{"id":251974,"date":"2025-07-11T04:30:26","date_gmt":"2025-07-11T04:30:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=251974"},"modified":"2025-07-11T04:30:28","modified_gmt":"2025-07-11T04:30:28","slug":"give-the-exact-value-of-each-of-the-following","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/give-the-exact-value-of-each-of-the-following\/","title":{"rendered":"Give the exact value of each of the following."},"content":{"rendered":"\n<p>Give the exact value of each of the following. cos pi\/ 6<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The exact value of cos\u2061(\u03c06)\\cos\\left(\\frac{\\pi}{6}\\right)cos(6\u03c0\u200b) is 32\\frac{\\sqrt{3}}{2}23\u200b\u200b.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To understand how we arrive at this value, let\u2019s first explore what \u03c06\\frac{\\pi}{6}6\u03c0\u200b represents. In radians, \u03c06\\frac{\\pi}{6}6\u03c0\u200b is equivalent to 30\u221830^\\circ30\u2218. The cosine of an angle in a right triangle corresponds to the ratio of the adjacent side to the hypotenuse. For common angles, such as 30\u221830^\\circ30\u2218, 45\u221845^\\circ45\u2218, and 60\u221860^\\circ60\u2218, we often use a unit circle or special right triangles to derive their exact trigonometric values.<\/p>\n\n\n\n<p>For a 30\u221830^\\circ30\u2218 or \u03c06\\frac{\\pi}{6}6\u03c0\u200b angle, we can use a special 30-60-90 triangle, where the ratios of the sides are well-known:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The length of the hypotenuse is 1 (since the unit circle has a radius of 1).<\/li>\n\n\n\n<li>The side opposite the 30\u221830^\\circ30\u2218 angle is 12\\frac{1}{2}21\u200b.<\/li>\n\n\n\n<li>The side opposite the 60\u221860^\\circ60\u2218 angle is 32\\frac{\\sqrt{3}}{2}23\u200b\u200b.<\/li>\n<\/ul>\n\n\n\n<p>In a unit circle, cos\u2061(\u03b8)\\cos(\\theta)cos(\u03b8) is the x-coordinate of the point on the circle corresponding to the angle \u03b8\\theta\u03b8. For the angle \u03c06\\frac{\\pi}{6}6\u03c0\u200b, or 30\u221830^\\circ30\u2218, the x-coordinate is 32\\frac{\\sqrt{3}}{2}23\u200b\u200b. Therefore, the exact value of cos\u2061(\u03c06)\\cos\\left(\\frac{\\pi}{6}\\right)cos(6\u03c0\u200b) is:cos\u2061(\u03c06)=32\\cos\\left(\\frac{\\pi}{6}\\right) = \\frac{\\sqrt{3}}{2}cos(6\u03c0\u200b)=23\u200b\u200b<\/p>\n\n\n\n<p>This value is derived from the geometry of the 30-60-90 triangle and the unit circle.<\/p>\n\n\n\n<p>The cosine function is one of the basic trigonometric functions, and understanding its values for common angles like 30\u221830^\\circ30\u2218 is fundamental to solving trigonometric problems.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-201.jpeg\" alt=\"\" class=\"wp-image-251975\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Give the exact value of each of the following. cos pi\/ 6 The Correct Answer and Explanation is: The exact value of cos\u2061(\u03c06)\\cos\\left(\\frac{\\pi}{6}\\right)cos(6\u03c0\u200b) is 32\\frac{\\sqrt{3}}{2}23\u200b\u200b. Explanation: To understand how we arrive at this value, let\u2019s first explore what \u03c06\\frac{\\pi}{6}6\u03c0\u200b represents. In radians, \u03c06\\frac{\\pi}{6}6\u03c0\u200b is equivalent to 30\u221830^\\circ30\u2218. The cosine of an angle in a right [&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-251974","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251974","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=251974"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251974\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=251974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=251974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=251974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}