{"id":257951,"date":"2025-07-17T18:50:50","date_gmt":"2025-07-17T18:50:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=257951"},"modified":"2025-07-17T18:50:52","modified_gmt":"2025-07-17T18:50:52","slug":"arctan-square-root-3-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/17\/arctan-square-root-3-3\/","title":{"rendered":"Arctan square root 3 \/3"},"content":{"rendered":"\n<p>Arctan square root 3 \/3<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The expression you provided is the inverse tangent of 33\\frac{\\sqrt{3}}{3}33\u200b\u200b, written as:arctan\u2061(33)\\arctan\\left(\\frac{\\sqrt{3}}{3}\\right)arctan(33\u200b\u200b)<\/p>\n\n\n\n<p>To find the exact value, we need to recall some fundamental trigonometric relationships. Specifically, we are looking for an angle \u03b8\\theta\u03b8 whose tangent value equals 33\\frac{\\sqrt{3}}{3}33\u200b\u200b. That is:tan\u2061(\u03b8)=33\\tan(\\theta) = \\frac{\\sqrt{3}}{3}tan(\u03b8)=33\u200b\u200b<\/p>\n\n\n\n<p>From trigonometry, we know that:tan\u2061(\u03c06)=33\\tan\\left(\\frac{\\pi}{6}\\right) = \\frac{\\sqrt{3}}{3}tan(6\u03c0\u200b)=33\u200b\u200b<\/p>\n\n\n\n<p>Thus, the angle \u03b8=\u03c06\\theta = \\frac{\\pi}{6}\u03b8=6\u03c0\u200b is the solution to the equation. Therefore:arctan\u2061(33)=\u03c06\\arctan\\left(\\frac{\\sqrt{3}}{3}\\right) = \\frac{\\pi}{6}arctan(33\u200b\u200b)=6\u03c0\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The inverse tangent function, arctan\u2061(x)\\arctan(x)arctan(x), gives the angle whose tangent is xxx. The tangent function, tan\u2061(\u03b8)\\tan(\\theta)tan(\u03b8), for a standard 30-60-90 right triangle, has known values for the angles:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At \u03b8=\u03c06\\theta = \\frac{\\pi}{6}\u03b8=6\u03c0\u200b or 30\u00b0, the ratio of the opposite side to the adjacent side is 13\\frac{1}{\\sqrt{3}}3\u200b1\u200b, or equivalently, 33\\frac{\\sqrt{3}}{3}33\u200b\u200b.<\/li>\n\n\n\n<li>In this case, we are dealing with the ratio 33\\frac{\\sqrt{3}}{3}33\u200b\u200b, which directly corresponds to the angle \u03c06\\frac{\\pi}{6}6\u03c0\u200b.<\/li>\n<\/ul>\n\n\n\n<p>So, the solution to the inverse tangent of 33\\frac{\\sqrt{3}}{3}33\u200b\u200b is:arctan\u2061(33)=\u03c06&nbsp;radians\\arctan\\left(\\frac{\\sqrt{3}}{3}\\right) = \\frac{\\pi}{6} \\text{ radians}arctan(33\u200b\u200b)=6\u03c0\u200b&nbsp;radians<\/p>\n\n\n\n<p>This is the simplest and most exact answer in radians. If you were to convert it to degrees, \u03c06\\frac{\\pi}{6}6\u03c0\u200b radians equals 30\u00b0.<\/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-banner6-850.jpeg\" alt=\"\" class=\"wp-image-257952\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Arctan square root 3 \/3 The Correct Answer and Explanation is: The expression you provided is the inverse tangent of 33\\frac{\\sqrt{3}}{3}33\u200b\u200b, written as:arctan\u2061(33)\\arctan\\left(\\frac{\\sqrt{3}}{3}\\right)arctan(33\u200b\u200b) To find the exact value, we need to recall some fundamental trigonometric relationships. Specifically, we are looking for an angle \u03b8\\theta\u03b8 whose tangent value equals 33\\frac{\\sqrt{3}}{3}33\u200b\u200b. That is:tan\u2061(\u03b8)=33\\tan(\\theta) = \\frac{\\sqrt{3}}{3}tan(\u03b8)=33\u200b\u200b From trigonometry, [&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-257951","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257951","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=257951"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257951\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257951"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257951"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257951"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}