{"id":252005,"date":"2025-07-11T06:11:46","date_gmt":"2025-07-11T06:11:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=252005"},"modified":"2025-07-11T06:11:49","modified_gmt":"2025-07-11T06:11:49","slug":"give-the-exact-value-of-each-of-the-following-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/give-the-exact-value-of-each-of-the-following-2\/","title":{"rendered":"Give the exact value of each of the following."},"content":{"rendered":"\n

Give the exact value of each of the following. cos pi\/ 6<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

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

Explanation:<\/h3>\n\n\n\n

To understand why, let’s first recall that \u03c0\\pi\u03c0 is approximately 3.14159, and \u03c06\\frac{\\pi}{6}6\u03c0\u200b corresponds to a 30\u00b0 angle in radians. We can find the cosine of a 30\u00b0 angle by referring to the unit circle or by using standard trigonometric values for commonly used angles (like 30\u00b0, 45\u00b0, 60\u00b0).<\/p>\n\n\n\n

Unit Circle:<\/h4>\n\n\n\n

On the unit circle, an angle of \u03c06\\frac{\\pi}{6}6\u03c0\u200b radians (or 30\u00b0) corresponds to a point on the circle. The coordinates of this point are (cos\u2061(\u03c06),sin\u2061(\u03c06))(\\cos(\\frac{\\pi}{6}), \\sin(\\frac{\\pi}{6}))(cos(6\u03c0\u200b),sin(6\u03c0\u200b)).<\/p>\n\n\n\n

For a 30\u00b0 angle, the cosine value (which is the x-coordinate of the point) is 32\\frac{\\sqrt{3}}{2}23\u200b\u200b.<\/p>\n\n\n\n

30\u00b0-60\u00b0-90\u00b0 Triangle:<\/h4>\n\n\n\n

Another way to derive this value is by considering the 30\u00b0-60\u00b0-90\u00b0 right triangle, which is a special triangle with known side ratios. In this triangle:<\/p>\n\n\n\n

    \n
  • The side opposite the 30\u00b0 angle is 111.<\/li>\n\n\n\n
  • The side opposite the 60\u00b0 angle is 3\\sqrt{3}3\u200b.<\/li>\n\n\n\n
  • The hypotenuse is 222.<\/li>\n<\/ul>\n\n\n\n

    The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse. For a 30\u00b0 angle:cos\u2061(30\u2218)=adjacent sidehypotenuse=32\\cos(30^\\circ) = \\frac{\\text{adjacent side}}{\\text{hypotenuse}} = \\frac{\\sqrt{3}}{2}cos(30\u2218)=hypotenuseadjacent side\u200b=23\u200b\u200b<\/p>\n\n\n\n

    Thus, 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

    Summary:<\/h3>\n\n\n\n
      \n
    • cos\u2061(\u03c06)=32\\cos\\left(\\frac{\\pi}{6}\\right) = \\frac{\\sqrt{3}}{2}cos(6\u03c0\u200b)=23\u200b\u200b.<\/li>\n\n\n\n
    • This result comes from both the unit circle and the 30\u00b0-60\u00b0-90\u00b0 triangle.<\/li>\n<\/ul>\n\n\n\n

      This value is widely used in trigonometry and is part of the set of standard trigonometric values for key angles (30\u00b0, 45\u00b0, 60\u00b0).<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      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 why, let’s first recall that \u03c0\\pi\u03c0 is approximately 3.14159, and \u03c06\\frac{\\pi}{6}6\u03c0\u200b corresponds to a 30\u00b0 angle in radians. We can find the cosine of a 30\u00b0 angle […]<\/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-252005","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252005","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=252005"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252005\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}