{"id":2713,"date":"2025-08-13T18:30:02","date_gmt":"2025-08-13T18:30:02","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2713"},"modified":"2025-10-10T17:38:24","modified_gmt":"2025-10-10T17:38:24","slug":"trigonometric-functions-background-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/trigonometric-functions-background-youll-need-3\/","title":{"raw":"Trigonometric Functions: Background You'll Need 3","rendered":"Trigonometric Functions: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Find the radius and diameter of a circle<\/span><\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<h3>radius and diameter<\/h3>\r\n<p data-start=\"2331\" data-end=\"2514\">A radius is the distance from the center of the circle to any point on the circle.<br data-start=\"2417\" data-end=\"2420\" \/>A diameter is twice as long\u2014it stretches all the way across the circle through the center.<\/p>\r\n<p data-start=\"2516\" data-end=\"2590\">[latex]\\text{Diameter} = 2r \\quad \\text{and} \\quad r = \\frac{d}{2}[\/latex]<\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<ol>\r\n \t<li data-start=\"2607\" data-end=\"2662\">Find the diameter if the radius is [latex]7[\/latex] cm.<\/li>\r\n \t<li data-start=\"2607\" data-end=\"2662\">Find the radius if the diameter is [latex]18[\/latex] inches.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"587446\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"587446\"][latex]d = 2r = 2(7) = 14 \\text{ cm}[\/latex] [latex]r = \\frac{d}{2} = \\frac{18}{2} = 9 \\text{ in.}[\/latex][\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313504[\/ohm_question]\r\n\r\n<\/section><section class=\"textbox proTip\" aria-label=\"Pro Tip\">The radius is always half the diameter, and the diameter is always twice the radius.\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Find the radius and diameter of a circle<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<h3>radius and diameter<\/h3>\n<p data-start=\"2331\" data-end=\"2514\">A radius is the distance from the center of the circle to any point on the circle.<br data-start=\"2417\" data-end=\"2420\" \/>A diameter is twice as long\u2014it stretches all the way across the circle through the center.<\/p>\n<p data-start=\"2516\" data-end=\"2590\">[latex]\\text{Diameter} = 2r \\quad \\text{and} \\quad r = \\frac{d}{2}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<ol>\n<li data-start=\"2607\" data-end=\"2662\">Find the diameter if the radius is [latex]7[\/latex] cm.<\/li>\n<li data-start=\"2607\" data-end=\"2662\">Find the radius if the diameter is [latex]18[\/latex] inches.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q587446\">Show Solution<\/button><\/p>\n<div id=\"q587446\" class=\"hidden-answer\" style=\"display: none\">[latex]d = 2r = 2(7) = 14 \\text{ cm}[\/latex] [latex]r = \\frac{d}{2} = \\frac{18}{2} = 9 \\text{ in.}[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313504\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313504&theme=lumen&iframe_resize_id=ohm313504&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">The radius is always half the diameter, and the diameter is always twice the radius.<\/p>\n<\/section>\n","protected":false},"author":67,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":178,"module-header":"background_you_need","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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2713"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2713\/revisions"}],"predecessor-version":[{"id":4606,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2713\/revisions\/4606"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/178"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2713\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2713"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2713"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2713"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}