{"id":235553,"date":"2025-06-15T13:34:35","date_gmt":"2025-06-15T13:34:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235553"},"modified":"2025-06-15T13:34:37","modified_gmt":"2025-06-15T13:34:37","slug":"find-the-angle-that-is-between-0-and-2pi-radians-that-is-coterminal-to-13pi-6-radians","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/find-the-angle-that-is-between-0-and-2pi-radians-that-is-coterminal-to-13pi-6-radians\/","title":{"rendered":"find the angle that is between 0 and 2pi radians that is coterminal to 13pi\/6 radians."},"content":{"rendered":"\n<p><br>find the angle that is between 0 and 2pi radians that is coterminal to 13pi\/6 radians. The coterminal is a(pi)\/b. find the value for a and b<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find an angle between 0 and 2\u03c02\\pi2\u03c0 that is <strong>coterminal<\/strong> with 13\u03c06\\frac{13\\pi}{6}613\u03c0\u200b, subtract or add multiples of 2\u03c02\\pi2\u03c0 until the result lies within the interval 0&lt;\u03b8&lt;2\u03c00 &lt; \\theta &lt; 2\\pi0&lt;\u03b8&lt;2\u03c0.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Express 2\u03c02\\pi2\u03c0 with denominator 6<\/h3>\n\n\n\n<p>2\u03c0=12\u03c062\\pi = \\frac{12\\pi}{6}2\u03c0=612\u03c0\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Subtract 2\u03c02\\pi2\u03c0 from 13\u03c06\\frac{13\\pi}{6}613\u03c0\u200b<\/h3>\n\n\n\n<p>13\u03c06\u221212\u03c06=\u03c06\\frac{13\\pi}{6} &#8211; \\frac{12\\pi}{6} = \\frac{\\pi}{6}613\u03c0\u200b\u2212612\u03c0\u200b=6\u03c0\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Final Answer<\/h3>\n\n\n\n<p>The angle coterminal with 13\u03c06\\frac{13\\pi}{6}613\u03c0\u200b and between 000 and 2\u03c02\\pi2\u03c0 is:\u03c06\\frac{\\pi}{6}6\u03c0\u200b<\/p>\n\n\n\n<p>This is in the form a\u03c0b\\frac{a\\pi}{b}ba\u03c0\u200b, where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=1a = 1a=1<\/li>\n\n\n\n<li>b=6b = 6b=6<\/li>\n<\/ul>\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>Coterminal angles differ by full rotations around the unit circle. A full rotation equals 2\u03c02\\pi2\u03c0 radians. When an angle exceeds 2\u03c02\\pi2\u03c0, subtracting 2\u03c02\\pi2\u03c0 reduces it back into the principal range of 000 to 2\u03c02\\pi2\u03c0. If an angle is negative, adding 2\u03c02\\pi2\u03c0 accomplishes the same.<\/p>\n\n\n\n<p>The given angle is 13\u03c06\\frac{13\\pi}{6}613\u03c0\u200b. This exceeds 2\u03c02\\pi2\u03c0, which is equivalent to 12\u03c06\\frac{12\\pi}{6}612\u03c0\u200b. Subtracting 12\u03c06\\frac{12\\pi}{6}612\u03c0\u200b from 13\u03c06\\frac{13\\pi}{6}613\u03c0\u200b yields \u03c06\\frac{\\pi}{6}6\u03c0\u200b. The result lies within the desired interval 0&lt;\u03b8&lt;2\u03c00 &lt; \\theta &lt; 2\\pi0&lt;\u03b8&lt;2\u03c0.<\/p>\n\n\n\n<p>Angles like 13\u03c06\\frac{13\\pi}{6}613\u03c0\u200b and \u03c06\\frac{\\pi}{6}6\u03c0\u200b are coterminal because they point to the same terminal side on the unit circle. Both produce identical trigonometric values. The difference of 2\u03c02\\pi2\u03c0 indicates a single full rotation between them.<\/p>\n\n\n\n<p>Coterminal angles are useful in trigonometry and periodic functions, allowing simplification of angle measures while retaining their sine, cosine, and tangent values. This concept also aids in solving equations and understanding wave behavior.<\/p>\n\n\n\n<p>Therefore, the equivalent angle between 000 and 2\u03c02\\pi2\u03c0 is \u03c06\\frac{\\pi}{6}6\u03c0\u200b, and the values of aaa and bbb are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=1a = 1a=1<\/li>\n\n\n\n<li>b=6b = 6b=6<\/li>\n<\/ul>\n\n\n\n<p>This expresses the final answer in the required form a\u03c0b\\frac{a\\pi}{b}ba\u03c0\u200b.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-598.jpeg\" alt=\"\" class=\"wp-image-235554\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>find the angle that is between 0 and 2pi radians that is coterminal to 13pi\/6 radians. The coterminal is a(pi)\/b. find the value for a and b The Correct Answer and Explanation is: To find an angle between 0 and 2\u03c02\\pi2\u03c0 that is coterminal with 13\u03c06\\frac{13\\pi}{6}613\u03c0\u200b, subtract or add multiples of 2\u03c02\\pi2\u03c0 until the result [&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-235553","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235553","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=235553"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235553\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235553"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235553"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}