{"id":3224,"date":"2025-08-15T23:33:15","date_gmt":"2025-08-15T23:33:15","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3224"},"modified":"2025-10-09T16:57:18","modified_gmt":"2025-10-09T16:57:18","slug":"arcs-and-sectors-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/arcs-and-sectors-apply-it\/","title":{"raw":"Arcs and Sectors: Apply It","rendered":"Arcs and Sectors: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Find the length of a circular arc.<\/li>\r\n \t<li>Find the area of a sector of a circle.<\/li>\r\n \t<li>Use linear and angular speed to describe motion on a circular path.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<div class=\"flex-1 flex flex-col gap-3 px-4 max-w-3xl mx-auto w-full pt-1\">\r\n<div data-test-render-count=\"1\">\r\n<div class=\"group relative pb-3\" data-is-streaming=\"false\">\r\n<div class=\"font-claude-response relative leading-[1.65rem] [&amp;_pre&gt;div]:bg-bg-000\/50 [&amp;_pre&gt;div]:border-0.5 [&amp;_pre&gt;div]:border-border-400 [&amp;_.ignore-pre-bg&gt;div]:bg-transparent [&amp;_.standard-markdown_:is(p,blockquote,h1,h2,h3,h4,h5,h6)]:pl-2 [&amp;_.standard-markdown_:is(p,blockquote,ul,ol,h1,h2,h3,h4,h5,h6)]:pr-8 [&amp;_.progressive-markdown_:is(p,blockquote,h1,h2,h3,h4,h5,h6)]:pl-2 [&amp;_.progressive-markdown_:is(p,blockquote,ul,ol,h1,h2,h3,h4,h5,h6)]:pr-8\">\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 standard-markdown\">\r\n<p class=\"whitespace-normal break-words\">Circular motion is everywhere\u2014from the hands of a clock to the rotation of a Ferris wheel, from irrigation systems watering crops to satellites orbiting Earth. Understanding arc length, sector area, and angular speed allows us to analyze and describe these circular motions precisely. In this page, you'll apply these concepts to analyze a real Ferris wheel attraction.<\/p>\r\n\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">The London Eye Ferris Wheel<\/h2>\r\n<p class=\"whitespace-normal break-words\">The London Eye is one of the world's largest observation wheels, located on the banks of the River Thames. This giant Ferris wheel allows passengers to view the entire city from enclosed capsules as it slowly rotates.<\/p>\r\n<p class=\"whitespace-normal break-words\"><strong>London Eye Specifications:<\/strong><\/p>\r\n\r\n<ul class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-disc space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">Radius: 60 meters (from center to passenger capsule)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">One complete rotation: 30 minutes<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Operates continuously during business hours<\/li>\r\n<\/ul>\r\n<section class=\"textbox recall\" aria-label=\"Recall\">Arc length - The distance along the curved path of a circle between two points, calculated using [latex]s = r\\theta[\/latex] where [latex]r[\/latex] is the radius and [latex]\\theta[\/latex] is the angle in radians.\r\n<p class=\"whitespace-normal break-words\">Sector - A region of a circle bounded by two radii and the intercepted arc, like a slice of pie. The area is calculated using [latex]A = \\frac{1}{2}\\theta r^2[\/latex] where [latex]\\theta[\/latex] is in radians.<\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-normal break-words\">A passenger boards the London Eye and stays on for a 10-minute segment of the ride.<\/p>\r\n\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li class=\"whitespace-normal break-words\">What angle (in both degrees and radians) does the wheel rotate through in 10 minutes?<\/li>\r\n \t<li class=\"whitespace-normal break-words\">What distance does the passenger travel along the circular path during these 10 minutes?<\/li>\r\n \t<li class=\"whitespace-normal break-words\">If the wheel is divided into 32 passenger capsules equally spaced around the circle, what is the area of the sector between two adjacent capsules?<\/li>\r\n \t<li class=\"whitespace-normal break-words\">What is the angular speed of the wheel in radians per minute?<\/li>\r\n \t<li class=\"whitespace-normal break-words\">What is the linear speed of a passenger in meters per minute? Convert this to kilometers per hour.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"856919\"]Show Solutions[\/reveal-answer]\r\n[hidden-answer a=\"856919\"]\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>\r\n<p class=\"whitespace-normal break-words\">The wheel completes one full rotation (360\u00b0 or [latex]2\\pi[\/latex] radians) in 30 minutes.