{"id":3398,"date":"2024-06-24T16:24:23","date_gmt":"2024-06-24T16:24:23","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3398"},"modified":"2025-08-17T15:59:19","modified_gmt":"2025-08-17T15:59:19","slug":"trigonometric-functions-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/trigonometric-functions-apply-it\/","title":{"raw":"Trigonometric Functions: Apply It","rendered":"Trigonometric Functions: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Switch between degree and radian measurements for angles<\/li>\r\n\t<li>Understand and use the basic rules and relationships in trigonometry<\/li>\r\n\t<li>Analyze trigonometric functions by examining their graphs, identifying cycles, and describing shifts in sine and cosine graphs<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Trigonometric Analysis of a Ferris Wheel<\/h2>\r\n<p class=\"whitespace-pre-wrap break-words\">Trigonometric functions are periodic in nature, meaning they repeat over and over again. Consider riding in a large ferris wheel which slowly rotates around. You enter the ride on a raised platform and complete one full rotation on the Ferris wheel.<\/p>\r\n\r\n[caption id=\"attachment_3915\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-3915\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168.jpeg\" alt=\"Ferris Wheel\" width=\"500\" height=\"375\" \/> Ferris Wheel[\/caption]\r\n\r\n<p>Your height in feet on the ferris wheel after t minutes is described by the equation<\/p>\r\n<p>&nbsp;<\/p>\r\n<p style=\"text-align: center;\">[latex]h(t)=-90 \\cos \\left( \\frac{\\pi}{6}t \\right)+100[\/latex]<\/p>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288224[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288225[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288226[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288227[\/ohm_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Switch between degree and radian measurements for angles<\/li>\n<li>Understand and use the basic rules and relationships in trigonometry<\/li>\n<li>Analyze trigonometric functions by examining their graphs, identifying cycles, and describing shifts in sine and cosine graphs<\/li>\n<\/ul>\n<\/section>\n<h2>Trigonometric Analysis of a Ferris Wheel<\/h2>\n<p class=\"whitespace-pre-wrap break-words\">Trigonometric functions are periodic in nature, meaning they repeat over and over again. Consider riding in a large ferris wheel which slowly rotates around. You enter the ride on a raised platform and complete one full rotation on the Ferris wheel.<\/p>\n<figure id=\"attachment_3915\" aria-describedby=\"caption-attachment-3915\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3915\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168.jpeg\" alt=\"Ferris Wheel\" width=\"500\" height=\"375\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168.jpeg 1000w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168-300x225.jpeg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168-768x576.jpeg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168-65x49.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168-225x169.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/15141423\/pexels-photo-2128168-350x263.jpeg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-3915\" class=\"wp-caption-text\">Ferris Wheel<\/figcaption><\/figure>\n<p>Your height in feet on the ferris wheel after t minutes is described by the equation<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]h(t)=-90 \\cos \\left( \\frac{\\pi}{6}t \\right)+100[\/latex]<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288224\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288224&theme=lumen&iframe_resize_id=ohm288224&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288225\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288225&theme=lumen&iframe_resize_id=ohm288225&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288226\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288226&theme=lumen&iframe_resize_id=ohm288226&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288227\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288227&theme=lumen&iframe_resize_id=ohm288227&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":15,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"White Ferris Wheel\",\"author\":\"Suliman Sallehi\",\"organization\":\"Pexels.com\",\"url\":\"https:\/\/www.pexels.com\/photo\/white-ferris-wheel-2128168\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":759,"module-header":"apply_it","content_attributions":[{"type":"original","description":"White Ferris Wheel","author":"Suliman 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