{"id":4547,"date":"2025-10-08T15:57:16","date_gmt":"2025-10-08T15:57:16","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=4547"},"modified":"2025-10-08T18:35:53","modified_gmt":"2025-10-08T18:35:53","slug":"angles-learn-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/angles-learn-it\/","title":{"raw":"Angles: Learn It 4","rendered":"Angles: Learn It 4"},"content":{"raw":"<h2>Degrees Minutes and Seconds<\/h2>\r\n<p class=\"whitespace-normal break-words\">Not all angles will be special angles, or even whole number values. Decimal degrees express angles as a decimal number (like 42.75\u00b0), while DMS form (degrees, minutes, seconds) breaks angles into whole degrees, minutes, and seconds (like 42\u00b0 45' 0\").<\/p>\r\n\r\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<div>\r\n<h3>DMS form (degrees, minutes, seconds)<\/h3>\r\nDMS is a notation used to express decimal valued angles.\r\n<ul>\r\n \t<li>One degree equals 60 minutes and<\/li>\r\n \t<li>One minute equals 60 seconds.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\nAngles in this form are represented as D\u00b0 M' S\".\r\n\r\n<\/div>\r\n<\/section>\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Converting from Decimal Degrees to DMS Form<\/h2>\r\n<p class=\"whitespace-normal break-words\">When converting from decimal degrees to DMS form, we separate the whole number part (degrees) from the decimal part, then convert the decimal portion into minutes and seconds.<\/p>\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-normal break-words\">Convert [latex]47.58\u00b0[\/latex] to DMS form.<\/p>\r\n<p class=\"whitespace-normal break-words\">[reveal-answer q=\"858241\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"858241\"]<\/p>\r\n<p class=\"whitespace-normal break-words\">The whole number is [latex]47[\/latex], so we have [latex]47\u00b0[\/latex].<\/p>\r\n<p class=\"whitespace-normal break-words\">Take the decimal part [latex]0.58[\/latex] and multiply by 60:<\/p>\r\n<p class=\"whitespace-normal break-words\">[latex]0.58 \\times 60 = 34.8[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">This gives us [latex]34[\/latex] minutes, with [latex]0.8[\/latex] remaining.<\/p>\r\n<p class=\"whitespace-normal break-words\">Take the decimal part [latex]0.8[\/latex] and multiply by 60:<\/p>\r\n<p class=\"whitespace-normal break-words\">[latex]0.8 \\times 60 = 48[\/latex] This gives us [latex]48[\/latex] seconds.<\/p>\r\n<p class=\"whitespace-normal break-words\">Therefore, [latex]47.58\u00b0 = 47\u00b0 34' 48\"[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\">\r\n<p class=\"whitespace-normal break-words\"><strong>How To: Converting Decimal Degrees to DMS<\/strong><\/p>\r\n\r\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">The whole number part is the degrees<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Multiply the decimal part by 60 to get minutes<\/li>\r\n \t<li class=\"whitespace-normal break-words\">If the minutes have a decimal part, multiply that decimal by 60 to get seconds<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Write your answer in DMS notation: degrees\u00b0 minutes' seconds\"<\/li>\r\n<\/ol>\r\n<\/section>\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Converting from DMS Form to Decimal Degrees<\/h2>\r\n<p class=\"whitespace-normal break-words\">To convert from DMS form to decimal degrees, we work backwards by converting minutes and seconds into decimal fractions of a degree.<\/p>\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">Convert [latex]38\u00b0 27' 36\"[\/latex] to decimal degree form.[reveal-answer q=\"274164\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"274164\"]Start with [latex]38\u00b0[\/latex].\r\n<ul>\r\n \t<li>Convert the minutes to a decimal:\r\n[latex]\\dfrac{27}{60} = 0.45\u00b0[\/latex]<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li>Convert the seconds to a decimal:\r\n[latex]\\dfrac{36}{3600} = 0.01\u00b0[\/latex]<\/li>\r\n \t<li>Add all parts together: [latex]38\u00b0 + 0.45\u00b0 + 0.01\u00b0 = 38.46\u00b0[\/latex]<\/li>\r\n<\/ul>\r\nTherefore, [latex]38\u00b0 27' 36\" = 38.46\u00b0[\/latex][\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\">\r\n<p class=\"whitespace-normal break-words\"><strong>How To: Converting DMS to Decimal Degrees<\/strong><\/p>\r\n\r\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">Start with the degrees as your base number<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Divide the minutes by 60 and add to the degrees<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Divide the seconds by 3600 (since 60 \u00d7 60 = 3600) and add to the result<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Write your answer with appropriate decimal places<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]156285[\/ohm_question]<\/section>\r\n\r\n<hr class=\"border-border-300 my-2\" \/>\r\n\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Using a Calculator for DMS Conversions<\/h2>\r\n<p class=\"whitespace-normal break-words\">Most scientific and graphing calculators have built-in functions to convert between decimal degrees and DMS form.