<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">In 10 minutes, the wheel completes: [latex]\\frac{10 \\text{ minutes}}{30 \\text{ minutes}} = \\frac{1}{3} \\text{ of a rotation}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">In degrees: [latex]\\frac{1}{3} \\times 360\u00b0 = 120\u00b0[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">In radians: [latex]\\frac{1}{3} \\times 2\\pi = \\frac{2\\pi}{3} \\text{ radians}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">The wheel rotates through 120\u00b0 or [latex]\\frac{2\\pi}{3}[\/latex] radians in 10 minutes.<\/p>\r\n<\/li>\r\n \t<li>\r\n<p class=\"whitespace-normal break-words\">Using the arc length formula [latex]s = r\\theta[\/latex], where [latex]\\theta[\/latex] must be in radians:<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} s &amp;= r\\theta \\\\ &amp;= 60 \\text{ meters} \\times \\frac{2\\pi}{3} \\\\ &amp;= \\frac{120\\pi}{3} \\\\ &amp;= 40\\pi \\\\ &amp;\\approx 125.66 \\text{ meters} \\end{aligned}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">The passenger travels approximately 125.66 meters along the circular path.<\/p>\r\n<\/li>\r\n \t<li>\r\n<p class=\"whitespace-normal break-words\">With 32 equally spaced capsules, the angle between adjacent capsules is:<\/p>\r\n<p class=\"whitespace-normal break-words\">[latex]\\theta = \\frac{2\\pi}{32} = \\frac{\\pi}{16} \\text{ radians}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">Using the sector area formula [latex]A = \\frac{1}{2}\\theta r^2[\/latex]:<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} A &amp;= \\frac{1}{2}\\theta r^2 \\\\ &amp;= \\frac{1}{2} \\times \\frac{\\pi}{16} \\times (60)^2 \\\\ &amp;= \\frac{1}{2} \\times \\frac{\\pi}{16} \\times 3600 \\\\ &amp;= \\frac{3600\\pi}{32} \\\\ &amp;= \\frac{225\\pi}{2} \\\\ &amp;\\approx 353.43 \\text{ square meters} \\end{aligned}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">The sector area between two adjacent capsules is approximately 353.43 square meters.<\/p>\r\n<\/li>\r\n \t<li>\r\n<p class=\"whitespace-normal break-words\">Angular speed is the rate of angular rotation, calculated as [latex]\\omega = \\frac{\\theta}{t}[\/latex].<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">For one complete rotation:\r\n\r\n[latex]\\begin{aligned} \\omega &amp;= \\frac{\\theta}{t} \\\\ &amp;= \\frac{2\\pi \\text{ radians}}{30 \\text{ minutes}} \\\\ &amp;= \\frac{2\\pi}{30} \\\\ &amp;= \\frac{\\pi}{15} \\\\ &amp;\\approx 0.209 \\text{ radians per minute} \\end{aligned}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">The angular speed of the London Eye is [latex]\\frac{\\pi}{15}[\/latex] radians per minute or approximately 0.209 rad\/min.<\/p>\r\n<\/li>\r\n \t<li>\r\n<p class=\"whitespace-normal break-words\">Linear speed is the actual distance traveled per unit time along the circular path. It relates to angular speed by [latex]v = r\\omega[\/latex].<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} v &amp;= r\\omega \\ &amp;= 60 \\text{ meters} \\times \\frac{\\pi}{15} \\text{ rad\/min} \\ &amp;= \\frac{60\\pi}{15} \\ &amp;= 4\\pi \\ &amp;\\approx 12.57 \\text{ meters per minute} \\end{aligned}[\/latex]<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">Converting to kilometers per hour: [latex]\\begin{aligned} v &amp;= 12.57 \\frac{\\text{meters}}{\\cancel{\\text{minute}}} \\times \\frac{1 \\text{ km}}{1000 \\text{ meters}} \\times \\frac{60 \\cancel{\\text{minutes}}}{1 \\text{ hour}} \\ &amp;= \\frac{12.57 \\times 60}{1000} \\\\ &amp;\\approx 0.754 \\text{ km\/h} \\end{aligned}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">The linear speed of a passenger is approximately 12.57 meters per minute or 0.754 km\/h.<\/p>\r\n<p class=\"whitespace-normal break-words\">This slow speed explains why passengers can easily board and exit while the wheel continues moving!<\/p>\r\n<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox proTip\" aria-label=\"Pro Tip\">Sector area [latex]A = \\frac{1}{2}\\theta r^2[\/latex] represents the fraction [latex]\\frac{\\theta}{2\\pi}[\/latex] of the total circle area [latex]\\pi r^2[\/latex]. This formula only works when [latex]\\theta[\/latex] is in radians.<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">A smaller Ferris wheel at a carnival has a radius of 8 meters and completes one full rotation every 2 minutes.<\/p>\r\n\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li class=\"whitespace-normal break-words\">What angle does the wheel rotate through in 45 seconds? Express your answer in radians.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">How far does a passenger travel in 45 seconds?<\/li>\r\n \t<li class=\"whitespace-normal break-words\">What is the angular speed of the wheel in radians per second?<\/li>\r\n \t<li class=\"whitespace-normal break-words\">What is the linear speed of a passenger in meters per second?<\/li>\r\n<\/ol>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Find the length of a circular arc.