$\\ \end{tabular} \right.$ \end{minipage} etex); endfig; beginfig(17); depart((0,0),(9,10),(5,5),1,1); axes; grille(1); graduantx.bot; graduanty.ulft; draw polaire1(0.001,pi/4-0.001,100,sqrt(4/tan(2*theta))) withcolor orange; draw polaire1(0.001,pi/4-0.001,100,-sqrt(4/tan(2*theta))) withcolor orange; draw polaire1(-pi/2+0.001,-pi/4-0.001,100,sqrt(4/tan(2*theta))) withcolor orange; draw polaire1(-pi/2+0.001,-pi/4-0.001,100,-sqrt(4/tan(2*theta))) withcolor orange; draw titre(placepoint(-3,-3),4,1.5,btex\begin{minipage}{4cm} Quartique régulière\\$\rho^2=\dfrac{4}{\tan2\theta}$\end{minipage} etex); endfig; beginfig(18); depart((0,0),(9,10),(2,5),0.25,2); axes; grille(1); graduationx(btex $+1$ etex); graduanty.ulft; draw courbe1(-8,28,200,exp(-x/4)*sin(x)) withcolor orange; draw titre(placepoint(12,1),22,0.5,btex Sinusoïde amortie : $y=e^{-\dfrac{x}{4}}\sin x$ etex); endfig; beginfig(19); depart((0,2),(9,10),(5,5),1,1); axes; grille(1); graduantx.bot; graduanty.ulft; draw polaire1(-23,21,500,3/(ch(theta/5))) withcolor orange; draw titre(placepoint(-3,4),3,1.5,btex\begin{minipage}{3cm} Spirale de Poinsot\\$\rho=\dfrac{3}{\mbox{ch}(\theta/5)}$\end{minipage} etex); endfig; end