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\351es polaires I \251 Pierre Lantagne (f\351vrier 2001)Coll\350ge de Maisonneuveplantag@edu.cmaisonneuve.qc.cahttp://math.cmaisonneuve.qc.ca/plantagne

Le plan polaire est le plan g\351om\351trique dont les points NiM3JCUickclJnRoZXRhRw== ont comme coordonn\351es cart\351siennes NiM3JCUieEclInlH de telle mani\350re queNiMvJSJ4RyomJSJyRyIiIi0lJGNvc0c2IyUmdGhldGFHRic= et NiMvJSJ5RyomJSJyRyIiIi0lJHNpbkc2IyUmdGhldGFHRic=Et r\351ciproquement, le plan cart\351sien est le plan g\351om\351trique dont les points NiM3JCUieEclInlH ont comme coordonn\351es polaires NiM3JCUickclJnRoZXRhRw== de telle mani\350re queNiMvKiQlInJHIiIjLCYqJCUieEdGJiIiIiokJSJ5R0YmRio= et NiMvLSUkdGFuRzYjJSZ0aGV0YUcqJiUieUciIiIlInhHISIiIllustrons le point de coordonn\351es polaires PNiM3JCIiIyomJSNQaUciIiIiIiQhIiI= dans le plan polaire en ex\351cutant les requ\352tes du bloc ci-dessous.Axe_polaire:=plot([[0,0],[2.5,0]],thickness=2,color=orange): Pole:=plottools[disk]([0,0], .03, color=orange): Arc:=plot([2*cos(theta),2*sin(theta),theta=0..Pi/3],thickness=3,color=navy): Rayon:=plot([[0,0],[2*cos(Pi/3),2*sin(Pi/3)]],color=orange,thickness=2): Point:=plottools[disk]([2*cos(Pi/3),2*sin(Pi/3)], .05, color=black): Texte_1:=plots[textplot]([0.5,1,`| r | = 2`],font=[TIMES,ROMAN,14],color=orange,align={ABOVE,LEFT}): Texte_2:=plots[textplot]([1.8,1,`q=p/3`],font=[SYMBOL,16],color=navy,align={ABOVE,RIGHT}): Texte_3:=plots[textplot]([2*cos(Pi/3)+.1,2*sin(Pi/3),`P`],font=[TIMES,ROMAN,16],color=navy,align={ABOVE,RIGHT}): Elements:=[Pole,Axe_polaire,Arc,Rayon,Point,Texte_1,Texte_2,Texte_3],scaling=constrained:with(plots,display): display(Elements,axes=none);Superposons les axes de coordonn\351es cart\351siennes \340 cette illustration.display(Elements,axes=normal,view=[-1..2,-1..2]);Comme coordonn\351e polaire, le nombre r peut \352tre n\351gatif. Dans ce cas, la distance s\351parant l'origine et le point P est -r, et le c\364t\351 terminal OP est celui d'un angle de NiMsJiUmdGhldGFHIiIiJSNQaUdGJQ==. Ainsi, les \351quationsNiMvLSUkY29zRzYjLCYlJnRoZXRhRyIiIiUjUGlHRikqJiUieEdGKSwkJSJyRyEiIkYv et NiMvLSUkc2luRzYjLCYlJnRoZXRhRyIiIiUjUGlHRikqJiUieUdGKSwkJSJyRyEiIkYv se ram\350nent \351galement aux \351quationsNiMvJSJ4RyomJSJyRyIiIi0lJGNvc0c2IyUmdGhldGFHRic= et NiMvJSJ5RyomJSJyRyIiIi0lJHNpbkc2IyUmdGhldGFHRic=

