{"id":249843,"date":"2025-07-10T05:40:56","date_gmt":"2025-07-10T05:40:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249843"},"modified":"2025-07-10T05:40:59","modified_gmt":"2025-07-10T05:40:59","slug":"find-the-terminal-point-on-the-unit-circle-determined-by-7pi-4-radians","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/find-the-terminal-point-on-the-unit-circle-determined-by-7pi-4-radians\/","title":{"rendered":"Find the terminal point on the unit circle determined by 7pi\/4 radians."},"content":{"rendered":"\n

Find the terminal point on the unit circle determined by 7pi\/4 radians. Use exact values, not decimal approximations.<\/p>\n\n\n\n

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

To find the terminal point on the unit circle determined by 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b radians, we need to determine both the reference angle and the coordinates of the terminal point.<\/p>\n\n\n\n

Step 1: Find the reference angle.<\/h3>\n\n\n\n

A reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b is greater than 2\u03c02\\pi2\u03c0 (a full revolution), we need to subtract 2\u03c02\\pi2\u03c0 to get the corresponding angle between 000 and 2\u03c02\\pi2\u03c0. 7\u03c04\u22122\u03c0=7\u03c04\u22128\u03c04=\u2212\u03c04\\frac{7\\pi}{4} – 2\\pi = \\frac{7\\pi}{4} – \\frac{8\\pi}{4} = -\\frac{\\pi}{4}47\u03c0\u200b\u22122\u03c0=47\u03c0\u200b\u221248\u03c0\u200b=\u22124\u03c0\u200b<\/p>\n\n\n\n

This tells us that 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b is coterminal with \u2212\u03c04-\\frac{\\pi}{4}\u22124\u03c0\u200b, which is the reference angle.<\/p>\n\n\n\n

Step 2: Identify the quadrant.<\/h3>\n\n\n\n

The angle 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b lies in the fourth quadrant. This is because:<\/p>\n\n\n\n

    \n
  • 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b is between 2\u03c02\\pi2\u03c0 (which is 8\u03c04\\frac{8\\pi}{4}48\u03c0\u200b) and 2\u03c0+\u03c042\\pi + \\frac{\\pi}{4}2\u03c0+4\u03c0\u200b, which is the fourth quadrant of the unit circle.<\/li>\n<\/ul>\n\n\n\n

    Step 3: Use the reference angle to determine the coordinates.<\/h3>\n\n\n\n

    The reference angle is \u03c04\\frac{\\pi}{4}4\u03c0\u200b, and the coordinates for an angle of \u03c04\\frac{\\pi}{4}4\u03c0\u200b on the unit circle are: (cos\u2061(\u03c04),sin\u2061(\u03c04))=(22,22)\\left( \\cos\\left(\\frac{\\pi}{4}\\right), \\sin\\left(\\frac{\\pi}{4}\\right) \\right) = \\left( \\frac{\\sqrt{2}}{2}, \\frac{\\sqrt{2}}{2} \\right)(cos(4\u03c0\u200b),sin(4\u03c0\u200b))=(22\u200b\u200b,22\u200b\u200b)<\/p>\n\n\n\n

    Since 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b lies in the fourth quadrant, the x-coordinate is positive, and the y-coordinate is negative. Therefore, the coordinates of the terminal point are: (22,\u221222)\\left( \\frac{\\sqrt{2}}{2}, -\\frac{\\sqrt{2}}{2} \\right)(22\u200b\u200b,\u221222\u200b\u200b)<\/p>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    The terminal point on the unit circle determined by 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b radians is: (22,\u221222)\\left( \\frac{\\sqrt{2}}{2}, -\\frac{\\sqrt{2}}{2} \\right)(22\u200b\u200b,\u221222\u200b\u200b)<\/p>\n\n\n\n

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

    Find the terminal point on the unit circle determined by 7pi\/4 radians. Use exact values, not decimal approximations. The Correct Answer and Explanation is: To find the terminal point on the unit circle determined by 7\u03c04\\frac{7\\pi}{4}47\u03c0\u200b radians, we need to determine both the reference angle and the coordinates of the terminal point. Step 1: Find […]<\/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-249843","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249843","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=249843"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249843\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249843"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249843"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}