<\/p>\r\n\r\n<section class=\"textbox interact\" aria-label=\"Interact\">\r\n<p class=\"whitespace-normal break-words\"><strong>For TI-84 Calculators:<\/strong><\/p>\r\n<p class=\"whitespace-normal break-words\"><strong>Converting Decimal to DMS:<\/strong><\/p>\r\n\r\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">Enter the decimal degree value<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Select option 4: [latex]\\boxed{\\text{\u25baDMS}}[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{ENTER}}[\/latex]<\/li>\r\n<\/ol>\r\n<p class=\"whitespace-normal break-words\">For example, entering [latex]47.58[\/latex] and using [latex]\\boxed{\\text{\u25baDMS}}[\/latex] displays [latex]47\u00b0 34' 48\"[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\"><strong>Converting DMS to Decimal:<\/strong><\/p>\r\n\r\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">Enter the degrees<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Select option 1: [latex]\\boxed{\u00b0}[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Enter the minutes<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Select option 2: [latex]\\boxed{'}[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Enter the seconds<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Select option 3: [latex]\\boxed{\"}[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{ENTER}}[\/latex]<\/li>\r\n<\/ol>\r\n<\/section>\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Converting Radians to DMS Form<\/h2>\r\n<p class=\"whitespace-normal break-words\">Sometimes you need to convert an angle given in radians to DMS form. This requires a two-step process: first convert radians to decimal degrees, then convert decimal degrees to DMS form.<\/p>\r\n\r\n<section class=\"textbox recall\" aria-label=\"Recall\">To convert from radians to degrees, use the conversion: [latex]\\text{degrees} = \\text{radians} \\times \\dfrac{180\u00b0}{\\pi}[\/latex]<\/section><section class=\"textbox example\" aria-label=\"Example\">Convert [latex]2.5[\/latex] radians to DMS form.[reveal-answer q=\"240812\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"240812\"]\r\n<p class=\"whitespace-normal break-words\"><strong>Step 1:<\/strong> Convert radians to decimal degrees.<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} \\text{degrees} &amp;= 2.5 \\times \\dfrac{180\u00b0}{\\pi} \\ &amp;= \\dfrac{450\u00b0}{\\pi} \\ &amp;\\approx 143.2394\u00b0 \\end{aligned}[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\"><strong>Step 2:<\/strong> Convert decimal degrees to DMS form.<\/p>\r\n<p class=\"whitespace-normal break-words\">The whole number is [latex]143[\/latex], so we have [latex]143\u00b0[\/latex].<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">Multiply the decimal part by 60: [latex]0.2394 \\times 60 = 14.364[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">This gives us [latex]14[\/latex] minutes.<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">Multiply the remaining decimal by 60: [latex]0.364 \\times 60 = 21.84 \\approx 22[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">This gives us approximately [latex]22[\/latex] seconds.<\/p>\r\n<p class=\"whitespace-normal break-words\">Therefore, [latex]2.5 \\text{ radians} \\approx 143\u00b0 14' 22\"[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313395[\/ohm_question]<\/section>","rendered":"<h2>Degrees Minutes and Seconds<\/h2>\n<p class=\"whitespace-normal break-words\">Not all angles will be special angles, or even whole number values. Decimal degrees express angles as a decimal number (like 42.75\u00b0), while DMS form (degrees, minutes, seconds) breaks angles into whole degrees, minutes, and seconds (like 42\u00b0 45&#8242; 0&#8243;).<\/p>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<div>\n<h3>DMS form (degrees, minutes, seconds)<\/h3>\n<p>DMS is a notation used to express decimal valued angles.