Les \351quations NiMvJSJ4RyomJSJyRyIiIi0lJGNvc0c2IyUmdGhldGFHRic= et NiMvJSJ5RyomJSJyRyIiIi0lJHNpbkc2IyUmdGhldGFHRic= serviront \340 d\351duire la forme cart\351sienne correspondant la forme polaire d'une \351quation et vice-et-versa.Trouvez l'\351quation cart\351sienne correspondant \340 l'\351quation polaire NiMvJSJyRyomJSJhRyIiIi0lJmNvc2VjRzYjJSZ0aGV0YUdGJw==.Eq1:=r=a*csc(theta);Eq2:=subs(csc(theta)=r/y,r=x^2+y^2,Eq1);Eq3:=Eq2/(x^2+y^2);Sol:=solve(Eq3,{y});L'\351quation polaire NiMvJSJyRyomJSJhRyIiIi0lJmNvc2VjRzYjJSZ0aGV0YUdGJw== repr\351sente donc dans le plan cart\351sien la famille de droites horizontales d'\351quation NiMvJSJ5RyUiYUc=.Trouvez l'\351quation ou les \351quations polaires correspondant \340 l'\351quation cart\351sienne NiMvLCYqJCUieEciIiMiIiIqJCUieUdGJyEiIiokJSJhR0YnEq1:=x^2-y^2 = a^2;Eq2:=subs(x=r*cos(theta),y=r*sin(theta),Eq1);Sol:=solve(Eq2,{r});simplify(Sol[1],[(sin^2)(theta)=(1-cos(2*theta))/2]); simplify(Sol[2],[(sin^2)(theta)=(1-cos(2*theta))/2]);

