{"id":16544,"date":"2023-03-10T14:06:33","date_gmt":"2023-03-10T13:06:33","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=16544"},"modified":"2023-06-29T11:16:58","modified_gmt":"2023-06-29T09:16:58","slug":"chapitre-15-trigonometrie","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-15-trigonometrie\/","title":{"rendered":"Chapitre 15 : Trigonom\u00e9trie"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"16544\" class=\"elementor elementor-16544\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-686551ac elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"686551ac\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;,&quot;shape_divider_bottom&quot;:&quot;wave-brush&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 283.5 27.8\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M283.5,9.7c0,0-7.3,4.3-14,4.6c-6.8,0.3-12.6,0-20.9-1.5c-11.3-2-33.1-10.1-44.7-5.7\ts-12.1,4.6-18,7.4c-6.6,3.2-20,9.6-36.6,9.3C131.6,23.5,99.5,7.2,86.3,8c-1.4,0.1-6.6,0.8-10.5,2c-3.8,1.2-9.4,3.8-17,4.7\tc-3.2,0.4-8.3,1.1-14.2,0.9c-1.5-0.1-6.3-0.4-12-1.6c-5.7-1.2-11-3.1-15.8-3.7C6.5,9.2,0,10.8,0,10.8V0h283.5V9.7z M260.8,11.3\tc-0.7-1-2-0.4-4.3-0.4c-2.3,0-6.1-1.2-5.8-1.1c0.3,0.1,3.1,1.5,6,1.9C259.7,12.2,261.4,12.3,260.8,11.3z M242.4,8.6\tc0,0-2.4-0.2-5.6-0.9c-3.2-0.8-10.3-2.8-15.1-3.5c-8.2-1.1-15.8,0-15.1,0.1c0.8,0.1,9.6-0.6,17.6,1.1c3.3,0.7,9.3,2.2,12.4,2.7\tC239.9,8.7,242.4,8.6,242.4,8.6z 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M34.5,12.4c-0.2,0,2.1,0.8,3.3,0.9c1.2,0.1,2,0.1,2-0.2c0-0.3-0.1-0.5-1.6-0.4C36.6,12.8,34.7,12.4,34.5,12.4z M152.2,21.1\tc-0.1,0.1-2.4-0.3-7.5-0.3c-5,0-13.6-2.4-17.2-3.5c-3.6-1.1,10,3.9,16.5,4.1C150.5,21.6,152.3,21,152.2,21.1z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M269.6,18c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC267.7,18.8,269.7,18,269.6,18z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M227.4,9.8c-0.2-0.1-4.5-1-9.5-1.2c-5-0.2-12.7,0.6-12.3,0.5c0.3-0.1,5.9-1.8,13.3-1.2\tS227.6,9.9,227.4,9.8z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M204.5,13.4c-0.1-0.1,2-1,3.2-1.1c1.2-0.1,2,0,2,0.3c0,0.3-0.1,0.5-1.6,0.4\tC206.4,12.9,204.6,13.5,204.5,13.4z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M201,10.6c0-0.1-4.4,1.2-6.3,2.2c-1.9,0.9-6.2,3.1-6.1,3.1c0.1,0.1,4.2-1.6,6.3-2.6\tS201,10.7,201,10.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-75cf729a\" data-id=\"75cf729a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7e5788d elementor-widget elementor-widget-heading\" data-id=\"7e5788d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 15<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7f707a0b elementor-widget elementor-widget-heading\" data-id=\"7f707a0b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Trigonom\u00e9trie<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-91e1497 elementor-widget elementor-widget-text-editor\" data-id=\"91e1497\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-53a3a034\" data-id=\"53a3a034\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7334d0a7 elementor-widget elementor-widget-image\" data-id=\"7334d0a7\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"192\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/cours-maths-4eme.png\" class=\"attachment-medium size-medium wp-image-15214\" alt=\"Cours de math\u00e9matiques de 4\u00e8me\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-066eeca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"066eeca\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cd872c5\" data-id=\"cd872c5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bfa3e8c elementor-widget elementor-widget-spacer\" data-id=\"bfa3e8c\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4bd75bc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4bd75bc\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0b2465f\" data-id=\"0b2465f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-204654a elementor-widget elementor-widget-heading\" data-id=\"204654a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 15 : Trigonom\u00e9trie<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-49face8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"49face8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2e79e07\" data-id=\"2e79e07\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2d84166 elementor-widget elementor-widget-spacer\" data-id=\"2d84166\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0038ae3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0038ae3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0bea944\" data-id=\"0bea944\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bf1b19f elementor-widget elementor-widget-heading\" data-id=\"bf1b19f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">A) Vocabulaire du triangle rectangle<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bcad4fa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bcad4fa\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ee985f3\" data-id=\"ee985f3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-adcc7cf elementor-widget elementor-widget-image\" data-id=\"adcc7cf\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"776\" height=\"298\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-1.png\" class=\"attachment-large size-large wp-image-16553\" alt=\"\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-1.png 776w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-1-300x115.