{"id":240294,"date":"2025-07-03T08:25:22","date_gmt":"2025-07-03T08:25:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=240294"},"modified":"2025-07-03T08:25:24","modified_gmt":"2025-07-03T08:25:24","slug":"find-the-exact-value-of-sin%e2%81%a15%cf%804","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/find-the-exact-value-of-sin%e2%81%a15%cf%804\/","title":{"rendered":"Find the exact value of\u00a0sin\u20615\u03c04."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

To find the exact value of sin\u2061(5\u03c04)\\sin \\left( \\frac{5\\pi}{4} \\right)sin(45\u03c0\u200b), we can follow these steps:<\/p>\n\n\n\n

    \n
  1. Identify the angle’s position on the unit circle:<\/strong>
    The angle 5\u03c04\\frac{5\\pi}{4}45\u03c0\u200b is in radians. To better understand its position, we can convert it to degrees. 5\u03c04\u00d7180\u2218\u03c0=225\u2218.\\frac{5\\pi}{4} \\times \\frac{180^\\circ}{\\pi} = 225^\\circ.45\u03c0\u200b\u00d7\u03c0180\u2218\u200b=225\u2218. The angle 225\u2218225^\\circ225\u2218 lies in the third quadrant of the unit circle, where the sine function is negative.<\/li>\n\n\n\n
  2. Find the reference angle:<\/strong>
    The reference angle is the acute angle that the terminal side of 225\u2218225^\\circ225\u2218 makes with the x-axis. To find this, subtract 180\u2218180^\\circ180\u2218 from 225\u2218225^\\circ225\u2218: 225\u2218\u2212180\u2218=45\u2218.225^\\circ – 180^\\circ = 45^\\circ.225\u2218\u2212180\u2218=45\u2218. Thus, the reference angle is 45\u221845^\\circ45\u2218 (or \u03c04\\frac{\\pi}{4}4\u03c0\u200b).<\/li>\n\n\n\n
  3. Determine the sine value:<\/strong>
    The sine of 45\u221845^\\circ45\u2218 or \u03c04\\frac{\\pi}{4}4\u03c0\u200b is known to be 22\\frac{\\sqrt{2}}{2}22\u200b\u200b. Since the angle 225\u2218225^\\circ225\u2218 is in the third quadrant, the sine function is negative in this quadrant. Therefore: sin\u2061(225\u2218)=\u221222.\\sin \\left( 225^\\circ \\right) = -\\frac{\\sqrt{2}}{2}.sin(225\u2218)=\u221222\u200b\u200b.<\/li>\n\n\n\n
  4. Conclusion:<\/strong>
    The exact value of sin\u2061(5\u03c04)\\sin \\left( \\frac{5\\pi}{4} \\right)sin(45\u03c0\u200b) is: sin\u2061(5\u03c04)=\u221222.\\sin \\left( \\frac{5\\pi}{4} \\right) = -\\frac{\\sqrt{2}}{2}.sin(45\u03c0\u200b)=\u221222\u200b\u200b.<\/li>\n<\/ol>\n\n\n\n
    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The Correct Answer and Explanation is: To find the exact value of sin\u2061(5\u03c04)\\sin \\left( \\frac{5\\pi}{4} \\right)sin(45\u03c0\u200b), we can follow these steps:<\/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-240294","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240294","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=240294"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240294\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240294"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240294"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}