Dans le plan cart\351sien, une \351quation de la forme NiMvJSJ5Ry0lImZHNiMlInhH d\351crit un certain lieu g\351om\351trique. Une \351quation polaire de la forme NiMvJSJyRy0lImZHNiMlJnRoZXRhRw== d\351crira donc, dans le plan polaire, un certain lieu g\351om\351trique \351galement. Le trac\351 de courbes d'\351quations polaires de la forme NiMvJSJyRy0lImZHNiMlJnRoZXRhRw== peut \352tre r\351alis\351 avec la macro-commande plot de la biblioth\350que principale en sp\351cifiant, en option, le syst\350me de coordonn\351es coords=polar. Par commodit\351, l'afficheur affichera tous les trac\351s avec un rep\350re cart\351sien plut\364t qu'avec un rep\350re polaire. La syntaxe param\351trique de la macro-commande plot est interpr\351t\351e par le simplificateur de telle sorte que - le premier argument de la liste est une fonction de NiMlInRH donnant la valeur du rayon r - le second argument de la liste est une fonction de NiMlInRH donnant la valeur de l'angle NiMlJnRoZXRhRw==plot([r(t),NiMtJSZ0aGV0YUc2IyUidEc=,NiMlInRH=NiMlImFH..NiMlImJH],h,v,coords=polar,options)Alors, pour le trac\351 de courbes d'\351quations polaires de la forme NiMvJSJyRy0lImZHNiMlJnRoZXRhRw==, il faudra prendrela fonction r comme une fonction du param\350tre t : NiMvLSUickc2IyUidEclJnJheW9uRw==la fonction NiMlJnRoZXRhRw== comme la fonction identit\351 NiMvLSUmdGhldGFHNiMlInRHRic=.plot([Rayon,NiMlInRH,NiMlInRH =a..b],h,v,coords=polar,options)Premier exemple: dans le plan polaire, tracez le lieu d'\351quation NiMvJSJyRyIiIg== pour NiMlJnRoZXRhRw== NiMlKGVwc2lsb25H NiM3JCIiISomIiIjIiIiJSNQaUdGJw==,C'est un cercle de rayon unit\351 centr\351 \340 l'origine.plot([1,theta,theta=0..2*Pi],-2..2,-2..2, coords=polar, color=navy, thickness=2, scaling=constrained);Second exemple: dans le plan polaire, tracez le lieu d'\351quation NiMvJSJyRyomIiIjIiIiLSUkc2luRzYjJSZ0aGV0YUdGJw== pour NiMlJnRoZXRhRw== NiMlKGVwc2lsb25H NiM3JCIiISUjUGlH.C'est un cercle de rayon 1 centr\351 au point C[0, 1]plot([2*sin(theta),theta,theta=0..Pi],-1.5..1.5,-0.5..2.5, coords=polar, color=navy, thickness=2, scaling=constrained);Remarquez que le contr\364le de l'affichage des deux graphiques pr\351c\351dents n'a pas \351t\351 fait avec l'option view. Cette fa\347on est propre \340 la syntaxe param\351trique ( plot,parametric ). L'option passe-partout view aurait pu tout aussi bien fait l'affaire bien s\373r.La macro-commande polarplot de la biblioth\350que plots fait de mani\350re plus conviviale le trac\351 d'\351quations polaires de la forme NiMvJSZyYXlvbkctJSJyRzYjJSZ0aGV0YUc=.polarplot(NiMtJSJyRzYjJSZ0aGV0YUc=,NiMlJnRoZXRhRw== =NiMlJmFscGhhRw==..NiMlJWJldGFH,options)Avec cette macro-commande, prenez note que l'\351valuateur consid\350re NiMtJSJyRzYjJSZ0aGV0YUc= comme \351tant la fonction donnant la valeur du rayon.with(plots,polarplot): polarplot(1, color=navy, thickness=2, scaling=constrained);polarplot(2*sin(theta), color=navy, thickness=2, scaling=constrained);ATTENTION: Si l'intervalle de valeurs d'angles NiMlJnRoZXRhRw== n'est pas sp\351cifi\351 dans la macro-commande polarplot, alors implicitement, l'intervalle sera par d\351faut l'intervalle -Pi <= NiMlJnRoZXRhRw== <= Pi .Avec la forme pr\351c\351dente de la macro-commande polarplot, l'unique mani\350re de contr\364ler l'affichage est d'utiliser l'option view.polarplot(2*sin(theta), color=navy, thickness=2, scaling=constrained, view=[-1.5..1.5,-0.5..2.5]);Dans un cas comme dans l'autre, plot avec l'option coords=polar et polarplot ne permettent pas le trac\351 de la r\351ciproque NiMvJSZ0aGV0YUctKSUiZkcsJCIiIiEiIjYjJSJyRw== ni le trac\351 des \351quations de la forme NiMvKiQlInJHIiIjLSUiZkc2IyUmdGhldGFH.Il y a une autre forme de la macro-commande polarplot qui permet le trac\351 d'\351quations polaires autres que celles de la forme NiMvJSJyRy0lImZHNiMlJnRoZXRhRw==.polarplot([NiQtJSJmRzYjJSJ0Ry0lImdHRiU=,NiMlInRH =NiMlJmFscGhhRw==..NiMlJWJldGFH],a..b,c..d,options)Cette forme est la forme param\351trique polaire de la macro-commande polarlot. L'\351valuateur assume quele premier terme de la liste est la formule qui pr\351cise le rayon NiMlInJH en fonction du param\350tre NiMlInRH : NiMvJSJyRy0lImZHNiMlInRH le deuxi\350me terme de la liste est la formule qui pr\351cise l'angle NiMlJnRoZXRhRw== en fonction du param\350tre NiMlInRH :NiMvJSZ0aGV0YUctJSJnRzYjJSJ0Rw==le troisi\350me terme de la liste est l'intervalle de nombres r\351els (radians) dans lequel variera le param\350tre t.polarplot([sin(theta),cos(theta),theta=0..2*Pi], thickness=2, color=orange, scaling=constrained);L'exemple suivant est utile \340 l'occasion de la Saint-Valentin.plottools[rotate](polarplot([abs(t/2),(t/2),t=-2*Pi..2*Pi], numpoints=200, thickness=2, axes=none, scaling=constrained),Pi/2);Les \351quations polaires de la forme NiMvJSJyRy0lImZHNiMlJnRoZXRhRw== peuvent \352tre trac\351es avec cette forme en prenant pour fonction g la fonction identit\351 NiMvLSUiZ0c2IyUidEdGJw==.polarplot([NiQtJSJmRzYjJSJ0R0Ym,NiMlInRH =NiMlJmFscGhhRw==..NiMlJWJldGFH],a..b,c..d,options)polarplot([1,theta,theta=0..2*Pi],-2..2,-2..2, color=navy, thickness=2, scaling=constrained);polarplot([2*sin(theta),theta,theta=0..Pi],-2..2,-1..2, color=navy, thickness=2, scaling=constrained);