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-1-768x295.png 768w\" sizes=\"auto, (max-width: 776px) 100vw, 776px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fe0d785 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fe0d785\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7fc2dfe\" data-id=\"7fc2dfe\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cb1a407 elementor-widget elementor-widget-video\" data-id=\"cb1a407\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/R6xGLbHXyMo&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3ce7183 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3ce7183\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f2143da\" data-id=\"f2143da\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e447b2c elementor-widget elementor-widget-spacer\" data-id=\"e447b2c\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c05166a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c05166a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9dfb6d7\" data-id=\"9dfb6d7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0ad6eaf elementor-widget elementor-widget-heading\" data-id=\"0ad6eaf\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">B) Cosinus d\u2019un angle aigu dans un triangle rectangle<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bff8e43 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bff8e43\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1676689\" data-id=\"1676689\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c0bb157 elementor-widget elementor-widget-text-editor\" data-id=\"c0bb157\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9 :<\/strong> Dans un triangle $ABC$ rectangle en $A$, le rapport $\\dfrac{BA}{BC}$ ne d\u00e9pend que de la mesure de l&rsquo;angle $\\widehat{ABC}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f12f159 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f12f159\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6febc28\" data-id=\"6febc28\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9277e5e elementor-widget elementor-widget-text-editor\" data-id=\"9277e5e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9monstration :<\/strong>\u00a0 Sur la figure ci-dessous, $ABC$ est un triangle rectangle en $A$ et $A&rsquo;BC&rsquo;$ est un triangle rectangle en $A&rsquo;$. Ces deux triangles ont leur angle aigu de sommet $B$ en commun.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16554 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-2.png\" alt=\"\" width=\"441\" height=\"381\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-2.png 441w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-2-300x259.png 300w\" sizes=\"auto, (max-width: 441px) 100vw, 441px\" \/><\/p><p>Les droites $(AC)$ et $(A&rsquo;C&rsquo;)$ sont toutes les deux perpendiculaires \u00e0 la droite $(AB)$ donc elles sont parall\u00e8les entre elles.<br \/>$A$ appartient au c\u00f4t\u00e9 $[BA&rsquo;]$.<br \/>$C$ appartient au c\u00f4t\u00e9 $[BC&rsquo;]$.<br \/>D&rsquo;apr\u00e8s le th\u00e9or\u00e8me de Thal\u00e8s :<br \/>\\[\\dfrac{BA}{BA&rsquo;}=\\dfrac{BC}{BC&rsquo;}(=\\dfrac{AC}{A&rsquo;C&rsquo;})\\]L&rsquo;\u00e9galit\u00e9 des produits en croix permet d&rsquo;\u00e9crire :<br \/>\\[BA\\times BC&rsquo;=BC\\times BA&rsquo;\\]Ainsi :<br \/>\\[\\dfrac{BA\\times BC&rsquo;}{BC\\times BC&rsquo;}=\\dfrac{BC\\times BA&rsquo;}{BC\\times BC&rsquo;}\\]Donc :<br \/>\\[\\dfrac{BA}{BC}=\\dfrac{BA&rsquo;}{BC&rsquo;}\\]Donc, le rapport $\\dfrac{BA}{BC}$ d\u00e9pend uniquement de la mesure de l&rsquo;angle $\\widehat{ABC}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9830869 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9830869\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d79e19e\" data-id=\"d79e19e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-280246e elementor-widget elementor-widget-text-editor\" data-id=\"280246e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9finition :<\/strong> Dans un triangle rectangle, le <strong>cosinus<\/strong> d\u2019un angle aigu est \u00e9gal au rapport:<br \/>\\[\\dfrac{\\text{longueur du c\u00f4t\u00e9 adjacent \u00e0 cet angle}}{\\text{longueur de l&rsquo; hypot\u00e9nuse}}\\]\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-39cc6f3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"39cc6f3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-8065874\" data-id=\"8065874\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d74be0a elementor-widget elementor-widget-text-editor\" data-id=\"d74be0a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :\u00a0<\/strong><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16555 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-3.png\" alt=\"\" width=\"316\" height=\"215\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-3.png 316w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-3-300x204.png 300w\" sizes=\"auto, (max-width: 316px) 100vw, 316px\" \/><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-d8dd375\" data-id=\"d8dd375\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3f3463f elementor-widget elementor-widget-text-editor\" data-id=\"3f3463f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>\u00a0<\/p><p>\u00a0<\/p><p>\\[cos(\\widehat{BAC})=\\dfrac{AB}{AC}\\]\\[cos(\\widehat{ACB})=\\dfrac{BC}{AC}\\]\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9f979e5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9f979e5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2917bd0\" data-id=\"2917bd0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-81c7a1d elementor-widget elementor-widget-text-editor\" data-id=\"81c7a1d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Remarques :<\/strong><\/p><ul><li>Un cosinus n&rsquo;a pas d&rsquo;unit\u00e9.