{"id":233646,"date":"2025-06-13T09:33:53","date_gmt":"2025-06-13T09:33:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233646"},"modified":"2025-06-13T09:33:54","modified_gmt":"2025-06-13T09:33:54","slug":"give-three-different-angles-in-degrees-where-the-cos-of-the-angle-is-0","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/give-three-different-angles-in-degrees-where-the-cos-of-the-angle-is-0\/","title":{"rendered":"Give three different angles, in degrees, where the cos of the angle is 0"},"content":{"rendered":"\n

Give three different angles, in degrees, where the cos of the angle is 0<\/p>\n\n\n\n

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

The three different angles (in degrees) where the cosine of the angle is 0 are:<\/p>\n\n\n\n

90\u00b0, 270\u00b0, and 450\u00b0.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

The cosine function, written as cos(\u03b8)<\/strong>, is one of the primary trigonometric functions. It represents the x-coordinate of a point on the unit circle that corresponds to the angle \u03b8<\/strong>, measured from the positive x-axis. On the unit circle, cosine is 0<\/strong> whenever the terminal side of the angle lies on the y-axis<\/strong>, because at those points the x-coordinate is zero.<\/p>\n\n\n\n

Let’s examine this more closely using the unit circle<\/strong>, which has a radius of 1 and is centered at the origin (0, 0):<\/p>\n\n\n\n

    \n
  1. At 90\u00b0<\/strong>, the point on the unit circle is (0, 1). The x-value is 0, so cos(90\u00b0) = 0<\/strong>.<\/li>\n\n\n\n
  2. At 270\u00b0<\/strong>, the point is (0, -1). Again, the x-value is 0, so cos(270\u00b0) = 0<\/strong>.<\/li>\n\n\n\n
  3. At 450\u00b0<\/strong>, which is one full revolution (360\u00b0) plus 90\u00b0, the point is again (0, 1), just like at 90\u00b0, so cos(450\u00b0) = 0<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    This pattern continues every 180\u00b0 after 90\u00b0, i.e., at 90\u00b0, 270\u00b0, 450\u00b0, 630\u00b0, etc. These are called co-terminal angles<\/strong> because they end at the same position on the unit circle.<\/p>\n\n\n\n

    Mathematically, the cosine of an angle \u03b8<\/strong> is zero when:cos\u2061(\u03b8)=0 whenever \u03b8=90\u00b0+180\u00b0\u00d7nwhere n is an integer\\cos(\u03b8) = 0 \\text{ whenever } \u03b8 = 90\u00b0 + 180\u00b0 \\times n \\quad \\text{where } n \\text{ is an integer}cos(\u03b8)=0 whenever \u03b8=90\u00b0+180\u00b0\u00d7nwhere n is an integer<\/p>\n\n\n\n

    Thus, the cosine function is zero<\/strong> at regular intervals, and you can find an infinite number of angles where this happens. However, in this problem, we only need three<\/strong>, so 90\u00b0, 270\u00b0, and 450\u00b0<\/strong> are sufficient.<\/p>\n\n\n\n

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

    Give three different angles, in degrees, where the cos of the angle is 0 The Correct Answer and Explanation is: The three different angles (in degrees) where the cosine of the angle is 0 are: 90\u00b0, 270\u00b0, and 450\u00b0. Explanation: The cosine function, written as cos(\u03b8), is one of the primary trigonometric functions. It represents […]<\/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-233646","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233646","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=233646"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233646\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}