<\/p>\n<ul>\n<li>One degree equals 60 minutes and<\/li>\n<li>One minute equals 60 seconds.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>Angles in this form are represented as D\u00b0 M&#8217; S&#8221;.<\/p>\n<\/div>\n<\/section>\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Converting from Decimal Degrees to DMS Form<\/h2>\n<p class=\"whitespace-normal break-words\">When converting from decimal degrees to DMS form, we separate the whole number part (degrees) from the decimal part, then convert the decimal portion into minutes and seconds.<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-normal break-words\">Convert [latex]47.58\u00b0[\/latex] to DMS form.<\/p>\n<p class=\"whitespace-normal break-words\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q858241\">Show Solution<\/button><\/p>\n<div id=\"q858241\" class=\"hidden-answer\" style=\"display: none\">\n<p class=\"whitespace-normal break-words\">The whole number is [latex]47[\/latex], so we have [latex]47\u00b0[\/latex].<\/p>\n<p class=\"whitespace-normal break-words\">Take the decimal part [latex]0.58[\/latex] and multiply by 60:<\/p>\n<p class=\"whitespace-normal break-words\">[latex]0.58 \\times 60 = 34.8[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">This gives us [latex]34[\/latex] minutes, with [latex]0.8[\/latex] remaining.<\/p>\n<p class=\"whitespace-normal break-words\">Take the decimal part [latex]0.8[\/latex] and multiply by 60:<\/p>\n<p class=\"whitespace-normal break-words\">[latex]0.8 \\times 60 = 48[\/latex] This gives us [latex]48[\/latex] seconds.<\/p>\n<p class=\"whitespace-normal break-words\">Therefore, [latex]47.58\u00b0 = 47\u00b0 34' 48\"[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\">\n<p class=\"whitespace-normal break-words\"><strong>How To: Converting Decimal Degrees to DMS<\/strong><\/p>\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">The whole number part is the degrees<\/li>\n<li class=\"whitespace-normal break-words\">Multiply the decimal part by 60 to get minutes<\/li>\n<li class=\"whitespace-normal break-words\">If the minutes have a decimal part, multiply that decimal by 60 to get seconds<\/li>\n<li class=\"whitespace-normal break-words\">Write your answer in DMS notation: degrees\u00b0 minutes&#8217; seconds&#8221;<\/li>\n<\/ol>\n<\/section>\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Converting from DMS Form to Decimal Degrees<\/h2>\n<p class=\"whitespace-normal break-words\">To convert from DMS form to decimal degrees, we work backwards by converting minutes and seconds into decimal fractions of a degree.<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">Convert [latex]38\u00b0 27' 36\"[\/latex] to decimal degree form.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q274164\">Show Solution<\/button><\/p>\n<div id=\"q274164\" class=\"hidden-answer\" style=\"display: none\">Start with [latex]38\u00b0[\/latex].<\/p>\n<ul>\n<li>Convert the minutes to a decimal:<br \/>\n[latex]\\dfrac{27}{60} = 0.45\u00b0[\/latex]<\/li>\n<\/ul>\n<ul>\n<li>Convert the seconds to a decimal:<br \/>\n[latex]\\dfrac{36}{3600} = 0.01\u00b0[\/latex]<\/li>\n<li>Add all parts together: [latex]38\u00b0 + 0.45\u00b0 + 0.01\u00b0 = 38.46\u00b0[\/latex]<\/li>\n<\/ul>\n<p>Therefore, [latex]38\u00b0 27' 36\" = 38.46\u00b0[\/latex]<\/p><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\">\n<p class=\"whitespace-normal break-words\"><strong>How To: Converting DMS to Decimal Degrees<\/strong><\/p>\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">Start with the degrees as your base number<\/li>\n<li class=\"whitespace-normal break-words\">Divide the minutes by 60 and add to the degrees<\/li>\n<li class=\"whitespace-normal break-words\">Divide the seconds by 3600 (since 60 \u00d7 60 = 3600) and add to the result<\/li>\n<li class=\"whitespace-normal break-words\">Write your answer with appropriate decimal places<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm156285\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=156285&theme=lumen&iframe_resize_id=ohm156285&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"border-border-300 my-2\" \/>\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Using a Calculator for DMS Conversions<\/h2>\n<p class=\"whitespace-normal break-words\">Most scientific and graphing calculators have built-in functions to convert between decimal degrees and DMS form.