{"id":2872,"date":"2018-07-30T12:06:43","date_gmt":"2018-07-30T12:06:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/?post_type=chapter&#038;p=2872"},"modified":"2018-07-30T12:06:43","modified_gmt":"2018-07-30T12:06:43","slug":"introduction-to-trigonometric-identities-and-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/chapter\/introduction-to-trigonometric-identities-and-equations\/","title":{"raw":"Introduction to Trigonometric Identities and Equations","rendered":"Introduction to Trigonometric Identities and Equations"},"content":{"raw":"<div class=\"splash\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"975\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3252\/2018\/07\/19143831\/CNX_Precalc_Figure_07_00_001_CAT.jpg\" alt=\"\" width=\"975\" height=\"429\" \/> <strong>Figure 1. <\/strong>A sine wave models disturbance. (credit: modification of work by Mikael Altemark, Flickr).[\/caption]\r\n\r\n<\/div>\r\n<p id=\"fs-id2436739\">Math is everywhere, even in places we might not immediately recognize. For example, mathematical relationships describe the transmission of images, light, and sound. The sinusoidal graph in <a class=\"autogenerated-content\" href=\"#Figure_07_00_001\">(Figure)<\/a> models music playing on a phone, radio, or computer. Such graphs are described using trigonometric equations and functions. In this chapter, we discuss how to manipulate trigonometric equations algebraically by applying various formulas and trigonometric identities. We will also investigate some of the ways that trigonometric equations are used to model real-life phenomena.<\/p>","rendered":"<div class=\"splash\">\n<div style=\"width: 985px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3252\/2018\/07\/19143831\/CNX_Precalc_Figure_07_00_001_CAT.jpg\" alt=\"\" width=\"975\" height=\"429\" \/><\/p>\n<p class=\"wp-caption-text\"><strong>Figure 1. <\/strong>A sine wave models disturbance. (credit: modification of work by Mikael Altemark, Flickr).<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id2436739\">Math is everywhere, even in places we might not immediately recognize. For example, mathematical relationships describe the transmission of images, light, and sound. The sinusoidal graph in <a class=\"autogenerated-content\" href=\"#Figure_07_00_001\">(Figure)<\/a> models music playing on a phone, radio, or computer. Such graphs are described using trigonometric equations and functions. In this chapter, we discuss how to manipulate trigonometric equations algebraically by applying various formulas and trigonometric identities. We will also investigate some of the ways that trigonometric equations are used to model real-life phenomena.<\/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-2872\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Algebra and Trigonometry. <strong>Authored by<\/strong>: Jay Abramson, et. al. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/13ac107a-f15f-49d2-97e8-60ab2e3b519c@11.1\">http:\/\/cnx.org\/contents\/13ac107a-f15f-49d2-97e8-60ab2e3b519c@11.1<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/13ac107a-f15f-49d2-97e8-60ab2e3b519c@11.1<\/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":53384,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Algebra and Trigonometry\",\"author\":\"Jay Abramson, et. al\",\"organization\":\"OpenStax CNX\",\"url\":\"http:\/\/cnx.org\/contents\/13ac107a-f15f-49d2-97e8-60ab2e3b519c@11.1\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/13ac107a-f15f-49d2-97e8-60ab2e3b519c@11.1\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2872","chapter","type-chapter","status-publish","hentry"],"part":2869,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/pressbooks\/v2\/chapters\/2872","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/wp\/v2\/users\/53384"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/pressbooks\/v2\/chapters\/2872\/revisions"}],"predecessor-version":[{"id":3687,"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/pressbooks\/v2\/chapters\/2872\/revisions\/3687"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/pressbooks\/v2\/parts\/2869"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/pressbooks\/v2\/chapters\/2872\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/wp\/v2\/media?parent=2872"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/pressbooks\/v2\/chapter-type?post=2872"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/wp\/v2\/contributor?post=2872"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-osalgebratrig\/wp-json\/wp\/v2\/license?post=2872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}