{"id":822,"date":"2015-12-11T08:47:35","date_gmt":"2015-12-11T13:47:35","guid":{"rendered":"http:\/\/pascal-tic.org\/math\/?page_id=822"},"modified":"2019-08-27T11:47:11","modified_gmt":"2019-08-27T16:47:11","slug":"fonctions-periodiques","status":"publish","type":"page","link":"https:\/\/pascal-tic.org\/math\/fonctions-periodiques\/","title":{"rendered":"Fonctions p\u00e9riodiques"},"content":{"rendered":"<section class=\"l-section wpb_row height_medium\"><div class=\"l-section-h i-cf\"><div class=\"g-cols vc_row via_flex valign_top type_default\"><div class=\"vc_col-sm-8 wpb_column vc_column_container\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"wpb_text_column\"><div class=\"wpb_wrapper\"><h4>Repr\u00e9sentation graphique<\/h4>\n<\/div><\/div><div class=\"w-image align_center us_animate_wfc\"><a href=\"https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/fonctionperiodique-1.png\" ref=\"magnificPopup\" aria-label=\"Lien\" class=\"w-image-h\"><img loading=\"lazy\" decoding=\"async\" width=\"650\" height=\"416\" src=\"https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/fonctionperiodique-1.png\" class=\"attachment-full size-full\" alt=\"\" srcset=\"https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/fonctionperiodique-1.png 650w, https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/fonctionperiodique-1-300x192.png 300w, https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/fonctionperiodique-1-600x384.png 600w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><\/div><\/div><\/div><\/div><div class=\"vc_col-sm-4 wpb_column vc_column_container\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"w-message color_blue with_icon\"><div class=\"w-message-icon\"><i class=\"fas fa-pencil-alt\"><\/i><\/div><div class=\"w-message-body\"><p>\u200bDans une fonction p\u00e9riodique, un <b>cycle<\/b> fait r\u00e9f\u00e9rence au motif qui se r\u00e9p\u00e8te alors que la <b>p\u00e9riode<\/b>\u200b est la dur\u00e9e du cycle selon l&rsquo;axe des x.<\/p>\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/section><section class=\"l-section wpb_row height_medium\"><div class=\"l-section-h i-cf\"><div class=\"g-cols vc_row via_flex valign_top type_default\"><div class=\"vc_col-sm-12 wpb_column vc_column_container\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"w-separator size_medium with_line width_default thick_2 style_solid color_border align_center\"><div class=\"w-separator-h\"><\/div><\/div><div class=\"g-cols wpb_row via_flex valign_top type_default\"><div class=\"vc_col-sm-4 wpb_column vc_column_container\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"wpb_text_column\"><div class=\"wpb_wrapper\"><h4>Exemple de probl\u00e8me<\/h4>\n<p>Voici a repr\u00e9sentation de la fonction p\u00e9riodique <em>f<\/em>. En observant le comportement de celle-ci, d\u00e9termine la valeur de f(8,4).<\/p>\n<\/div><\/div><\/div><\/div><\/div><div class=\"vc_col-sm-8 wpb_column vc_column_container\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"w-image align_center us_animate_afr\"><div class=\"w-image-h\"><img loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"424\" src=\"https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/graphiquefctper_20150325144314_20150325144432-1.png\" class=\"attachment-full size-full\" alt=\"\" srcset=\"https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/graphiquefctper_20150325144314_20150325144432-1.png 606w, https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/graphiquefctper_20150325144314_20150325144432-1-300x210.png 300w, https:\/\/pascal-tic.org\/math\/wp-content\/uploads\/2015\/12\/graphiquefctper_20150325144314_20150325144432-1-600x420.png 600w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"w-tabs style_default switch_click accordion type_togglable has_scrolling\" style=\"--sections-title-size:inherit\"><div class=\"w-tabs-sections titles-align_none icon_chevron cpos_right\"><div class=\"w-tabs-section\" id=\"y32d\"><button aria-controls=\"content-y32d\" class=\"w-tabs-section-header with_icon\"><i class=\"fas fa-puzzle-piece\"><\/i><div class=\"w-tabs-section-title\">Explications<\/div><div class=\"w-tabs-section-control\"><\/div><\/button><div  class=\"w-tabs-section-content\" id=\"content-y32d\" aria-expanded=\"false\"><div class=\"w-tabs-section-content-h i-cf\"><div class=\"wpb_text_column\"><div class=\"wpb_wrapper\"><p>D\u2019abord, lorsque je te demande f(8,4), c&rsquo;est comme si je te demandais de calculer la valeur de y lorsque x vaut 8,4.<\/p>\n<p>Maintenant, observons l&rsquo;\u00e9volution du graphique. La longueur de la p\u00e9riode est 2 et compte trois sections : bleu, rouge et orange. Le nombre de sections importe peu. J&rsquo;ai mis des couleurs uniquement pour t&rsquo;aider \u00e0 bien visualiser le graphique et je vais m&rsquo;y r\u00e9f\u00e9rer par la suite.<\/p>\n<p>La question que l&rsquo;on doit se poser est : <strong>\u00ab Sur quelle section du graphique nous allons tomber lorsque x sera \u00e9gal \u00e0 8,4? \u00bb<\/strong>.<\/p>\n<p>La r\u00e9ponse \u00e0 cette question est <strong>la bleue<\/strong>, car cette partie du graphique d\u00e9bute \u00e0 0, 2, 4, etc. Donc, on peut tr\u00e8s bien s&rsquo;imaginer qu&rsquo;elle aura un d\u00e9part \u00e0 8. De plus, elle se termine \u00e0 1, 3, 5. On peut aussi s&rsquo;imaginer qu&rsquo;elle se termine \u00e0 9. Que retrouve-t-on entre 8 et 9 ? 8,4!<\/p>\n<p>Tu pensais que c&rsquo;\u00e9tait fini? Eh bien non! <strong>Tu dois maintenant trouver l&rsquo;\u00e9quation associ\u00e9 \u00e0 ce segment.<\/strong><\/p>\n<p>On peut d\u00e9duire les coordonn\u00e9es des extr\u00e9mit\u00e9s du segment, puis-ce que cette fonction est p\u00e9riodique et ensuite trouver l&rsquo;\u00e9quation associ\u00e9e : (8 ; 1,5) et (9 ; 2)<\/p>\n<p><strong>\u00c9quation<\/strong> : f(x) = 0,5x &#8211; 2,5<\/p>\n<p>Donc, f(8,4) = 0,5*8,4 &#8211; 2,5 = 1,7<\/p>\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"Repr\u00e9sentation graphique \u200bDans une fonction p\u00e9riodique, un cycle fait r\u00e9f\u00e9rence au motif qui se r\u00e9p\u00e8te alors que la p\u00e9riode\u200b est la dur\u00e9e du cycle selon l'axe des x. Exemple de probl\u00e8me Voici a repr\u00e9sentation de la fonction p\u00e9riodique f. En observant le comportement de celle-ci, d\u00e9termine la valeur de f(8,4). ExplicationsD\u2019abord, lorsque je te demande...","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-822","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages\/822","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/comments?post=822"}],"version-history":[{"count":7,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages\/822\/revisions"}],"predecessor-version":[{"id":2035,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages\/822\/revisions\/2035"}],"wp:attachment":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/media?parent=822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}