{"id":237816,"date":"2025-06-17T16:23:02","date_gmt":"2025-06-17T16:23:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237816"},"modified":"2025-06-17T16:23:03","modified_gmt":"2025-06-17T16:23:03","slug":"the-least-positive-value-x-for-which-cotx-0-is-ie-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/the-least-positive-value-x-for-which-cotx-0-is-ie-2\/","title":{"rendered":"The least positive value x for which cot(x) = 0 is \u00cf\u20ac\/2."},"content":{"rendered":"\n

The least positive value x for which cot(x) = 0 is \u00cf\u20ac\/2.
<\/p>\n\n\n\n

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

The least positive value of x for which cot(x) = 0 is \u03c0\/2<\/strong>.<\/p>\n\n\n\n

To understand this result, consider the definition of the cotangent function. The cotangent of an angle x is given by cot(x) = 1\/tan(x). This means cot(x) is zero wherever tan(x) approaches infinity or is undefined.<\/p>\n\n\n\n

The tangent function is defined as tan(x) = sin(x)\/cos(x). This function is zero whenever sin(x) = 0, which occurs at integer multiples of \u03c0 such as 0, \u03c0, and 2\u03c0. However, tangent is undefined when cos(x) = 0, which happens at odd multiples of \u03c0\/2, including \u03c0\/2, 3\u03c0\/2, and 5\u03c0\/2. Since cotangent is the reciprocal of tangent, cotangent is zero at precisely these points where tangent is undefined.<\/p>\n\n\n\n

To determine the least positive x where cot(x) = 0, focus on the smallest positive odd multiple of \u03c0\/2. The first instance where cosine equals zero is at \u03c0\/2<\/strong>, making this the smallest solution.<\/p>\n\n\n\n

A deeper analysis confirms this result by considering the unit circle. The cotangent function is represented by the ratio of the adjacent side to the opposite side in a right triangle. At \u03c0\/2<\/strong>, the opposite side (sine value) reaches its maximum while the adjacent side (cosine value) becomes zero. Since cotangent is the reciprocal of tangent, this leads cotangent to equal zero.<\/p>\n\n\n\n

In summary, the smallest positive value of x that satisfies cot(x) = 0 is \u03c0\/2<\/strong>, as this is the first instance where cosine is zero and tangent is undefined, forcing cotangent to take the value zero.<\/p>\n\n\n\n

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

The least positive value x for which cot(x) = 0 is \u00cf\u20ac\/2. The Correct Answer and Explanation is: The least positive value of x for which cot(x) = 0 is \u03c0\/2. To understand this result, consider the definition of the cotangent function. The cotangent of an angle x is given by cot(x) = 1\/tan(x). This […]<\/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-237816","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237816","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=237816"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237816\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}