{"id":251912,"date":"2025-07-11T03:48:18","date_gmt":"2025-07-11T03:48:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=251912"},"modified":"2025-07-11T03:48:20","modified_gmt":"2025-07-11T03:48:20","slug":"find-the-value-of-arctan-sqrt-of-3-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/find-the-value-of-arctan-sqrt-of-3-3\/","title":{"rendered":"find the value of arctan sqrt of 3 \/3"},"content":{"rendered":"\n

find the value of arctan sqrt of 3 \/3<\/p>\n\n\n\n

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

The value of arctan\u2061(33)\\arctan\\left(\\frac{\\sqrt{3}}{3}\\right)arctan(33\u200b\u200b) can be found by recognizing that it corresponds to an angle whose tangent is 33\\frac{\\sqrt{3}}{3}33\u200b\u200b.<\/p>\n\n\n\n

We know that the tangent of standard angles is frequently used in trigonometric calculations. The angle \u03b8\\theta\u03b8 in radians or degrees where tan\u2061(\u03b8)=33\\tan(\\theta) = \\frac{\\sqrt{3}}{3}tan(\u03b8)=33\u200b\u200b is a well-known value in trigonometry. Specifically, this is the angle 30\u221830^\\circ30\u2218 or \u03c06\\frac{\\pi}{6}6\u03c0\u200b radians.<\/p>\n\n\n\n

Step-by-step explanation:<\/h3>\n\n\n\n
    \n
  1. The tangent function is defined as: tan\u2061(\u03b8)=oppositeadjacent\\tan(\\theta) = \\frac{\\text{opposite}}{\\text{adjacent}}tan(\u03b8)=adjacentopposite\u200b In this case, we are looking for an angle where the ratio of the opposite side to the adjacent side equals 33\\frac{\\sqrt{3}}{3}33\u200b\u200b.<\/li>\n\n\n\n
  2. For angles in a 30-60-90 triangle, we know the following:\n
      \n
    • The tangent of 30\u221830^\\circ30\u2218 (or \u03c06\\frac{\\pi}{6}6\u03c0\u200b radians) is: tan\u2061(30\u2218)=13=33\\tan(30^\\circ) = \\frac{1}{\\sqrt{3}} = \\frac{\\sqrt{3}}{3}tan(30\u2218)=3\u200b1\u200b=33\u200b\u200b<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Therefore, when tan\u2061(\u03b8)=33\\tan(\\theta) = \\frac{\\sqrt{3}}{3}tan(\u03b8)=33\u200b\u200b, the angle \u03b8\\theta\u03b8 is exactly 30\u221830^\\circ30\u2218 or \u03c06\\frac{\\pi}{6}6\u03c0\u200b radians.<\/li>\n<\/ol>\n\n\n\n

      Conclusion:<\/h3>\n\n\n\n

      arctan\u2061(33)=30\u2218=\u03c06 radians\\arctan\\left(\\frac{\\sqrt{3}}{3}\\right) = 30^\\circ = \\frac{\\pi}{6} \\text{ radians}arctan(33\u200b\u200b)=30\u2218=6\u03c0\u200b radians<\/p>\n\n\n\n

      This is the correct angle whose tangent equals 33\\frac{\\sqrt{3}}{3}33\u200b\u200b.<\/p>\n\n\n\n

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

      find the value of arctan sqrt of 3 \/3 The Correct Answer and Explanation is: The value of arctan\u2061(33)\\arctan\\left(\\frac{\\sqrt{3}}{3}\\right)arctan(33\u200b\u200b) can be found by recognizing that it corresponds to an angle whose tangent is 33\\frac{\\sqrt{3}}{3}33\u200b\u200b. We know that the tangent of standard angles is frequently used in trigonometric calculations. The angle \u03b8\\theta\u03b8 in radians or degrees […]<\/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-251912","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251912","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=251912"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251912\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=251912"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=251912"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=251912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}