<\/li><li>Le cosinus d&rsquo;un angle aigu est un nombre toujours compris entre $0$ et $1$.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5a2e68e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5a2e68e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-fd16821\" data-id=\"fd16821\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e3331ac elementor-widget elementor-widget-text-editor\" data-id=\"e3331ac\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Soit $ABC$ un triangle rectangle en $C$ tel que $AB=5~\\text{cm}$<span style=\"font-size: 18px;\"> et $\\widehat{ABC}=25$\u00b0. Calculer la longueur $BC$, arrondir au dixi\u00e8me.<\/span><\/p><p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-4.png\" alt=\"\" width=\"262\" height=\"316\" \/><br \/>Le triangle $ABC$ est rectangle en $C$:<br \/>\\begin{eqnarray*}<br \/>cos(\\widehat{ABC})&amp;=&amp;\\dfrac{BC}{AB}\\\\<br \/>cos(25\\text{\u00b0})&amp;=&amp;\\dfrac{BC}{5}\\\\<br \/>\\dfrac{cos(25\\text{\u00b0})}{1}&amp;=&amp;\\dfrac{BC}{5}\\\\<br \/>BC&amp;=&amp;\\dfrac{5\\times cos(25\\text{\u00b0})}{1}\\\\<br \/>BC&amp;\\approx &amp;4,5~~\\text{cm (On utilise la touche cos de la calculatrice).}<br \/>\\end{eqnarray*}<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-67b4541 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"67b4541\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4e65e3d\" data-id=\"4e65e3d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f986987 elementor-widget elementor-widget-text-editor\" data-id=\"f986987\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :\u00a0<\/strong> Soit $ABC$ un triangle rectangle en $C$ tel que $AC=2~\\text{cm}$ et $BC=5~\\text{cm}$. Calculer la mesure de l\u2019angle $\\widehat{BAC}$, arrondir au degr\u00e9 pr\u00e8s.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16557 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-5.png\" alt=\"\" width=\"254\" height=\"315\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-5.png 254w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/03\/cosinus-5-242x300.png 242w\" sizes=\"auto, (max-width: 254px) 100vw, 254px\" \/><br \/>Le triangle $ABC$ est rectangle en $C$, d&rsquo;apr\u00e8s le th\u00e9or\u00e8me de Pythagore :<br \/>\\begin{eqnarray*}<br \/>AB^{2}&amp;=&amp;AC^{2}+BC^{2}\\\\<br \/>AB^{2}&amp;=&amp;2^{2}+5^{2}\\\\<br \/>AB^{2}&amp;=&amp;4+25\\\\<br \/>AB^{2}&amp;=&amp;29\\\\<br \/>AB&amp;=&amp;\\sqrt{29}\\\\<br \/>AB&amp;\\approx &amp;5,4~\\text{cm}<br \/>\\end{eqnarray*}<br \/>\\begin{eqnarray*}<br \/>cos(\\widehat{BAC})&amp;=&amp;\\dfrac{AC}{AB}\\\\<br \/>cos(\\widehat{BAC})&amp;=&amp;\\dfrac{2}{5,4}\\\\<br \/>\\widehat{BAC}&amp;\\approx &amp;68\\text{\u00b0 (On utilise la touche arccos de la calculatrice).}<br \/>\\end{eqnarray*}<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-24d958b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"24d958b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d52d215\" data-id=\"d52d215\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a2ee758 elementor-widget elementor-widget-video\" data-id=\"a2ee758\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/4cSvjPcSeOI&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ad510e9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ad510e9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-456c33a\" data-id=\"456c33a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f63e489 elementor-widget elementor-widget-spacer\" data-id=\"f63e489\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1f5c062 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1f5c062\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c9ec164\" data-id=\"c9ec164\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-54a7952 elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"54a7952\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/nuage02.apps.education.fr\/index.php\/s\/cke2azETYSctHmE\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-arrow-alt-circle-right\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Exercices corrig\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8611bf8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8611bf8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b7659b4\" data-id=\"b7659b4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a793380 elementor-widget elementor-widget-spacer\" data-id=\"a793380\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Chapitre 15 Trigonom\u00e9trie Chapitre 15 : Trigonom\u00e9trie A) Vocabulaire du triangle rectangle B) Cosinus d\u2019un angle aigu dans un triangle rectangle Propri\u00e9t\u00e9 : Dans un triangle $ABC$ rectangle en $A$, le rapport $dfrac{BA}{BC}$ ne d\u00e9pend que de la mesure de l&rsquo;angle $widehat{ABC}$. D\u00e9monstration :\u00a0 Sur la figure ci-dessous, $ABC$ est un triangle rectangle en $A$ [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":16547,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"page-builder","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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