<\/li>\n<li>Find the area of a sector of a circle.<\/li>\n<li>Use linear and angular speed to describe motion on a circular path.<\/li>\n<\/ul>\n<\/section>\n<div class=\"flex-1 flex flex-col gap-3 px-4 max-w-3xl mx-auto w-full pt-1\">\n<div data-test-render-count=\"1\">\n<div class=\"group relative pb-3\" data-is-streaming=\"false\">\n<div class=\"font-claude-response relative leading-[1.65rem] [&amp;_pre&gt;div]:bg-bg-000\/50 [&amp;_pre&gt;div]:border-0.5 [&amp;_pre&gt;div]:border-border-400 [&amp;_.ignore-pre-bg&gt;div]:bg-transparent [&amp;_.standard-markdown_:is(p,blockquote,h1,h2,h3,h4,h5,h6)]:pl-2 [&amp;_.standard-markdown_:is(p,blockquote,ul,ol,h1,h2,h3,h4,h5,h6)]:pr-8 [&amp;_.progressive-markdown_:is(p,blockquote,h1,h2,h3,h4,h5,h6)]:pl-2 [&amp;_.progressive-markdown_:is(p,blockquote,ul,ol,h1,h2,h3,h4,h5,h6)]:pr-8\">\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 standard-markdown\">\n<p class=\"whitespace-normal break-words\">Circular motion is everywhere\u2014from the hands of a clock to the rotation of a Ferris wheel, from irrigation systems watering crops to satellites orbiting Earth. Understanding arc length, sector area, and angular speed allows us to analyze and describe these circular motions precisely. In this page, you&#8217;ll apply these concepts to analyze a real Ferris wheel attraction.<\/p>\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">The London Eye Ferris Wheel<\/h2>\n<p class=\"whitespace-normal break-words\">The London Eye is one of the world&#8217;s largest observation wheels, located on the banks of the River Thames. This giant Ferris wheel allows passengers to view the entire city from enclosed capsules as it slowly rotates.<\/p>\n<p class=\"whitespace-normal break-words\"><strong>London Eye Specifications:<\/strong><\/p>\n<ul class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-disc space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">Radius: 60 meters (from center to passenger capsule)<\/li>\n<li class=\"whitespace-normal break-words\">One complete rotation: 30 minutes<\/li>\n<li class=\"whitespace-normal break-words\">Operates continuously during business hours<\/li>\n<\/ul>\n<section class=\"textbox recall\" aria-label=\"Recall\">Arc length &#8211; The distance along the curved path of a circle between two points, calculated using [latex]s = r\\theta[\/latex] where [latex]r[\/latex] is the radius and [latex]\\theta[\/latex] is the angle in radians.<\/p>\n<p class=\"whitespace-normal break-words\">Sector &#8211; A region of a circle bounded by two radii and the intercepted arc, like a slice of pie. The area is calculated using [latex]A = \\frac{1}{2}\\theta r^2[\/latex] where [latex]\\theta[\/latex] is in radians.<\/p>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-normal break-words\">A passenger boards the London Eye and stays on for a 10-minute segment of the ride.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li class=\"whitespace-normal break-words\">What angle (in both degrees and radians) does the wheel rotate through in 10 minutes?<\/li>\n<li class=\"whitespace-normal break-words\">What distance does the passenger travel along the circular path during these 10 minutes?<\/li>\n<li class=\"whitespace-normal break-words\">If the wheel is divided into 32 passenger capsules equally spaced around the circle, what is the area of the sector between two adjacent capsules?<\/li>\n<li class=\"whitespace-normal break-words\">What is the angular speed of the wheel in radians per minute?<\/li>\n<li class=\"whitespace-normal break-words\">What is the linear speed of a passenger in meters per minute? Convert this to kilometers per hour.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q856919\">Show Solutions<\/button><\/p>\n<div id=\"q856919\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\n<p class=\"whitespace-normal break-words\">The wheel completes one full rotation (360\u00b0 or [latex]2\\pi[\/latex] radians) in 30 minutes.<\/p>\n<p class=\"whitespace-pre-wrap break-words\">In 10 minutes, the wheel completes: [latex]\\frac{10 \\text{ minutes}}{30 \\text{ minutes}} = \\frac{1}{3} \\text{ of a rotation}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">In degrees: [latex]\\frac{1}{3} \\times 360\u00b0 = 120\u00b0[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">In radians: [latex]\\frac{1}{3} \\times 2\\pi = \\frac{2\\pi}{3} \\text{ radians}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">The wheel rotates through 120\u00b0 or [latex]\\frac{2\\pi}{3}[\/latex] radians in 10 minutes.