{"id":3161,"date":"2012-08-21T22:27:01","date_gmt":"2012-08-21T22:27:01","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=3161"},"modified":"2014-12-02T08:32:06","modified_gmt":"2014-12-02T08:32:06","slug":"trigonometric-ratios-of-standard-angles","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/trigonometric-ratios-of-standard-angles\/","title":{"rendered":"Trigonometric Ratios of Standard Angles"},"content":{"rendered":"

Usually, a calculator is used to find the trigonometric ratios at different values. But sometimes, the problem may ask to solve it without using a calculator where it involves some standard angles. The standard angles are 0, 300<\/sup>, 450<\/sup>, 600<\/sup> and 900<\/sup>. Let us learn how to find the values of trigonometric ratios of these standard angles without using a calculator.<\/p>\n

Trigonometric ratios of 300<\/sup> and 600<\/sup>:<\/strong><\/p>\n

Consider an equilateral triangle ABC whose side is 2 units.<\/p>\n

Then AB=BC=CA=2.<\/strong><\/p>\n

Let AD<\/strong> be the altitude.<\/p>\n

Then BD=1.<\/strong><\/p>\n

From Pythagoras theorem, we get AD = \u221a3.<\/strong><\/p>\n

\"\"<\/a><\/p>\n

From \u0394ABD, (using definitions of trigonometric ratios)<\/p>\n

Sin 60 = \u221a3\/2 => Cosec 60 = 2\/ \u221a3<\/strong><\/p>\n

Cos 60 = 1\/2 => Sec 60 = 2<\/strong><\/p>\n

Tan 60 = \u221a3 => Cot 60 = 1\/\u221a3<\/strong><\/p>\n

Again from \u0394ABD<\/strong>, (using definitions of trigonometric ratios)<\/p>\n

Sin 30 = 1\/2 => Cosec 30 = 2<\/strong><\/p>\n

Cos 30 = \u221a3\/2 => Sec 30 = 2\/\u221a3<\/strong><\/p>\n

Tan 30 = 1\/\u221a3 => Cot 30 = \u221a3.<\/strong><\/p>\n

Trigonometric ratios of 450<\/sup>:<\/h5>\n

Consider an isosceles right angled triangle ABC<\/strong> with right angle at B<\/strong> where AB=BC =1<\/strong> unit.<\/p>\n

\"\"<\/a><\/p>\n

Using definitions of trigonometric ratios,<\/p>\n

Sin 45 = 1\/\u221a2 => Cosec 45 = \u221a2<\/strong><\/p>\n

Cos 45 = 1\/\u221a2 => Sec 45 = \u221a2<\/strong><\/p>\n

Tan 45 = 1 => Cot 45 = 1.<\/strong><\/p>\n

Based on the above data, the following table is formed.<\/p>\n

\"\"<\/a><\/p>\n

Still need help with Mathematics? Please read more about our Math tutoring services<\/a>.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Palos Verdes Estates visit: Tutoring in Palos Verdes Estates.<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Usually, a calculator is used to find the trigonometric ratios at different values. But sometimes, the problem may ask to solve it without using a calculator where it involves some standard angles. The standard angles are 0, 300, 450, 600 and 900. Let us learn how to find the values of trigonometric ratios of these […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[18],"tags":[94,1721,1860],"class_list":["post-3161","post","type-post","status-publish","format-standard","hentry","category-trigonometry","tag-angle","tag-standard","tag-trigonometric-ratio"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=3161"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3161\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=3161"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=3161"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=3161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}