Avec une \351quation lin\351aire de la forme NiMvLCgqJiUiYUciIiIlInhHRidGJyomJSJiR0YnJSJ5R0YnRiclImNHRiciIiE=, les \351quations NiMvJSJ4RyomJSJyRyIiIi0lJGNvc0c2IyUmdGhldGFHRic= et NiMvJSJ5RyomJSJyRyIiIi0lJHNpbkc2IyUmdGhldGFHRic= nous conduisent \340 l'\351quationNiMvJSJyRyomLCQlImNHISIiIiIiLCYqJiUiYUdGKS0lJGNvc0c2IyUmdGhldGFHRilGKSomJSJiR0YpLSUkc2luR0YvRilGKUYoEn effet,Eq:=a*x+b*y+c=0;### WARNING: persistent store makes one-argument readlib obsolete readlib(isolate): isolate(subs(x = r*cos(theta),y = r*sin(theta),Eq),r);Obtenez l'\351quation polaire de la droite d'\351quation cart\351sienne NiMvLCgqJiIiIyIiIiUieEdGJ0YnKiYiIiRGJyUieUdGJ0YnRiZGJyIiIQ==. Tracez ensuite cette \351quation polaire.Eq1:=2*x+3*y+2 = 0;Eq2:=subs(x=r*cos(theta),y=r*sin(theta),Eq1);Sol:=isolate(Eq2,r);polarplot([rhs(Sol),theta,theta=-Pi/6..2*Pi],-10..10,-6..8, color=orange);Lorsque NiMvJSJjRyIiIQ==, la droite passe alors par l'origine. Alors, de telles droites ne peuvent s'exprimer par la forme NiMvJSJyRyomLCQlImNHISIiIiIiLCYqJiUiYUdGKS0lJGNvc0c2IyUmdGhldGFHRilGKSomJSJiR0YpLSUkc2luR0YvRilGKUYo.Dans le plan polaire, les droites passant par le p\364le sont \351videmment de la forme NiMlJnRoZXRhRw== = constante. Il suffit donc de conna\356tre leur inclinaision NiMlJnRoZXRhRw==.Tracez la droite d'\351quation polaire NiMvJSZ0aGV0YUcsJComJSNQaUciIiIiIichIiJGKg==.polarplot([t,-Pi/6, t=-8..8],color=orange);Tracez la droite d'\351quation NiMvLCYlInhHIiIiKiYiIidGJiUieUdGJiEiIiIiIQ==.Eq:=x-6*y=0;Sol:=isolate(Eq,y);Puisque NiMvJSJtRyomIiIiRiYiIichIiI=, alors NiMvJSZ0aGV0YUctJSdhcmN0YW5HNiMqJiIiIkYpIiInISIi.polarplot([t,arctan(1/6), t=-12..12],color=orange,view=[-12..12,-4..4]);Dans les cas de droites horizontales NiMvJSJ4RyUiYUc= et des droites verticales NiMvJSJ5RyUiYkc=, la transformation est directe:NiMvKiYlInJHIiIiLSUkY29zRzYjJSZ0aGV0YUdGJiUiYUc= et NiMvKiYlInJHIiIiLSUkc2luRzYjJSZ0aGV0YUdGJiUiYkc=REMARQUE: faire attention aux valeurs de discontinuit\351. droites horizontales: NiMvJSJyRyomJSJhRyIiIi0lJGNvc0c2IyUmdGhldGFHISIi droites verticales: NiMvJSJyRyomJSJhRyIiIi0lJHNpbkc2IyUmdGhldGFHISIiTracer la droite d'\351quation NiMvJSJ4RyIiJA==.polarplot(3/cos(theta),theta=-Pi/4..Pi/4, color=navy, thickness=3, scaling=unconstrained);Tracer la droite d'\351quation NiMvJSJ5RyomIiIkIiIiIiIjISIi.polarplot(3/2/sin(theta),theta=Pi/3..2*Pi/3, color=navy, thickness=3, scaling=unconstrained);

