The tangent function is undefined when the cosine of the angle is equal to zero. The tangent of an angle is given by the ratio:tan\u2061(x)=sin\u2061(x)cos\u2061(x)\\tan(x) = \\frac{\\sin(x)}{\\cos(x)}tan(x)=cos(x)sin(x)\u200b<\/p>\n\n\n\n
For tan\u2061(x)\\tan(x)tan(x) to be undefined, the denominator (cos\u2061(x)\\cos(x)cos(x)) must be zero. The cosine function equals zero at odd multiples of \u03c02\\frac{\\pi}{2}2\u03c0\u200b, i.e., at:x=\u03c02+n\u03c0where n is any integerx = \\frac{\\pi}{2} + n\\pi \\quad \\text{where } n \\text{ is any integer}x=2\u03c0\u200b+n\u03c0where n is any integer<\/p>\n\n\n\n
These points correspond to the values where the tangent function has vertical asymptotes and becomes undefined. The cosine function equals zero at values like \u03c02\\frac{\\pi}{2}2\u03c0\u200b, 3\u03c02\\frac{3\\pi}{2}23\u03c0\u200b, 5\u03c02\\frac{5\\pi}{2}25\u03c0\u200b, and so on, which are odd multiples of \u03c02\\frac{\\pi}{2}2\u03c0\u200b.<\/p>\n\n\n\n
Thus, the correct answer is:<\/p>\n\n\n\n
X is an odd multiple of \u03c02\\frac{\\pi}{2}2\u03c0\u200b.<\/strong><\/p>\n\n\n\n The periodicity of the sine and cosine functions is key to understanding where the tangent function becomes undefined. Both the sine and cosine functions repeat every 2\u03c02\\pi2\u03c0, but the cosine function crosses zero at regular intervals of odd multiples of \u03c02\\frac{\\pi}{2}2\u03c0\u200b, which causes the tangent function to be undefined at these points.<\/p>\n\n\n\n For example, at x=\u03c02x = \\frac{\\pi}{2}x=2\u03c0\u200b, the cosine of the angle is zero, making tan\u2061(x)\\tan(x)tan(x) undefined. This same pattern repeats at x=3\u03c02x = \\frac{3\\pi}{2}x=23\u03c0\u200b, x=5\u03c02x = \\frac{5\\pi}{2}x=25\u03c0\u200b, and so on, where the cosine function again equals zero.<\/p>\n\n\n\n Therefore, the tangent function is undefined at these odd multiples of \u03c02\\frac{\\pi}{2}2\u03c0\u200b.<\/p>\n\n\n\n ‘Where is the tangent function undefined? Choose the correct answer below: Xis an even multiple of 2 Xis an odd multiple of x} {x: xis an even multiple of z} Xis an odd multiple of 2}’ The Correct Answer and Explanation is: The tangent function is undefined when the cosine of the angle is equal […]<\/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-245565","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245565","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=245565"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245565\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"