{"id":13771,"date":"2018-06-14T23:49:52","date_gmt":"2018-06-14T23:49:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/introduction-to-the-unit-circle-and-sine-and-cosine-functions\/"},"modified":"2021-10-16T20:27:57","modified_gmt":"2021-10-16T20:27:57","slug":"introduction-to-the-unit-circle-and-sine-and-cosine-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/introduction-to-the-unit-circle-and-sine-and-cosine-functions\/","title":{"raw":"Introduction to the Unit Circle and Sine and Cosine Functions","rendered":"Introduction to the Unit Circle and Sine and Cosine Functions"},"content":{"raw":"\n<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Find function values for the sine and cosine of [latex]30^\\circ \\text{ or }\\left(\\frac{\\pi }{6}\\right),45^\\circ \\text{ or }\\left(\\frac{\\pi }{4}\\right)[\/latex] and [latex]{60^\\circ }^{}\\text{or}\\left(\\frac{\\pi }{3}\\right)[\/latex].<\/li>\n<li>Identify the domain and range of sine and cosine functions.<\/li>\n<li>Use reference angles to evaluate trigonometric functions.<\/li>\n<\/ul>\n<\/div>\n<figure id=\"Figure_05_02_001\" class=\"small\">\n[caption id=\"\" align=\"aligncenter\" width=\"488\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3360\/2018\/06\/14234951\/CNX_Precalc_Figure_05_02_0012.jpg\" alt=\"Photo of a ferris wheel.\" width=\"488\" height=\"325\" data-media-type=\"image\/jpg\"> <b>Figure 1.<\/b> The Singapore Flyer is the world\u2019s tallest Ferris wheel. (credit: \"Vibin JK\"\/Flickr)[\/caption]\n<\/figure>\n<p>Looking for a thrill? Then consider a ride on the Singapore Flyer, the world\u2019s tallest Ferris wheel. Located in Singapore, the Ferris wheel soars to a height of 541 feet\u2014a little more than a tenth of a mile! Described as an observation wheel, riders enjoy spectacular views as they travel from the ground to the peak and down again in a repeating pattern. In this section, we will examine this type of revolving motion around a circle. To do so, we need to define the type of circle first, and then place that circle on a coordinate system. Then we can discuss circular motion in terms of the coordinate pairs.<\/p>\n\n","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Find function values for the sine and cosine of [latex]30^\\circ \\text{ or }\\left(\\frac{\\pi }{6}\\right),45^\\circ \\text{ or }\\left(\\frac{\\pi }{4}\\right)[\/latex] and [latex]{60^\\circ }^{}\\text{or}\\left(\\frac{\\pi }{3}\\right)[\/latex].<\/li>\n<li>Identify the domain and range of sine and cosine functions.<\/li>\n<li>Use reference angles to evaluate trigonometric functions.<\/li>\n<\/ul>\n<\/div>\n<figure id=\"Figure_05_02_001\" class=\"small\">\n<div style=\"width: 498px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3360\/2018\/06\/14234951\/CNX_Precalc_Figure_05_02_0012.jpg\" alt=\"Photo of a ferris wheel.\" width=\"488\" height=\"325\" data-media-type=\"image\/jpg\" \/><\/p>\n<p class=\"wp-caption-text\"><b>Figure 1.<\/b> The Singapore Flyer is the world\u2019s tallest Ferris wheel. (credit: &#8220;Vibin JK&#8221;\/Flickr)<\/p>\n<\/div>\n<\/figure>\n<p>Looking for a thrill? Then consider a ride on the Singapore Flyer, the world\u2019s tallest Ferris wheel. Located in Singapore, the Ferris wheel soars to a height of 541 feet\u2014a little more than a tenth of a mile! Described as an observation wheel, riders enjoy spectacular views as they travel from the ground to the peak and down again in a repeating pattern. In this section, we will examine this type of revolving motion around a circle. To do so, we need to define the type of circle first, and then place that circle on a coordinate system. Then we can discuss circular motion in terms of the coordinate pairs.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-13771\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":23485,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-13771","chapter","type-chapter","status-publish","hentry"],"part":13723,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/13771","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/23485"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/13771\/revisions"}],"predecessor-version":[{"id":15506,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/13771\/revisions\/15506"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/13723"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/13771\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=13771"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=13771"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=13771"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=13771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}