{"id":186393,"date":"2025-01-24T19:47:39","date_gmt":"2025-01-24T19:47:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186393"},"modified":"2025-01-24T19:47:41","modified_gmt":"2025-01-24T19:47:41","slug":"question-5-of-10-mark-the-statements-that-are-true","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/24\/question-5-of-10-mark-the-statements-that-are-true\/","title":{"rendered":"Question 5 ?of 10 Mark the statements that are true"},"content":{"rendered":"\n

Question 5 ?of 10<\/p>\n\n\n\n

Mark the statements that are true.<\/p>\n\n\n\n

A. ?An angle that measures 30\u00b0 ?also measures ??3 ?radians.<\/p>\n\n\n\n

B. ?An angle that measures 180\u00b0 ?also measures ??2 ?radians.<\/p>\n\n\n\n

C. ?An angle that measures ??6 ?radians also measures 30\u00b0.<\/p>\n\n\n\n

D. ?An angle that measures ??3 ?radians also measures 60\u00b0.<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

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

B and D<\/strong> are true.<\/p>\n\n\n\n

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

Understanding this problem requires knowledge of the relationship between degrees and radians. The key formula to convert between degrees and radians is: Radians=Degrees\u00d7\u03c0180\\text{Radians} = \\text{Degrees} \\times \\frac{\\pi}{180}<\/p>\n\n\n\n

Let’s evaluate each statement:<\/h3>\n\n\n\n

A. An angle that measures 30\u00b0 also measures 33 radians.<\/strong><\/h4>\n\n\n\n
    \n
  • Using the formula: Radians=30\u00d7\u03c0180=\u03c06\\text{Radians} = 30 \\times \\frac{\\pi}{180} = \\frac{\\pi}{6} This means 30\u00b0 equals \u03c06\\frac{\\pi}{6} radians, not 33 radians.
    This statement is false.<\/strong><\/li>\n<\/ul>\n\n\n\n

    B. An angle that measures 180\u00b0 also measures 22 radians.<\/strong><\/h4>\n\n\n\n
      \n
    • Using the formula: Radians=180\u00d7\u03c0180=\u03c0\\text{Radians} = 180 \\times \\frac{\\pi}{180} = \\pi For 180\u00b0, the radian measure is \u03c0\\pi, which is equivalent to 22 radians.
      This statement is true.<\/strong><\/li>\n<\/ul>\n\n\n\n

      C. An angle that measures 66 radians also measures 30\u00b0.<\/strong><\/h4>\n\n\n\n
        \n
      • To convert 66 radians into degrees: Degrees=6\u00d7180\u03c0\u2248343.77\u00b0\\text{Degrees} = 6 \\times \\frac{180}{\\pi} \\approx 343.77\u00b0 This shows that 66 radians is much greater than 30\u00b0.
        This statement is false.<\/strong><\/li>\n<\/ul>\n\n\n\n

        D. An angle that measures 33 radians also measures 60\u00b0.<\/strong><\/h4>\n\n\n\n
          \n
        • Using the formula: Degrees=3\u00d7180\u03c0\u2248171.89\u00b0\\text{Degrees} = 3 \\times \\frac{180}{\\pi} \\approx 171.89\u00b0 33 radians does not equal 60\u00b0 but is closer to 172\u00b0172\u00b0. Misinterpreting this can lead to confusion. If the question is wrong clarify,<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

          Question 5 ?of 10 Mark the statements that are true. A. ?An angle that measures 30\u00b0 ?also measures ??3 ?radians. B. ?An angle that measures 180\u00b0 ?also measures ??2 ?radians. C. ?An angle that measures ??6 ?radians also measures 30\u00b0. D. ?An angle that measures ??3 ?radians also measures 60\u00b0. The correct answer and explanation […]<\/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-186393","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186393","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=186393"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186393\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186393"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186393"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}