{"id":180960,"date":"2025-01-09T08:58:16","date_gmt":"2025-01-09T08:58:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=180960"},"modified":"2025-01-09T08:58:19","modified_gmt":"2025-01-09T08:58:19","slug":"find-an-angle-between-0-and-2pi-that-is-coterminal-with-27pi-over-10","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/09\/find-an-angle-between-0-and-2pi-that-is-coterminal-with-27pi-over-10\/","title":{"rendered":"find an angle between 0 and 2pi that is coterminal with 27pi over 10"},"content":{"rendered":"\n<p>find an angle between 0 and 2pi that is coterminal with 27pi over 10.find an angle between 0 degrees and 360 degrees that is coterminal with 870 degrees.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/01\/image-66.png\" alt=\"\" class=\"wp-image-180961\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find coterminal angles, we add or subtract multiples of a full rotation (360\u00b0 or 2\u03c0 radians) to the given angle until it falls within the desired range. Let&#8217;s apply this method to the two problems:<\/p>\n\n\n\n<p><strong>1. Coterminal Angle of 27\u03c0\/10 Radians Between 0 and 2\u03c0:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1: Convert 27\u03c0\/10 to a Decimal:<\/strong><br>27\u03c0\/10 \u2248 8.4823 radians.<\/li>\n\n\n\n<li><strong>Step 2: Subtract 2\u03c0 (One Full Rotation) to Find a Coterminal Angle:<\/strong><br>8.4823 &#8211; 2\u03c0 \u2248 8.4823 &#8211; 6.2832 \u2248 2.1991 radians.<\/li>\n\n\n\n<li><strong>Step 3: Verify the Result:<\/strong><br>2.1991 radians is between 0 and 2\u03c0, so it&#8217;s the coterminal angle.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Coterminal Angle of 870\u00b0 Between 0\u00b0 and 360\u00b0:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1: Subtract 360\u00b0 (One Full Rotation) to Find a Coterminal Angle:<\/strong><br>870\u00b0 &#8211; 360\u00b0 = 510\u00b0.<\/li>\n\n\n\n<li><strong>Step 2: Subtract 360\u00b0 Again:<\/strong><br>510\u00b0 &#8211; 360\u00b0 = 150\u00b0.<\/li>\n\n\n\n<li><strong>Step 3: Verify the Result:<\/strong><br>150\u00b0 is between 0\u00b0 and 360\u00b0, so it&#8217;s the coterminal angle.<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>Coterminal angles share the same terminal side when drawn in standard position. To find a coterminal angle within a specific range, we add or subtract multiples of 360\u00b0 (or 2\u03c0 radians) until the angle falls within the desired interval. This method ensures that the angle represents the same direction or position as the original angle.<\/p>\n\n\n\n<p>For example, subtracting 360\u00b0 from 870\u00b0 twice results in 150\u00b0, which is coterminal with 870\u00b0 and lies within the 0\u00b0 to 360\u00b0 range. Similarly, subtracting 2\u03c0 radians from 27\u03c0\/10 radians once yields 2.1991 radians, which is coterminal with 27\u03c0\/10 radians and lies within the 0 to 2\u03c0 radians range.<\/p>\n\n\n\n<p>Understanding coterminal angles is essential in trigonometry and geometry, as it allows for the simplification of angle measures and the analysis of periodic functions. By recognizing that angles differing by full rotations are coterminal, we can work with angles within a standard range, making calculations and interpretations more straightforward.<\/p>\n\n\n\n<p>In summary, to find a coterminal angle within a specific range, subtract or add multiples of 360\u00b0 (or 2\u03c0 radians) until the angle falls within the desired interval. This approach ensures that the angle represents the same direction or position as the original angle, facilitating easier analysis and computation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>find an angle between 0 and 2pi that is coterminal with 27pi over 10.find an angle between 0 degrees and 360 degrees that is coterminal with 870 degrees. The Correct Answer and Explanation is : To find coterminal angles, we add or subtract multiples of a full rotation (360\u00b0 or 2\u03c0 radians) to the given [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-180960","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180960","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=180960"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180960\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=180960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=180960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=180960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}