{"id":33552,"date":"2025-06-23T09:24:17","date_gmt":"2025-06-23T09:24:17","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33552"},"modified":"2025-06-23T09:24:19","modified_gmt":"2025-06-23T09:24:19","slug":"convert-the-following-angle-from-degrees-to-radians","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/convert-the-following-angle-from-degrees-to-radians\/","title":{"rendered":"Convert the following angle from degrees to radians."},"content":{"rendered":"\n<p>Convert the following angle from degrees to radians. Express your answer in simplest form. 555\u00b0 Answer Attempt 1 out of 2 ?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p>To convert <strong>555\u00b0<\/strong> to radians:<\/p>\n\n\n\n<p>We use the formula:Radians=Degrees\u00d7\u03c0180\\text{Radians} = \\text{Degrees} \\times \\frac{\\pi}{180}Radians=Degrees\u00d7180\u03c0\u200b<\/p>\n\n\n\n<p>Substituting the given angle:555\u2218\u00d7\u03c0180=555\u03c0180555^\\circ \\times \\frac{\\pi}{180} = \\frac{555\\pi}{180}555\u2218\u00d7180\u03c0\u200b=180555\u03c0\u200b<\/p>\n\n\n\n<p>Next, simplify the fraction:<\/p>\n\n\n\n<p>First, find the greatest common divisor (GCD) of 555 and 180.<\/p>\n\n\n\n<p><strong>Prime factorization:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>555 = 5 \u00d7 111 = 5 \u00d7 3 \u00d7 37<\/li>\n\n\n\n<li>180 = 2\u00b2 \u00d7 3\u00b2 \u00d7 5<\/li>\n<\/ul>\n\n\n\n<p>The common factors are <strong>3<\/strong> and <strong>5<\/strong>, so GCD is <strong>15<\/strong>.<\/p>\n\n\n\n<p>Now divide numerator and denominator by 15:555\u03c0180=555\u00f715\u00d7\u03c0180\u00f715=37\u03c012\\frac{555\\pi}{180} = \\frac{555 \u00f7 15 \\times \\pi}{180 \u00f7 15} = \\frac{37\\pi}{12}180555\u03c0\u200b=180\u00f715555\u00f715\u00d7\u03c0\u200b=1237\u03c0\u200b<\/p>\n\n\n\n<p>Thus, the angle in radians is:37\u03c012\\boxed{\\frac{37\\pi}{12}}1237\u03c0\u200b\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Angles are commonly measured in two units: degrees and radians. Degrees divide a full circle into 360 equal parts, while radians use the arc length of a circle in relation to its radius. In mathematical and scientific applications, radians are often preferred because they simplify formulas involving trigonometry and calculus.<\/p>\n\n\n\n<p>To convert degrees to radians, the conversion factor is used:\u03c0&nbsp;radians180\u2218\\frac{\\pi \\text{ radians}}{180^\\circ}180\u2218\u03c0&nbsp;radians\u200b<\/p>\n\n\n\n<p>This relationship comes from the fact that a full circle is 360 degrees, which equals 2\u03c02\\pi2\u03c0 radians.<\/p>\n\n\n\n<p>In this problem, we are converting <strong>555 degrees<\/strong> to radians. First, multiply 555 by \u03c0\\pi\u03c0 and divide by 180:555\u2218\u00d7\u03c0180=555\u03c0180555^\\circ \\times \\frac{\\pi}{180} = \\frac{555\\pi}{180}555\u2218\u00d7180\u03c0\u200b=180555\u03c0\u200b<\/p>\n\n\n\n<p>To simplify, both 555 and 180 share common factors. Their greatest common divisor (GCD) is 15. Dividing both the numerator and denominator by 15:555\u00f715\u00d7\u03c0180\u00f715=37\u03c012\\frac{555 \u00f7 15 \\times \\pi}{180 \u00f7 15} = \\frac{37\\pi}{12}180\u00f715555\u00f715\u00d7\u03c0\u200b=1237\u03c0\u200b<\/p>\n\n\n\n<p>Therefore, <strong>555 degrees<\/strong> is equivalent to 37\u03c012\\frac{37\\pi}{12}1237\u03c0\u200b radians in simplest form. This form is exact and preferable in mathematics to maintain precision. Using radians is particularly helpful when dealing with periodic functions like sine, cosine, and tangent, especially in higher-level math topics.<\/p>\n\n\n\n<p>The final simplified answer is:37\u03c012\\boxed{\\frac{37\\pi}{12}}1237\u03c0\u200b\u200b<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-522.jpeg\" alt=\"\" class=\"wp-image-33559\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-522.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-522-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-522-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Convert the following angle from degrees to radians. Express your answer in simplest form. 555\u00b0 Answer Attempt 1 out of 2 ? The Correct Answer and Explanation is: Correct Answer: To convert 555\u00b0 to radians: We use the formula:Radians=Degrees\u00d7\u03c0180\\text{Radians} = \\text{Degrees} \\times \\frac{\\pi}{180}Radians=Degrees\u00d7180\u03c0\u200b Substituting the given angle:555\u2218\u00d7\u03c0180=555\u03c0180555^\\circ \\times \\frac{\\pi}{180} = \\frac{555\\pi}{180}555\u2218\u00d7180\u03c0\u200b=180555\u03c0\u200b Next, simplify the fraction: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-33552","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=33552"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33552\/revisions"}],"predecessor-version":[{"id":33560,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33552\/revisions\/33560"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}