{"id":2716,"date":"2025-08-13T18:30:15","date_gmt":"2025-08-13T18:30:15","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2716"},"modified":"2025-10-10T17:15:22","modified_gmt":"2025-10-10T17:15:22","slug":"trigonometric-functions-background-youll-need-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/trigonometric-functions-background-youll-need-4\/","title":{"raw":"Trigonometric Functions: Background You'll Need 4","rendered":"Trigonometric Functions: Background You&#8217;ll Need 4"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Find the area and circumference of a circle<\/span><\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<h3>area and circumference of a circle<\/h3>\r\n<p data-start=\"91\" data-end=\"155\">A circle has two key measurements you\u2019ll often need to find:<\/p>\r\n\r\n<ul data-start=\"157\" data-end=\"274\">\r\n \t<li data-start=\"157\" data-end=\"221\">\r\n<p data-start=\"159\" data-end=\"221\">The circumference is the distance around the circle. The formula for circumference is [latex]C = 2\\pi r \\quad \\text{or} \\quad C = \\pi d[\/latex]<\/p>\r\n<\/li>\r\n \t<li data-start=\"222\" data-end=\"274\">\r\n<p data-start=\"224\" data-end=\"274\">The area (A) is the space inside the circle. The formula for area is [latex]A = \\pi r^2[\/latex]<\/p>\r\n<\/li>\r\n<\/ul>\r\n<p data-start=\"383\" data-end=\"471\">where [latex]r[\/latex] is the radius and [latex]d[\/latex] is the diameter of the circle.<\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p data-start=\"493\" data-end=\"581\">Find the circumference and area of a circle with radius [latex]6[\/latex] meters.<\/p>\r\n<p data-start=\"493\" data-end=\"581\">[reveal-answer q=\"213596\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"213596\"]<\/p>\r\n<p data-start=\"684\" data-end=\"757\">Circumference: [latex] C = 2\\pi r = 2\\pi(6) = 12\\pi \\approx 37.7 \\text{ m} [\/latex]<\/p>\r\n<p data-start=\"684\" data-end=\"757\">Area: [latex] A = \\pi r^2 = \\pi(6)^2 = 36\\pi \\approx 113.1 \\text{ m}^2 [\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/section><section class=\"textbox proTip\" aria-label=\"Pro Tip\">Although calculators have a [latex]\\pi[\/latex] button, it's best to complete the calculations on your calculator <em>without<\/em> [latex]\\pi[\/latex] and then writing [latex]\\pi[\/latex] at the end to give an exact answer in terms of [latex]\\pi[\/latex].<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313503[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Find the area and circumference of a circle<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<h3>area and circumference of a circle<\/h3>\n<p data-start=\"91\" data-end=\"155\">A circle has two key measurements you\u2019ll often need to find:<\/p>\n<ul data-start=\"157\" data-end=\"274\">\n<li data-start=\"157\" data-end=\"221\">\n<p data-start=\"159\" data-end=\"221\">The circumference is the distance around the circle. The formula for circumference is [latex]C = 2\\pi r \\quad \\text{or} \\quad C = \\pi d[\/latex]<\/p>\n<\/li>\n<li data-start=\"222\" data-end=\"274\">\n<p data-start=\"224\" data-end=\"274\">The area (A) is the space inside the circle. The formula for area is [latex]A = \\pi r^2[\/latex]<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"383\" data-end=\"471\">where [latex]r[\/latex] is the radius and [latex]d[\/latex] is the diameter of the circle.<\/p>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p data-start=\"493\" data-end=\"581\">Find the circumference and area of a circle with radius [latex]6[\/latex] meters.<\/p>\n<p data-start=\"493\" data-end=\"581\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q213596\">Show Solution<\/button><\/p>\n<div id=\"q213596\" class=\"hidden-answer\" style=\"display: none\">\n<p data-start=\"684\" data-end=\"757\">Circumference: [latex]C = 2\\pi r = 2\\pi(6) = 12\\pi \\approx 37.7 \\text{ m}[\/latex]<\/p>\n<p data-start=\"684\" data-end=\"757\">Area: [latex]A = \\pi r^2 = \\pi(6)^2 = 36\\pi \\approx 113.1 \\text{ m}^2[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">Although calculators have a [latex]\\pi[\/latex] button, it&#8217;s best to complete the calculations on your calculator <em>without<\/em> [latex]\\pi[\/latex] and then writing [latex]\\pi[\/latex] at the end to give an exact answer in terms of [latex]\\pi[\/latex].<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313503\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313503&theme=lumen&iframe_resize_id=ohm313503&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":67,"menu_order":5,"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\/2716"}],"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":5,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2716\/revisions"}],"predecessor-version":[{"id":4605,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2716\/revisions\/4605"}],"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\/2716\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2716"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2716"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2716"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}