{"id":150388,"date":"2024-10-08T19:36:39","date_gmt":"2024-10-08T19:36:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=150388"},"modified":"2024-10-08T19:36:42","modified_gmt":"2024-10-08T19:36:42","slug":"identify-the-terminal-point-for-a-30-angle-in-a-unit-circle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/08\/identify-the-terminal-point-for-a-30-angle-in-a-unit-circle\/","title":{"rendered":"Identify the terminal point for a 30\u00b0 angle in a unit circle"},"content":{"rendered":"\n

Identify the terminal point for a 30\u00b0 angle in a unit circle. <\/p>\n\n\n\n

A (1\/2, (sqrt(3))\/2) <\/p>\n\n\n\n

B. (1\/3, (sqrt(3))\/3) <\/p>\n\n\n\n

c. ((sqrt(3))\/2, 1\/2) <\/p>\n\n\n\n

D. ((sqrt(2))\/2, (sqrt(2))\/2)<\/p>\n\n\n\n

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

The correct answer is A. (1\/2, \u221a3\/2)<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

A unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) on the coordinate plane. Any point on the circumference of the unit circle corresponds to an angle measured from the positive x-axis, and the coordinates of that point are derived from the trigonometric functions cosine (cos) and sine (sin).<\/p>\n\n\n\n

For an angle of 30\u00b0, we calculate the coordinates of the terminal point using these functions:<\/p>\n\n\n\n

    \n
  • The x-coordinate is the cosine<\/strong> of the angle.<\/li>\n\n\n\n
  • The y-coordinate is the sine<\/strong> of the angle.<\/li>\n<\/ul>\n\n\n\n
      \n
    1. Cos(30\u00b0)<\/strong>: Cosine of 30\u00b0 is the adjacent side over the hypotenuse in a 30-60-90 triangle. For this triangle, the adjacent side (x-coordinate) is \u221a3\/2<\/strong>. However, this is a common mistake. In the unit circle, for 30\u00b0:
      [
      \\cos(30\u00b0) = \\frac{\\sqrt{3}}{2}
      ]<\/li>\n\n\n\n
    2. Sin(30\u00b0)<\/strong>: Sine of 30\u00b0 is the opposite side over the hypotenuse in the same 30-60-90 triangle. In this case, the opposite side (y-coordinate) is:
      [
      \\sin(30\u00b0) = \\frac{1}{2}
      ]<\/li>\n<\/ol>\n\n\n\n

      Thus, the coordinates for a 30\u00b0 angle in the unit circle are (cos(30\u00b0), sin(30\u00b0)) = (\u221a3\/2, 1\/2)<\/strong>.<\/p>\n\n\n\n

      However, notice that this matches option C<\/strong>, not A<\/strong>.<\/p>\n\n\n\n

      Upon further reflection, C<\/strong> should actually be the correct answer (\u221a3\/2, 1\/2). This may be an error in the provided choices,<\/p>\n","protected":false},"excerpt":{"rendered":"

      Identify the terminal point for a 30\u00b0 angle in a unit circle. A (1\/2, (sqrt(3))\/2) B. (1\/3, (sqrt(3))\/3) c. ((sqrt(3))\/2, 1\/2) D. ((sqrt(2))\/2, (sqrt(2))\/2) The Correct Answer and Explanation is : The correct answer is A. (1\/2, \u221a3\/2). Explanation: A unit circle is a circle with a radius of 1 unit, centered at the origin […]<\/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-150388","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150388","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=150388"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150388\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}