L'\351quation cart\351sienne NiMvLCYqJCUieEciIiMiIiIqJCUieUdGJ0YoKiQlImFHRic= se transforme en \351quation polaire NiMvKiQlInJHIiIjKiQlImFHRiY=. En effet,Eq1:=x^2+y^2 = a^2;Eq2:=subs(x=r*cos(theta),y=r*sin(theta),Eq1);Eq3:=simplify(Eq2);solve(Eq3,{r});Nous avons donc NiMvJSJyRyUiYUc= ou NiMvJSJyRywkJSJhRyEiIg==. Avec des intervalles d'angles NiMlJnRoZXRhRw== appropri\351s, ces deux \351quations repr\351sentent, dans le plan cart\351sien, le m\352me cercle centr\351 \340 l'origine.polarplot(2,theta=0..2*Pi, color=navy, thickness=2, scaling=constrained);polarplot(-2,theta=-Pi..Pi, color=navy, thickness=2, scaling=constrained);Obtenez l'\351quation polaire d'un cercle d'\351quation cart\351sienne NiMvLCYqJCwmJSJ4RyIiIiUiYUchIiIiIiNGKCokJSJ5R0YrRigqJEYpRis=. On reconna\356t que cette \351quation repr\351sente la famille de cercles de rayon |a| centr\351s au point C[a,0].Eq1:=(x-a)^2+y^2=a^2; Eq2:=subs(x=r*cos(theta),y=r*sin(theta),Eq1); Sol:=solve(Eq2,{r});La solution NiMmJSRTb2xHNiMiIiI=,NiMvJSJyRyIiIQ== est \340 rejeter.simplify(Sol[2]);Comme exemple, tracez donc le lieu d'\351quation polaire NiMvJSJyRyomIiIlIiIiLSUkY29zRzYjJSZ0aGV0YUdGJw==.polarplot(4*cos(theta),theta=-Pi..Pi, color=navy, thickness=2, scaling=constrained);Il s'agit effectivement d'un cercle de rayon 2 centr\351 au point C(2,0).Dans le plan polaire, une \351quation polaire de la forme NiMvJSJyRyUiYUc= est celle d'un cercle de centre: (0,0) et de rayon a NiMvJSJyRyooIiIjIiIiJSJhR0YnLSUkY29zRzYjJSZ0aGV0YUdGJw== est celle d'un cercle de centre: (a,0) et de rayon a NiMvJSJyRyooIiIjIiIiJSJhR0YnLSUkc2luRzYjJSZ0aGV0YUdGJw== est celle d'un cercle de centre: (0,a) et de rayon a

Le graphique de l'\351quation polaire NiMvJSJyRy0lImZHNiMsJiUmdGhldGFHIiIiJSZhbHBoYUchIiI= est celui du graphique polaire de NiMvJSJyRy0lImZHNiMlJnRoZXRhRw== ayant subit une rotation d'un angle NiMlJmFscGhhRw==.Si l'angle NiMlJmFscGhhRw== est positif, le graphique initial subit une rotation dans le sens anti-horaire, et si l'angle NiMlJmFscGhhRw== est n\351gatif, la rotation est dans le sens horaire.Dans un m\352me graphique, superposons le trac\351 du cercle pr\351c\351dent et celui de sa rotation d'un angle NiMvJSZhbHBoYUciIyEq degr\351s.Cercle:=polarplot(4*cos(theta),theta=-Pi..Pi, color=navy, thickness=2): Cercle_Rot:=polarplot(4*cos(theta-Pi/2),theta=-Pi..Pi, color=orange, thickness=2):display({Cercle,Cercle_Rot},scaling=constrained);Alors, une \351quation polaire de la forme NiMvJSJyRyooIiIjIiIiJSJhR0YnLSUkY29zRzYjLCYlJnRoZXRhR0YnJSZhbHBoYUchIiJGJw== d\351crit, dans le plan polaire, un cercle de rayon a centr\351 au point CNiM3JCUiYUclJmFscGhhRw==

\300 l'aide de la macro-commande setoptions de l'extension plots, rendons globales les options suivantes: color= orange thickness=2 scaling=constrained.with(plots,setoptions): setoptions(color=orange,thickness=2,scaling=constrained):

Formes g\351n\351rales: NiMvJSJyRywmJSJhRyIiIiomJSJiR0YnLSUkY29zRzYjJSZ0aGV0YUdGJ0Yn et NiMvJSJyRywmJSJhRyIiIiomJSJiR0YnLSUkc2luRzYjJSZ0aGV0YUdGJ0Yn En g\351n\351ral: |a| >= |b| cardio\357de |a| < |b| lima\347onpolarplot(2+2*cos(theta),theta=0..2*Pi);polarplot(-2+2*cos(theta),theta=0..2*Pi);polarplot(1+2*cos(theta),theta=0..2*Pi);polarplot(3+2*cos(theta),theta=0..2*Pi);

