Find the exact value of sin 60 degree<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n The exact value<\/strong> of sin 60\u00b0<\/strong> is:<\/p>\n\n\n\n $$ To understand why $\\sin 60^\\circ = \\frac{\\sqrt{3}}{2}$, let\u2019s explore the geometry and trigonometry<\/strong> behind it.<\/p>\n\n\n\n A 30\u00b0-60\u00b0-90\u00b0 triangle<\/strong> is a special right triangle where the angles are 30\u00b0, 60\u00b0, and 90\u00b0. In this triangle, the sides follow a consistent ratio<\/strong>:<\/p>\n\n\n\n These ratios come from splitting an equilateral triangle<\/strong> in half. Here\u2019s how:<\/p>\n\n\n\n $$ So now, we have:<\/p>\n\n\n\n By definition in trigonometry:<\/p>\n\n\n\n $$ For $\\theta = 60^\\circ$, the opposite side is $\\sqrt{3}$, and the hypotenuse is 2:<\/p>\n\n\n\n $$ On the unit circle<\/strong>, the coordinates of a point at 60\u00b0 (or $\\frac{\\pi}{3}$ radians) are:<\/p>\n\n\n\n $$ Again, we see that:<\/p>\n\n\n\n $$ $$ Find the exact value of sin 60 degree The correct answer and explanation is : The exact value of sin 60\u00b0 is: $$\\sin 60^\\circ = \\frac{\\sqrt{3}}{2}$$ \ud83d\udd0d Explanation (300+ words): To understand why $\\sin 60^\\circ = \\frac{\\sqrt{3}}{2}$, let\u2019s explore the geometry and trigonometry behind it. \ud83c\udf1f Using a Special Triangle \u2013 The 30\u00b0-60\u00b0-90\u00b0 Triangle: A […]<\/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-211445","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211445","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=211445"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211445\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211445"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211445"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211445"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\sin 60^\\circ = \\frac{\\sqrt{3}}{2}
$$<\/p>\n\n\n\n
\n\n\n\n\ud83d\udd0d Explanation (300+ words):<\/h3>\n\n\n\n
\ud83c\udf1f Using a Special Triangle \u2013 The 30\u00b0-60\u00b0-90\u00b0 Triangle:<\/h4>\n\n\n\n
\n
\n
\\text{height} = \\sqrt{2^2 – 1^2} = \\sqrt{4 – 1} = \\sqrt{3}
$$<\/p>\n\n\n\n\n
\ud83d\udcd0 Using the Definition of Sine:<\/h4>\n\n\n\n
\\sin \\theta = \\frac{\\text{opposite}}{\\text{hypotenuse}}
$$<\/p>\n\n\n\n
\\sin 60^\\circ = \\frac{\\sqrt{3}}{2}
$$<\/p>\n\n\n\n\u2705 Verification with Unit Circle:<\/h4>\n\n\n\n
\\left(\\cos 60^\\circ, \\sin 60^\\circ\\right) = \\left(\\frac{1}{2}, \\frac{\\sqrt{3}}{2}\\right)
$$<\/p>\n\n\n\n
\\sin 60^\\circ = \\frac{\\sqrt{3}}{2}
$$<\/p>\n\n\n\n
\n\n\n\n\u2705 Final Answer:<\/h3>\n\n\n\n
\\boxed{\\frac{\\sqrt{3}}{2}}
$$<\/p>\n","protected":false},"excerpt":{"rendered":"