The given expression is tan\u207b\u00b9(\u221a3\/3)<\/strong>, which represents the inverse tangent or arctangent of \u221a3\/3<\/strong>.<\/p>\n\n\n\n We are looking for an angle whose tangent equals \u221a3\/3<\/strong>. We can rewrite this in terms of a right triangle to understand it better. Recall that the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.<\/p>\n\n\n\n If tan(\u03b8) = \u221a3\/3<\/strong>, then the opposite side of the triangle is \u221a3<\/strong>, and the adjacent side is 3<\/strong>.<\/p>\n\n\n\n The tangent of an angle is equal to \u221a3\/3<\/strong> at a specific standard angle. We can compare the given ratio with the known values for the tangent of standard angles in trigonometry. In fact, the tangent of 30\u00b0 or \u03c0\/6 radians<\/strong> is 1\/\u221a3<\/strong>, which is equivalent to \u221a3\/3<\/strong> when simplified.<\/p>\n\n\n\n Thus, the angle \u03b8 whose tangent is \u221a3\/3<\/strong> is 30\u00b0<\/strong> or \u03c0\/6 radians<\/strong>.<\/p>\n\n\n\n Therefore, the value of tan\u207b\u00b9(\u221a3\/3)<\/strong> is 30\u00b0<\/strong> or \u03c0\/6 radians<\/strong>.<\/p>\n\n\n\n Inverse trigonometric functions are used to find angles from known ratios. Here, we used the fact that the inverse tangent function, tan\u207b\u00b9<\/strong>, returns an angle whose tangent equals the given ratio. By recognizing \u221a3\/3<\/strong> as the ratio of tangent at 30\u00b0<\/strong> or \u03c0\/6 radians<\/strong>, we were able to conclude that the inverse tangent of \u221a3\/3<\/strong> is 30\u00b0<\/strong> or \u03c0\/6<\/strong>.<\/p>\n\n\n\n In trigonometric terms:<\/p>\n\n\n\n The inverse tangent function returns the principal value (usually between -90\u00b0 and 90\u00b0, or -\u03c0\/2 and \u03c0\/2 radians) corresponding to the given ratio, making 30\u00b0<\/strong> the correct solution.<\/p>\n\n\n\n find the value of Tan-1 square root 3\/3 The Correct Answer and Explanation is: The given expression is tan\u207b\u00b9(\u221a3\/3), which represents the inverse tangent or arctangent of \u221a3\/3. Step 1: Recognizing the Ratio We are looking for an angle whose tangent equals \u221a3\/3. We can rewrite this in terms of a right triangle to understand […]<\/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-253006","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253006","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=253006"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253006\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253006"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253006"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253006"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Recognizing the Ratio<\/h3>\n\n\n\n
Step 2: Identify the Angle<\/h3>\n\n\n\n
Step 3: Conclusion<\/h3>\n\n\n\n
Explanation in Context<\/h3>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"