Forme g\351n\351rale: NiMvJSJyRyomJSJhRyIiIi0lJGNvc0c2IyomJSJuR0YnJSZ0aGV0YUdGJ0Yn et NiMvJSJyRyomJSJhRyIiIi0lJHNpbkc2IyUmdGhldGFHRic=polarplot(4*cos(2*theta),theta=0..2*Pi,color=navy);polarplot(5*sin(4*theta),theta=0..2*Pi,color=navy);polarplot(4*cos(2*(theta+Pi/4)),theta=0..2*Pi,color=navy);

Forme g\351n\351rale: NiMvKiQlInJHIiIjKiYlImFHRiYtJSRjb3NHNiMqJkYmIiIiJSZ0aGV0YUdGLUYt.A:=polarplot(4*cos(2*theta),theta=-Pi/4..Pi/4): B:=polarplot(-4*cos(2*theta),theta=-Pi/4..Pi/4):plots[display](A,B);

Soit les cercles d'\351quations polaires NiMvJSJyRyomIiIlIiIiLSUkc2luRzYjJSZ0aGV0YUdGJw== et NiMvJSJyRyomIiIlIiIiLSUkY29zRzYjJSZ0aGV0YUdGJw==. Trouvez les coordonn\351es des points d'intersection de ces deux cercles.C1:=polarplot(4*sin(theta),theta=0..Pi): C2:=polarplot(4*cos(theta),theta=0..Pi,color=navy):plots[display]([C1,C2]);Eq_1:= r=4*sin(theta); Eq_2:= r=4*cos(theta);solve({Eq_1,Eq_2},{r,theta});Le graphique pr\351c\351dent montre clairement que l'origine est aussi un point d'intersection.M\352me si nous voulions obtenir de l'\351valuateur toutes les solutions, on ne pourra pas d\351duire ce point d'intersection. En effet,_EnvAllSolutions:=true;solve({Eq_1,Eq_2},{r,theta});Ce point d'intersection ne peut pas \352tre rep\351r\351e par la r\351solution simultan\351e des deux \351quations polaires. La valeur NiMvJSJyRyIiIQ== ne peut \352tre obtenue dans les deux \351quations simultan\351ment par un m\352me angle NiMlJnRoZXRhRw==. On doit donc s'inspirer des trac\351s des deux graphiques.Les deux points d'intersection sont donc NiMtJSJQRzYkIiIhRiY= et NiMtJSJRRzYkKiYiIiMiIiItJSVzcXJ0RzYjRidGKComJSNQaUdGKCIiJSEiIg==.REMARQUETrouver les points d'intersection de deux courbes consiste, en quelque sorte, \340 r\351soudre simultan\351ment leurs \351quations. La r\351solution simultan\351e de deux \351quations polaires ne donnent pas, s'il existe, le point d'intersection au p\364le. Il ne faut pas en \352tre surpris, car la coordonn\351e NiMlJnRoZXRhRw== du p\364le est ind\351termin\351e. Dans ce cas, s'il existe NiMmJSZ0aGV0YUc2IyIiIg==et NiMmJSZ0aGV0YUc2IyIiIw==o\371 NiMvJSJyRyYlImZHNiMiIiI=(NiMmJSZ0aGV0YUc2IyIiIg==) = 0 et NiMvJSJyRyYlImZHNiMiIiM=(NiMmJSZ0aGV0YUc2IyIiIw==) = 0, alors les deux courbes se rencontrent au p\364le.

Trouvez les coordonn\351es des points d'intersection entre la cardio\357de NiMvJSJyRywmIiIjIiIiKiZGJkYnLSUkY29zRzYjJSZ0aGV0YUdGJ0Yn et le cercle NiMvJSJyRyIiJA==.C1:=polarplot(2+2*cos(theta),theta=0..2*Pi): C2:=polarplot(3,theta=0..2*Pi,color=navy):plots[display]([C1,C2]);Eq_1:= r=2+2*cos(theta); Eq_2:= r=3;solve({Eq_1,Eq_2},{r,theta});Les deux points d'intersections sont obtenus avec NiMvJSZ0aGV0YUcqJiUjUGlHIiIiIiIkISIi (_B1 = 0 et _Z1 = 0) et avec NiMvJSZ0aGV0YUcsJComJSNQaUciIiIiIiQhIiJGKg== (_B1 = 1 et _Z1 = 0).Dans les deux cas, r = 3.Les points d'intersections NiMtJSJQRzYkIiIkLCQqJiUjUGlHIiIiRiYhIiJGKw== et NiMtJSJRRzYkIiIkKiYlI1BpRyIiIkYmISIi.