<\/p>\n<section class=\"textbox interact\" aria-label=\"Interact\">\n<p class=\"whitespace-normal break-words\"><strong>For TI-84 Calculators:<\/strong><\/p>\n<p class=\"whitespace-normal break-words\"><strong>Converting Decimal to DMS:<\/strong><\/p>\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">Enter the decimal degree value<\/li>\n<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\n<li class=\"whitespace-normal break-words\">Select option 4: [latex]\\boxed{\\text{\u25baDMS}}[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{ENTER}}[\/latex]<\/li>\n<\/ol>\n<p class=\"whitespace-normal break-words\">For example, entering [latex]47.58[\/latex] and using [latex]\\boxed{\\text{\u25baDMS}}[\/latex] displays [latex]47\u00b0 34' 48\"[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\"><strong>Converting DMS to Decimal:<\/strong><\/p>\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">Enter the degrees<\/li>\n<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\n<li class=\"whitespace-normal break-words\">Select option 1: [latex]\\boxed{\u00b0}[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Enter the minutes<\/li>\n<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\n<li class=\"whitespace-normal break-words\">Select option 2: [latex]\\boxed{'}[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Enter the seconds<\/li>\n<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{2nd}}[\/latex] then [latex]\\boxed{\\text{APPS}}[\/latex] (ANGLE menu)<\/li>\n<li class=\"whitespace-normal break-words\">Select option 3: [latex]\\boxed{\"}[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Press [latex]\\boxed{\\text{ENTER}}[\/latex]<\/li>\n<\/ol>\n<\/section>\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Converting Radians to DMS Form<\/h2>\n<p class=\"whitespace-normal break-words\">Sometimes you need to convert an angle given in radians to DMS form. This requires a two-step process: first convert radians to decimal degrees, then convert decimal degrees to DMS form.<\/p>\n<section class=\"textbox recall\" aria-label=\"Recall\">To convert from radians to degrees, use the conversion: [latex]\\text{degrees} = \\text{radians} \\times \\dfrac{180\u00b0}{\\pi}[\/latex]<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">Convert [latex]2.5[\/latex] radians to DMS form.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q240812\">Show Solution<\/button><\/p>\n<div id=\"q240812\" class=\"hidden-answer\" style=\"display: none\">\n<p class=\"whitespace-normal break-words\"><strong>Step 1:<\/strong> Convert radians to decimal degrees.<\/p>\n<p class=\"whitespace-pre-wrap break-words\">[latex]\\begin{aligned} \\text{degrees} &= 2.5 \\times \\dfrac{180\u00b0}{\\pi} \\ &= \\dfrac{450\u00b0}{\\pi} \\ &\\approx 143.2394\u00b0 \\end{aligned}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\"><strong>Step 2:<\/strong> Convert decimal degrees to DMS form.<\/p>\n<p class=\"whitespace-normal break-words\">The whole number is [latex]143[\/latex], so we have [latex]143\u00b0[\/latex].<\/p>\n<p class=\"whitespace-pre-wrap break-words\">Multiply the decimal part by 60: [latex]0.2394 \\times 60 = 14.364[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">This gives us [latex]14[\/latex] minutes.<\/p>\n<p class=\"whitespace-pre-wrap break-words\">Multiply the remaining decimal by 60: [latex]0.364 \\times 60 = 21.84 \\approx 22[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">This gives us approximately [latex]22[\/latex] seconds.<\/p>\n<p class=\"whitespace-normal break-words\">Therefore, [latex]2.5 \\text{ radians} \\approx 143\u00b0 14' 22\"[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313395\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313395&theme=lumen&iframe_resize_id=ohm313395&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":9,"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":"- Select Header -","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\/4547"}],"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\/13"}],"version-history":[{"count":6,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/4547\/revisions"}],"predecessor-version":[{"id":4566,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/4547\/revisions\/4566"}],"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\/4547\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=4547"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=4547"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=4547"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=4547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}