<\/p>\n<\/li>\n<li>\n<p class=\"whitespace-normal break-words\">Using the arc length formula [latex]s = r\\theta[\/latex], where [latex]\\theta[\/latex] must be in radians:<\/p>\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} s &= r\\theta \\\\ &= 60 \\text{ meters} \\times \\frac{2\\pi}{3} \\\\ &= \\frac{120\\pi}{3} \\\\ &= 40\\pi \\\\ &\\approx 125.66 \\text{ meters} \\end{aligned}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">The passenger travels approximately 125.66 meters along the circular path.<\/p>\n<\/li>\n<li>\n<p class=\"whitespace-normal break-words\">With 32 equally spaced capsules, the angle between adjacent capsules is:<\/p>\n<p class=\"whitespace-normal break-words\">[latex]\\theta = \\frac{2\\pi}{32} = \\frac{\\pi}{16} \\text{ radians}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">Using the sector area formula [latex]A = \\frac{1}{2}\\theta r^2[\/latex]:<\/p>\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} A &= \\frac{1}{2}\\theta r^2 \\\\ &= \\frac{1}{2} \\times \\frac{\\pi}{16} \\times (60)^2 \\\\ &= \\frac{1}{2} \\times \\frac{\\pi}{16} \\times 3600 \\\\ &= \\frac{3600\\pi}{32} \\\\ &= \\frac{225\\pi}{2} \\\\ &\\approx 353.43 \\text{ square meters} \\end{aligned}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">The sector area between two adjacent capsules is approximately 353.43 square meters.<\/p>\n<\/li>\n<li>\n<p class=\"whitespace-normal break-words\">Angular speed is the rate of angular rotation, calculated as [latex]\\omega = \\frac{\\theta}{t}[\/latex].<\/p>\n<p class=\"whitespace-pre-wrap break-words\">For one complete rotation:<\/p>\n<p>[latex]\\begin{aligned} \\omega &= \\frac{\\theta}{t} \\\\ &= \\frac{2\\pi \\text{ radians}}{30 \\text{ minutes}} \\\\ &= \\frac{2\\pi}{30} \\\\ &= \\frac{\\pi}{15} \\\\ &\\approx 0.209 \\text{ radians per minute} \\end{aligned}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">The angular speed of the London Eye is [latex]\\frac{\\pi}{15}[\/latex] radians per minute or approximately 0.209 rad\/min.<\/p>\n<\/li>\n<li>\n<p class=\"whitespace-normal break-words\">Linear speed is the actual distance traveled per unit time along the circular path. It relates to angular speed by [latex]v = r\\omega[\/latex].<\/p>\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} v &= r\\omega \\ &= 60 \\text{ meters} \\times \\frac{\\pi}{15} \\text{ rad\/min} \\ &= \\frac{60\\pi}{15} \\ &= 4\\pi \\ &\\approx 12.57 \\text{ meters per minute} \\end{aligned}[\/latex]<\/p>\n<p class=\"whitespace-pre-wrap break-words\">Converting to kilometers per hour: [latex]\\begin{aligned} v &= 12.57 \\frac{\\text{meters}}{\\cancel{\\text{minute}}} \\times \\frac{1 \\text{ km}}{1000 \\text{ meters}} \\times \\frac{60 \\cancel{\\text{minutes}}}{1 \\text{ hour}} \\ &= \\frac{12.57 \\times 60}{1000} \\\\ &\\approx 0.754 \\text{ km\/h} \\end{aligned}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">The linear speed of a passenger is approximately 12.57 meters per minute or 0.754 km\/h.<\/p>\n<p class=\"whitespace-normal break-words\">This slow speed explains why passengers can easily board and exit while the wheel continues moving!<\/p>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">Sector area [latex]A = \\frac{1}{2}\\theta r^2[\/latex] represents the fraction [latex]\\frac{\\theta}{2\\pi}[\/latex] of the total circle area [latex]\\pi r^2[\/latex]. This formula only works when [latex]\\theta[\/latex] is in radians.<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\">A smaller Ferris wheel at a carnival has a radius of 8 meters and completes one full rotation every 2 minutes.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li class=\"whitespace-normal break-words\">What angle does the wheel rotate through in 45 seconds? Express your answer in radians.<\/li>\n<li class=\"whitespace-normal break-words\">How far does a passenger travel in 45 seconds?<\/li>\n<li class=\"whitespace-normal break-words\">What is the angular speed of the wheel in radians per second?<\/li>\n<li class=\"whitespace-normal break-words\">What is the linear speed of a passenger in meters per second?<\/li>\n<\/ol>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":67,"menu_order":17,"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":"apply_it","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\/3224"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3224\/revisions"}],"predecessor-version":[{"id":4586,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3224\/revisions\/4586"}],"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\/3224\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=3224"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=3224"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=3224"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=3224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}