Trouvez les coordonn\351es des points d'intersection entre la cardio\357de NiMvJSJyRywmIiIiRiYtJSRzaW5HNiMlJnRoZXRhRyEiIg== et le cercle NiMvJSJyRy0lJHNpbkc2IyUmdGhldGFH.C1:=polarplot(1-sin(theta),theta=0..2*Pi): C2:=polarplot(sin(theta),theta=0..2*Pi,color=navy):plots[display]([C1,C2]);Eq_1:= r=1-sin(theta); Eq_2:= r=sin(theta);solve({Eq_1,Eq_2},{r,theta});Deux points d'intersection sont obtenus avec NiMvJSZ0aGV0YUcqJiUjUGlHIiIiIiInISIi (_B1 = 0 et _Z1 = 0) et avec NiMvJSZ0aGV0YUcqKCIiJiIiIiUjUGlHRiciIichIiI= (_B1 = 1 et _Z1 = 0).Dans les deux cas, NiMvJSJyRyomIiIiRiYiIiMhIiI=. En effetr=sin(Pi/6); r=sin(5*Pi/6);Le troisi\350me point d'intersection peut \352tre d\351duit \340 l'aide du graphique.Les points d'intersection sont donc NiMtJSJQRzYkIiIhRiY=, NiMtJSJRRzYkKiYiIiJGJyIiIyEiIiomJSNQaUdGJyIiJ0Yp et NiMtJSJSRzYkKiYiIiJGJyIiIyEiIiooIiImRiclI1BpR0YnIiInRik=.

Trouvez les coordonn\351es des points d'intersection entre la rosace NiMvJSJyRyomIiIlIiIiLSUkY29zRzYjKiYiIiNGJyUmdGhldGFHRidGJw== et le cercle NiMvJSJyRyIiIw==.C1:=polarplot(4*cos(2*theta),theta=0..2*Pi): C2:=polarplot(2,theta=0..2*Pi,color=navy):plots[display]([C1,C2]);Trouvons les coordonn\351es des huit points d'intersection.Eq_1:= r=4*cos(2*theta); Eq_2:= r=2;solve({Eq_1,Eq_2},{r,theta});L'\351valuateur nous r\351v\350le seulement quatre points d'intersection obtenus avec NiMvJSZ0aGV0YUcqJiUjUGlHIiIiIiInISIi (_B1 = 0 et _Z1 = 0), NiMvJSZ0aGV0YUcqKCIiJiIiIiUjUGlHRiciIichIiI= (_B1 = 1 et _Z1 = 1), NiMvJSZ0aGV0YUcqKCIiKCIiIiUjUGlHRiciIichIiI= (_B1 = 0 et _Z1 = 1), NiMvJSZ0aGV0YUcqKCIjNiIiIiUjUGlHRiciIichIiI= (_B1 = 1 et _Z1 = 2).Pour obtenir les quatres autres points d'intersection, on doit alors s'inspirer des trac\351s des deux graphiques. En fait, il faut s'inspirer de leurs caract\351ristiques de sym\351trie par rapport aux droites NiMvJSJ5RyomJSNQaUciIiIiIiUhIiI= et NiMvJSJ5RyooIiIkIiIiJSNQaUdGJyIiJSEiIg==. NiMvJSZ0aGV0YUcqJiUjUGlHIiIiIiIkISIi , NiMvJSZ0aGV0YUcqKCIiIyIiIiUjUGlHRiciIiQhIiI= , NiMvJSZ0aGV0YUcqKCIiJSIiIiUjUGlHRiciIiQhIiI= , NiMvJSZ0aGV0YUcqKCIiJiIiIiUjUGlHRiciIiQhIiI= .Les huit points d'intersection sont: NiMtJSJQRzYkIiIjKiYlI1BpRyIiIiIiJyEiIg==, NiMtJSJQRzYkIiIjKiYlI1BpRyIiIiIiJCEiIg==, NiMtJSJQRzYkIiIjKihGJiIiIiUjUGlHRigiIiQhIiI=, NiMtJSJQRzYkIiIjKigiIiYiIiIlI1BpR0YpIiInISIi, NiMtJSJQRzYkIiIjKigiIigiIiIlI1BpR0YpIiInISIi, NiMtJSJQRzYkIiIjKigiIiUiIiIlI1BpR0YpIiIkISIi, NiMtJSJQRzYkIiIjKigiIiYiIiIlI1BpR0YpIiIkISIi et NiMtJSJQRzYkIiIjKigiIzYiIiIlI1BpR0YpIiInISIi.REMARQUELa difficult\351 de trouver toutes les solutions d\351coule du fait qu'un m\352me point en coordonn\351es polaires poss\350de une multitude de repr\351sentation. Il en d\351coule que l'\351quation polaire d'un lieu peut ne pas \352tre unique. Par exemple, l'\351quation NiMvJSJyRyomIiIlIiIiLSUkY29zRzYjKiYiIiNGJyUmdGhldGFHRidGJw== et l'\351quation NiMvJSJyRywkKiYiIiUiIiItJSRjb3NHNiMsJiomIiIjRiglJnRoZXRhR0YoRiglI1BpR0YoRighIiI= repr\351sentent le m\352me lieu. En effet,Lieux_A:=polarplot([2,4*cos(2*theta)],theta=0..2*Pi, color=[navy,orange]):Lieux_B:=polarplot([-2,-4*cos(2*theta+Pi)],theta=0..2*Pi, color=[navy,orange]):Lieux:=array(1..2,[Lieux_A,Lieux_B]):display(Lieux);Alors, r\351solvons simultan\351ment NiMvJSJyRywkIiIjISIi et NiMvJSJyRywkKiYiIiUiIiItJSRjb3NHNiMsJiomIiIjRiglJnRoZXRhR0YoRiglI1BpR0YoRighIiI=.solve({r=-2,r=-4*cos(2*theta+Pi)},{r,theta});

