Evaluate. Write your answers in simplified, rationalized forms. Do not round.
sin 30\u00b0 =
COS 30\u00b0=
tan 30\u00b0 =<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n The values for sin 30\u00b0, cos 30\u00b0, and tan 30\u00b0 are commonly known, and they are derived from the properties of a 30\u00b0-60\u00b0-90\u00b0 triangle, which has specific ratios for its sides.<\/p>\n\n\n\n For a 30\u00b0 angle in a right triangle, the opposite side is half the length of the hypotenuse. The ratio of the opposite side to the hypotenuse is defined as sine. In a 30\u00b0-60\u00b0-90\u00b0 triangle, the sides have a ratio of 1:\u221a3:2. Therefore, the sine of 30\u00b0 is: sin\u206130\u00b0=12\\sin 30\u00b0 = \\frac{1}{2}<\/p>\n\n\n\n The cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse. For a 30\u00b0-60\u00b0-90\u00b0 triangle, the adjacent side for 30\u00b0 is \u221a3, and the hypotenuse is 2. So: cos\u206130\u00b0=32\\cos 30\u00b0 = \\frac{\\sqrt{3}}{2}<\/p>\n\n\n\n The tangent of an angle is the ratio of the opposite side to the adjacent side. In a 30\u00b0-60\u00b0-90\u00b0 triangle, for the 30\u00b0 angle, the opposite side is 1, and the adjacent side is \u221a3. Therefore: tan\u206130\u00b0=13\\tan 30\u00b0 = \\frac{1}{\\sqrt{3}}<\/p>\n\n\n\n To rationalize the denominator: tan\u206130\u00b0=13\u00d733=33\\tan 30\u00b0 = \\frac{1}{\\sqrt{3}} \\times \\frac{\\sqrt{3}}{\\sqrt{3}} = \\frac{\\sqrt{3}}{3}<\/p>\n\n\n\n These values are derived from the special properties of a 30\u00b0-60\u00b0-90\u00b0 triangle, where the ratios of the sides are consistent and can be used to determine trigonometric values for these angles.<\/p>\n","protected":false},"excerpt":{"rendered":" Evaluate. Write your answers in simplified, rationalized forms. Do not round.sin 30\u00b0 =COS 30\u00b0=tan 30\u00b0 = The correct answer and explanation is: The values for sin 30\u00b0, cos 30\u00b0, and tan 30\u00b0 are commonly known, and they are derived from the properties of a 30\u00b0-60\u00b0-90\u00b0 triangle, which has specific ratios for its sides. sin 30\u00b0: […]<\/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-272964","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/272964","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=272964"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/272964\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=272964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=272964"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=272964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}sin 30\u00b0:<\/h3>\n\n\n\n
cos 30\u00b0:<\/h3>\n\n\n\n
tan 30\u00b0:<\/h3>\n\n\n\n
Summary of answers:<\/h3>\n\n\n\n
\n