{"id":3421,"date":"2024-06-24T16:35:54","date_gmt":"2024-06-24T16:35:54","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3421"},"modified":"2025-08-17T22:54:27","modified_gmt":"2025-08-17T22:54:27","slug":"derivatives-of-trigonometric-functions-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/derivatives-of-trigonometric-functions-apply-it\/","title":{"raw":"Derivatives of Trigonometric Functions: Apply It","rendered":"Derivatives of Trigonometric Functions: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate the derivatives of sine and cosine functions, including second derivatives and beyond<\/li>\r\n\t<li>Determine the derivatives for basic trig functions like tangent, cotangent, secant, and cosecant<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Diving Board Dynamics: Unveiling the Secrets of Oscillation<\/h2>\r\n\r\n[caption id=\"attachment_3963\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-3963\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140.jpeg\" alt=\"Point of View of a Person on a Diving Board\" width=\"500\" height=\"375\" \/> View from a diving board[\/caption]\r\n\r\n<p>After a swimmer jumps from a diving board, the end of the board will oscillate (bounce up and down).\u00a0 This oscillation can be modeled by the trigonometric function [latex]s(t)=-15\\cos{t}[\/latex] centimeters [latex]t[\/latex] seconds after the jump.<br \/>\r\n<br \/>\r\n<\/p>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]287934[\/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]287935[\/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]287936[\/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]287937[\/ohm_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate the derivatives of sine and cosine functions, including second derivatives and beyond<\/li>\n<li>Determine the derivatives for basic trig functions like tangent, cotangent, secant, and cosecant<\/li>\n<\/ul>\n<\/section>\n<h2>Diving Board Dynamics: Unveiling the Secrets of Oscillation<\/h2>\n<figure id=\"attachment_3963\" aria-describedby=\"caption-attachment-3963\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3963\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140.jpeg\" alt=\"Point of View of a Person on a Diving Board\" width=\"500\" height=\"375\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140.jpeg 1000w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140-300x225.jpeg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140-768x576.jpeg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140-65x49.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140-225x169.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16171536\/pexels-photo-8688140-350x263.jpeg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-3963\" class=\"wp-caption-text\">View from a diving board<\/figcaption><\/figure>\n<p>After a swimmer jumps from a diving board, the end of the board will oscillate (bounce up and down).\u00a0 This oscillation can be modeled by the trigonometric function [latex]s(t)=-15\\cos{t}[\/latex] centimeters [latex]t[\/latex] seconds after the jump.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm287934\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=287934&theme=lumen&iframe_resize_id=ohm287934&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm287935\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=287935&theme=lumen&iframe_resize_id=ohm287935&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm287936\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=287936&theme=lumen&iframe_resize_id=ohm287936&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm287937\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=287937&theme=lumen&iframe_resize_id=ohm287937&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br 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