<!DOCTYPE html> <html xmlns="http://www.w3.org/1999/xhtml"><head> <!--[ GuppY v5.0.9 CeCILL Copyright (C) 2004-2014 by Laurent Duveau - http://www.freeguppy.org/ ]--> <meta http-equiv="content-type" content="text/html; charset=UTF-8"> <meta name="application-name" content="Casyopée - Fonctions à valeur dans IR² et courbes paramétrées"> <title>Casyopée - Fonctions à valeur dans IR² et courbes paramétrées</title> <meta name="description" content="Casyopée: a learning environment dedicated to functions"> <meta name="generator" content="GuppY CMS"> <meta name="author" content="lagrange"> <meta name="keywords" content="casyopée, functions, mathematics, geodynamic geometry, cas, symbolic computation,"> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"> <meta name="apple-mobile-web-app-capable" content="yes"> <meta name="apple-mobile-web-app-status-bar-style" content="black"> <link rel="shortcut icon" href="https://casyopee.math.univ-paris-diderot.fr/guppy.ico"> <link rel="alternate" type="application/rss+xml" title="Casyopée : Actualité" hreflang="fr" href="https://casyopee.math.univ-paris-diderot.fr/data/fr-news.xml"> <link type="text/css" rel="stylesheet" href="skins/casyop/style.css"> <link type="text/css" rel="stylesheet" href="skins/casyop/jqstyle.css"> <style type="text/css" media="screen"> @import url(inc/auto.css); </style> <style type="text/css" media="print"> @import url(inc/print.css); </style> <link type="text/css" rel="stylesheet" href="inc/csshead/fotorama.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/menubox.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/slidesjs.css"> <script type="text/javascript"> //<![CDATA[ <!-- var charset = "UTF-8"; var site0 = "Casyopée"; var site3 = "https://casyopee.math.univ-paris-diderot.fr/"; var sValue = screen.width + "||" + screen.height + "||" + screen.availWidth + "||" + screen.availHeight; var today = new Date(), expires = new Date(); expires.setTime(today.getTime() + (365*24*60*60*1000)); document.cookie = "GuppYScreen" + "=" + encodeURIComponent(sValue) + ";expires=" + expires.toGMTString(); //--> //]]> </script> <script type="text/javascript" src="inc/hpage.js"></script> <script type="text/javascript" src="inc/jquery-min.js"></script> <script type="text/javascript" src="inc/jquery-migrate-min.js"></script> <script type="text/javascript" src="inc/jqscript.js"></script> <script type="text/javascript" src="inc/jshead/boxmenu_toggle.js"></script> <script type="text/javascript" src="inc/jshead/fotorama.js"></script> <script type="text/javascript" src="inc/jshead/jquery.imagecube.min.js"></script> <script type="text/javascript" src="inc/jshead/sidephoto.js"></script> <script type="text/javascript" src="inc/jshead/slides.min.jquery.js"></script> <script type="text/javascript" src="inc/jshead/slidesjs.js"></script> </head><body> <div style="text-align: center;" class="titre"> <h1>Fonctions à valeur dans IR² et courbes paramétrées</h1> </div> <div style="padding: 6px;"> <p style="margin-left: 24pt;"><a href="pg95.htm#_Toc364184548"><em>Fonctions à valeur dans IR²</em></a></p> <p style="margin-left: 24pt;"><a href="pg95.htm#_Toc364184549"><em>Courbes paramétrées</em></a></p> <h3><span style=""><span style=""><span style=""><a name="_Toc364184548"><span style="font-family: &quot;Times New Roman&quot;;">Fonctions à valeur dans IR²</span></a></span></span></span><span style=""><span style=""><span style=""><span style="font-family: &quot;Times New Roman&quot;;"><o:p></o:p></span></span></span></span></h3> <p class="MsoNormal"><span style=""><span style=""><span style="">Les fonctions à valeur dans IR ² sont entrées par le menu <b>créer fonction</b> entrée <b>par domaine + formule</b>. La seule différence avec les fonctions à valeur dans IR est que dans le champ de saisie, on entre deux formules séparées par une virgule entre crochets, ce qui est cohérent avec les habitudes en mathématiques.</span></span></span></p> <p class="MsoNormal" style="text-align: center;" align="center"><span style=""><span style=""><span style=""><!--[if gte vml 1]><v:shape id="_x0000_i1179" type="#_x0000_t75" style='width:409.5pt;height:159.75pt'> <v:imagedata src="/help/imgFrHelp/image265.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image266.jpg" v:shapes="_x0000_i1179" border="0" height="213" width="546"><!--[endif]--></span></span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span style=""><span style=""><a name="_Toc364193868"></a><a name="_Ref307423608"><span style="">Figure </span></a></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423608'><span style='mso-bookmark:_Toc364193868'></span></span></span></span></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423608'><span style='mso-bookmark:_Toc364193868'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element: field-separator'></span></span></span></span></span></span><![endif]--><span style=""><span style=""><span style=""><span style=""><span style=""><span style="">111</span></span></span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423608'><span style='mso-bookmark:_Toc364193868'></span></span></span></span></span><span style='mso-element:field-end'></span><![endif]--><span style=""><span style=""><span style=""><span style="">&nbsp;: Entrée d une fonction à valeur dans IR ²</span></span></span></span></p> <p class="MsoNormal"><span style=""><span style=""><span style="">L affichage dans le volet algèbre est le même que pour les fonctions à valeur dans IR. On peut faire les mêmes transformations et obtenir chaque sous-fonction par l entrée sous-expressions.