{"id":162145,"date":"2024-11-06T08:57:16","date_gmt":"2024-11-06T08:57:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=162145"},"modified":"2024-11-06T08:58:03","modified_gmt":"2024-11-06T08:58:03","slug":"what-is-cos-60-degrees-in-fraction-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/06\/what-is-cos-60-degrees-in-fraction-form\/","title":{"rendered":"What is cos 60 degrees in fraction form"},"content":{"rendered":"\n

What is cos 60 degrees in fraction form?<\/p>\n\n\n\n

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

The correct answer is 1\/2<\/p>\n\n\n\n

The value of cos\u2061(60\u2218)\\cos(60^\\circ)cos(60\u2218) in fraction form is 12\\frac{1}{2}21\u200b.<\/p>\n\n\n\n

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

The cosine function, cos\u2061(\u03b8)\\cos(\\theta)cos(\u03b8), is a trigonometric function that is defined on the unit circle. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. The cosine of an angle \u03b8\\theta\u03b8 is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.<\/p>\n\n\n\n

To understand why cos\u2061(60\u2218)=12\\cos(60^\\circ) = \\frac{1}{2}cos(60\u2218)=21\u200b, we need to recall the basic properties of the unit circle and specific angles. The angle 60\u221860^\\circ60\u2218 (or \u03c03\\frac{\\pi}{3}3\u03c0\u200b radians) is one of the special angles in trigonometry, and we can calculate the cosine of 60\u221860^\\circ60\u2218 using the coordinates of the point on the unit circle that corresponds to this angle.<\/p>\n\n\n\n

Unit Circle Reference:<\/h3>\n\n\n\n

At 60\u221860^\\circ60\u2218, the corresponding point on the unit circle has coordinates (cos\u2061(60\u2218),sin\u2061(60\u2218))\\left( \\cos(60^\\circ), \\sin(60^\\circ) \\right)(cos(60\u2218),sin(60\u2218)). This point is located on the first quadrant of the unit circle, where both x and y values are positive.<\/p>\n\n\n\n

From the known values of trigonometric functions for standard angles, we have:<\/p>\n\n\n\n

    \n
  • cos\u2061(60\u2218)=12\\cos(60^\\circ) = \\frac{1}{2}cos(60\u2218)=21\u200b<\/li>\n\n\n\n
  • sin\u2061(60\u2218)=32\\sin(60^\\circ) = \\frac{\\sqrt{3}}{2}sin(60\u2218)=23\u200b\u200b<\/li>\n<\/ul>\n\n\n\n

    Thus, the x-coordinate of the point on the unit circle at 60\u221860^\\circ60\u2218 is 12\\frac{1}{2}21\u200b, which is the value of cos\u2061(60\u2218)\\cos(60^\\circ)cos(60\u2218).<\/p>\n\n\n\n

    Why This Is True:<\/h3>\n\n\n\n

    In a 30-60-90 triangle, which is a right triangle with angles of 30\u221830^\\circ30\u2218, 60\u221860^\\circ60\u2218, and 90\u221890^\\circ90\u2218, the ratio of the lengths of the sides opposite these angles is well-known:<\/p>\n\n\n\n

      \n
    • The side opposite the 30\u221830^\\circ30\u2218 angle has a length of 12\\frac{1}{2}21\u200b.<\/li>\n\n\n\n
    • The side opposite the 60\u221860^\\circ60\u2218 angle has a length of 32\\frac{\\sqrt{3}}{2}23\u200b\u200b.<\/li>\n\n\n\n
    • The hypotenuse of the triangle has a length of 1 (since we are working on the unit circle).<\/li>\n<\/ul>\n\n\n\n

      Using this triangle, we can confirm that cos\u2061(60\u2218)\\cos(60^\\circ)cos(60\u2218), which corresponds to the ratio of the adjacent side to the hypotenuse, is 12\\frac{1}{2}21\u200b.<\/p>\n\n\n\n

      Thus, cos\u2061(60\u2218)=12\\cos(60^\\circ) = \\frac{1}{2}cos(60\u2218)=21\u200b.<\/p>\n","protected":false},"excerpt":{"rendered":"

      What is cos 60 degrees in fraction form? The Correct Answer and Explanation is: The correct answer is 1\/2 The value of cos\u2061(60\u2218)\\cos(60^\\circ)cos(60\u2218) in fraction form is 12\\frac{1}{2}21\u200b. Explanation: The cosine function, cos\u2061(\u03b8)\\cos(\\theta)cos(\u03b8), is a trigonometric function that is defined on the unit circle. The unit circle is a circle with a radius of 1, […]<\/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-162145","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162145","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=162145"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162145\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=162145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=162145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=162145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}