Spirale \351quiangulairepolarplot(theta/12,theta=0..18*Pi);Spirale logarithmiquepolarplot(4*exp(-theta/12),theta=0..18*Pi);Papillonpolarplot(exp(cos(theta))-2*cos(4*theta),theta=0..2*Pi);Rotation dans le sens trigonom\351trique d'un angle de NiMqJiUjUGlHIiIiIiIjISIi radian.polarplot(exp(cos(theta-Pi/2))-2*cos(4*(theta-Pi/2)),theta=-Pi/2..3*Pi/2);Autres courbespolarplot(2+7*sin(3*theta),theta=0..2*Pi);polarplot(cos(7*theta/4),theta=0..8*Pi);plot([theta,1+cos(theta/2),theta=0..4*Pi]);polarplot(1+cos(theta/2),theta=0..4*Pi);NiMvKiQlInJHIiIjKiYiIiUiIiItJSRjb3NHNiMlJnRoZXRhR0YpA:=polarplot(sqrt(4*cos(theta)),theta=-Pi/2..Pi/2,numpoints=200): B:=polarplot(-sqrt(4*cos(theta)),theta=-Pi/2..Pi/2,numpoints=200):plots[display](A,B);Rotation dans le sens anti-horaire d'un angle de NiMqJiUjUGlHIiIiIiIkISIi radian.NiMvKiQlInJHIiIjKiYiIiUiIiItJSRjb3NHNiMsJiUmdGhldGFHRikqJiUjUGlHRikiIiQhIiJGMkYpA:=polarplot(sqrt(4*cos(theta-Pi/3)),theta=-Pi/6..5*Pi/6,numpoints=200): B:=polarplot(-sqrt(4*cos(theta-Pi/3)),theta=-Pi/6..5*Pi/6,numpoints=200):plots[display](A,B);NiMvKiQlInJHIiIjKiYiIiUiIiItJSRzaW5HNiMqJkYmRiklJnRoZXRhR0YpRik=A:=polarplot(sqrt(4*sin(2*theta)),theta=0..Pi/2,numpoints=200): B:=polarplot(-sqrt(4*sin(2*theta)),theta=0..Pi/2,numpoints=200):plots[display](A,B);NiMvKiQlInJHIiIlKiZGJiIiIi0lJHNpbkc2IyomIiIjRiglJnRoZXRhR0YoRig=A:=polarplot(surd(4*sin(2*(theta)),4),theta=0..Pi/2,numpoints=200): B:=polarplot(-surd(4*sin(2*(theta)),4),theta=0..Pi/2,numpoints=200):plots[display](A,B);