</span></span></span></p> <p class="MsoNormal"><span style=""><span style=""><span style=""><!--[if gte vml 1]><v:shape id="_x0000_i1180" type="#_x0000_t75" style='width:523.5pt;height:267pt'> <v:imagedata src="/help/imgFrHelp/image267.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image268.jpg" v:shapes="_x0000_i1180" border="0" height="356" width="698"><!--[endif]--></span></span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span style=""><span style=""><a name="_Toc364193869">Figure </a></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Toc364193869'></span></span></span></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Toc364193869'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span></span></span></span><![endif]--><span style=""><span style=""><span style=""><span style=""><span style="">112</span></span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Toc364193869'></span></span></span></span><span style='mso-element:field-end'></span><![endif]--><span style=""><span style=""><span style=""><span style="">&nbsp;: Fonction à valeur dans IR ²&nbsp;: Transformations et graphes</span></span></span></span></p> <p class="MsoNormal"><span style=""><span style=""><span style="">Le volet graphique affiche avec la même couleur les deux graphes. Le viseur de la trace est plus gros pour la première. C est celui qu il faut déplacer.</span></span></span></p> <h3><span style=""><span style=""><span style=""><a name="_Toc364184549"><span style="font-family: &quot;Times New Roman&quot;;">Courbes paramétrées</span></a></span></span></span><span style=""><span style=""><span style=""><span style="font-family: &quot;Times New Roman&quot;;"> <o:p></o:p></span></span></span></span></h3> <p class="MsoNormal"><span style=""><span style=""><span style="">Une fonction à valeur dans IR² étant entrée, la courbe paramétrée est affichée par le menu <b>créer courbe</b> du volet Géométrie. Quand on déplace le viseur dans la fenêtre graphique, une marque se déplace à la position correspondante sur la courbe (<span style="">Figure <span style="">113</span><!--[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300300037003400320033003600320038000000</w:data> </xml><![endif]--></span>).</span></span></span></p> <p class="MsoNormal" style="text-align: center;" align="center"><span style=""><span style=""><span style=""><!--[if gte vml 1]><v:shape id="_x0000_i1181" type="#_x0000_t75" style='width:442.5pt;height:244.5pt'> <v:imagedata src="/help/imgFrHelp/image269.png" o:title="" cropbottom="3768f"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image270.jpg" v:shapes="_x0000_i1181" border="0" height="326" width="590"><!--[endif]--></span></span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span style=""><span style=""><a name="_Toc364193870"></a><a name="_Ref307423628"><span style="">Figure </span></a></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423628'><span style='mso-bookmark:_Toc364193870'></span></span></span></span></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423628'><span style='mso-bookmark:_Toc364193870'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element: field-separator'></span></span></span></span></span></span><![endif]--><span style=""><span style=""><span style=""><span style=""><span style=""><span style="">113</span></span></span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423628'><span style='mso-bookmark:_Toc364193870'></span></span></span></span></span><span style='mso-element:field-end'></span><![endif]--><span style=""><span style=""><span style=""><span style="">&nbsp;: Courbe paramétrée</span></span></span></span></p> <p class="MsoNormal"><span style=""><span style=""><span style="">On peut bien sûr changer la valeur du paramètre (<span style="">Figure <span style="">114</span><!--[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300300037003400320033003600360035000000</w:data> </xml><![endif]--></span>). </span></span></span></p> <p class="MsoNormal" style="text-align: center;" align="center"><span style=""><span style=""><span style=""><!--[if gte vml 1]><v:shape id="_x0000_i1182" type="#_x0000_t75" style='width:423.75pt;height:235.5pt'> <v:imagedata src="/help/imgFrHelp/image271.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image272.jpg" v:shapes="_x0000_i1182" border="0" height="314" width="565"><!--[endif]--></span></span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span style=""><span style=""><a name="_Toc364193871"></a><a name="_Ref307423665"><span style="">Figure </span></a></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423665'><span style='mso-bookmark:_Toc364193871'></span></span></span></span></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423665'><span style='mso-bookmark:_Toc364193871'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element: field-separator'></span></span></span></span></span></span><![endif]--><span style=""><span style=""><span style=""><span style=""><span style=""><span style="">114</span></span></span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337918'><span style='mso-bookmark:_Ref275337902'><span style='mso-bookmark:_Ref275337737'><span style='mso-bookmark:_Ref307423665'><span style='mso-bookmark:_Toc364193871'></span></span></span></span></span><span style='mso-element:field-end'></span><![endif]--><span style=""><span style=""><span style=""><span style="">&nbsp;: Courbe paramétrée</span></span></span></span></p> </div> </body></html>