![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-63.png\")
<\/figure>\n\n\n\nThe Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Of course. Here is the solution with all the steps and a diagram as requested.<\/p>\n\n\n\n Final Answer:<\/strong> Step 1: Locate the Angle<\/strong><\/p>\n\n\n\n First, we need to determine the position of the angle 11\u03c0\/6 on the unit circle. An angle is measured counterclockwise from the positive x-axis. We know that a full circle is 2\u03c0 radians.<\/p>\n\n\n\n To make it easier to locate, we can express 2\u03c0 with a denominator of 6: The angle 11\u03c0\/6 is slightly less than 12\u03c0\/6. This means the terminal side of the angle 11\u03c0\/6 lies in the fourth quadrant (Quadrant IV)<\/strong>.<\/p>\n\n\n\n Step 2: Find the Reference Angle<\/strong><\/p>\n\n\n\n The reference angle is the acute angle that the terminal side of 11\u03c0\/6 makes with the x-axis. Since the angle is in Quadrant IV, we can find the reference angle (\u03b1) by subtracting 11\u03c0\/6 from the full circle (2\u03c0).<\/p>\n\n\n\n Reference Angle (\u03b1) = 2\u03c0 – 11\u03c0\/6 The reference angle is \u03c0\/6. This means the trigonometric values of 11\u03c0\/6 will have the same magnitude as the values for \u03c0\/6, but the sign will be determined by the quadrant.<\/p>\n\n\n\n Step 3: Determine the Sign of Cotangent in Quadrant IV<\/strong><\/p>\n\n\n\n The cotangent function is defined as cot(\u03b8) = cos(\u03b8) \/ sin(\u03b8). On the unit circle, this corresponds to the ratio of the x-coordinate to the y-coordinate (x\/y).<\/p>\n\n\n\n Therefore, cotangent is negative in Quadrant IV because (positive) \/ (negative) = negative.<\/p>\n\n\n\n Step 4: Calculate the Exact Value<\/strong><\/p>\n\n\n\n Now, we calculate the value of cotangent for the reference angle, \u03c0\/6.<\/p>\n\n\n\n cot(\u03c0\/6) = cos(\u03c0\/6) \/ sin(\u03c0\/6)<\/p>\n\n\n\n We know the standard values for \u03c0\/6:<\/p>\n\n\n\n So, cot(\u03c0\/6) = (\u221a3 \/ 2) \/ (1\/2) = \u221a3.<\/p>\n\n\n\n Finally, we apply the negative sign we determined in Step 3.<\/p>\n\n\n\n cot(11\u03c0\/6) = -cot(\u03c0\/6) = -\u221a3<\/strong><\/p>\n\n\n\n The following diagram illustrates the angle 11\u03c0\/6 in standard position on the unit circle.Generated code<\/p>\n\n\n\n \u00a0<\/p>\n\n\n\n Diagram Explanation:<\/strong> Question 4 (4 points) State the exact value for . Show all steps. Include a diagram as part of your solution The Correct Answer and Explanation is: Of course. Here is the solution with all the steps and a diagram as requested. Final Answer:The exact value of cot(11\u03c0\/6) is -\u221a3. Step-by-Step Solution Step 1: Locate the […]<\/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-240922","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240922","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=240922"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240922\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
The exact value of cot(11\u03c0\/6) is -\u221a3<\/strong>.<\/p>\n\n\n\nStep-by-Step Solution<\/strong><\/h3>\n\n\n\n
2\u03c0 = 12\u03c0\/6<\/p>\n\n\n\n
\u03b1 = 12\u03c0\/6 – 11\u03c0\/6
\u03b1 = \u03c0\/6<\/p>\n\n\n\n\n
\n
Diagram<\/strong><\/h3>\n\n\n\n
y-axis\n ^\n |\n |\n QII | QI\n |\n--------|--------> x-axis\n |\n QIII | QIV\n | \/\n | \/ \u03b1 = \u03c0\/6\n | \/\n | \/ <-- Terminal side of 11\u03c0\/6\n * (\u221a3\/2, -1\/2)<\/code><\/pre>\n\n\n\n
The diagram shows the angle 11\u03c0\/6 starting from the positive x-axis and rotating counterclockwise, ending in the fourth quadrant. The reference angle, \u03b1 = \u03c0\/6, is the acute angle between the terminal side and the positive x-axis. The point where the terminal side intersects the unit circle has coordinates (cos(11\u03c0\/6), sin(11\u03c0\/6)), which are (\u221a3\/2, -1\/2). The cotangent is the x-coordinate divided by the y-coordinate, confirming the result: (\u221a3\/2) \/ (-1\/2) = -\u221a3<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-148.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"