{"id":985,"date":"2025-06-20T17:26:53","date_gmt":"2025-06-20T17:26:53","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/?post_type=chapter&#038;p=985"},"modified":"2025-12-17T16:51:03","modified_gmt":"2025-12-17T16:51:03","slug":"fundamentals-of-parametric-equations-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/fundamentals-of-parametric-equations-apply-it\/","title":{"raw":"Fundamentals of Parametric Equations: Apply It","rendered":"Fundamentals of Parametric Equations: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Create and sketch graphs of curves given their parametric equations<\/li>\r\n \t<li>Convert parametric equations into a regular y = f(x) form by eliminating the parameter<\/li>\r\n \t<li>Recognize and describe the curve called a cycloid<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Designing Motion Paths<\/h2>\r\n<p class=\"whitespace-normal break-words\">You're working with a local community center to design an interactive art installation that will be accessible to families from all backgrounds. The installation features moving lights that trace beautiful paths in a darkened room, creating patterns that visitors can observe and enjoy together.<\/p>\r\n<p class=\"whitespace-normal break-words\">The installation has several components:<\/p>\r\n\r\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\"><strong>Linear Light Paths<\/strong>: Some lights move along straight lines<\/li>\r\n \t<li class=\"whitespace-normal break-words\"><strong>Circular and Elliptical Orbits<\/strong>: Other lights follow curved paths<\/li>\r\n \t<li class=\"whitespace-normal break-words\"><strong>Special Pattern Wheels<\/strong>: A mechanical component creates cycloid patterns using rolling wheels<\/li>\r\n<\/ol>\r\n<p class=\"whitespace-normal break-words\">Your job is to analyze the mathematical equations that control these light movements and ensure the installation works as designed.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313699[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313700[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313701[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313702[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Create and sketch graphs of curves given their parametric equations<\/li>\n<li>Convert parametric equations into a regular y = f(x) form by eliminating the parameter<\/li>\n<li>Recognize and describe the curve called a cycloid<\/li>\n<\/ul>\n<\/section>\n<h2>Designing Motion Paths<\/h2>\n<p class=\"whitespace-normal break-words\">You&#8217;re working with a local community center to design an interactive art installation that will be accessible to families from all backgrounds. The installation features moving lights that trace beautiful paths in a darkened room, creating patterns that visitors can observe and enjoy together.<\/p>\n<p class=\"whitespace-normal break-words\">The installation has several components:<\/p>\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\"><strong>Linear Light Paths<\/strong>: Some lights move along straight lines<\/li>\n<li class=\"whitespace-normal break-words\"><strong>Circular and Elliptical Orbits<\/strong>: Other lights follow curved paths<\/li>\n<li class=\"whitespace-normal break-words\"><strong>Special Pattern Wheels<\/strong>: A mechanical component creates cycloid patterns using rolling wheels<\/li>\n<\/ol>\n<p class=\"whitespace-normal break-words\">Your job is to analyze the mathematical equations that control these light movements and ensure the installation works as designed.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313699\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313699&theme=lumen&iframe_resize_id=ohm313699&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313700\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313700&theme=lumen&iframe_resize_id=ohm313700&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313701\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313701&theme=lumen&iframe_resize_id=ohm313701&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313702\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313702&theme=lumen&iframe_resize_id=ohm313702&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":675,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/985"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":13,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/985\/revisions"}],"predecessor-version":[{"id":2518,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/985\/revisions\/2518"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/675"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/985\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=985"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=985"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=985"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=985"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}