{"id":20021,"date":"2022-09-10T06:56:57","date_gmt":"2022-09-10T06:56:57","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7564"},"modified":"2022-09-10T06:56:57","modified_gmt":"2022-09-10T06:56:57","slug":"special-angles","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/10\/special-angles\/","title":{"rendered":"Special Angles"},"content":{"rendered":"\n<p>We will first look into the trigonometric functions of the angles 30\u00b0, 45\u00b0 and 60\u00b0.<\/p>\n\n\n\n<p>Let us consider 30\u00b0 and 60\u00b0.<\/p>\n\n\n\n<p>These two angles form a 30\u00b0-60\u00b0-90\u00b0 right triangle as shown.<\/p>\n\n\n\n<p>The ratio of the sides of the triangle is<br>1 : \u221a3 : 2<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometry-angles1.jpg\" alt=\"30-60-90 triangle\" title=\"30-60-90 triangle\"\/><\/figure>\n\n\n\n<p>From the triangle we get the ratios as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/sin-cos-tan-30-60.png\" alt=\"sin cos tan 30, 60\" title=\"sin cos tan 30, 60\"\/><\/figure>\n\n\n\n<p>Next, we consider the 45\u02da angle that forms a 45\u00b0-45\u00b0-90\u00b0 right triangle as shown. The ratio of the sides of the triangle is<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/sin-cos-tan-45.png\" alt=\"sin cos tan 45\" title=\"sin cos tan 45\"\/><\/figure>\n\n\n\n<p>Combining the two tables we get:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometry-angles4.jpg\" alt=\"sin cos tan 30, 45, 60 table\" title=\"sin cos tan 30, 45, 60 table\"\/><\/figure>\n\n\n\n<p><strong>Example:<\/strong><br>Evaluate the following without using a calculator:<br>a) 2 sin 30\u02da + 3 cos 60\u02da \u2013 3 tan 45\u02da<br>b) 3(cos 30\u02da)<sup>2<\/sup>&nbsp;+ 2 (sin 30\u02da )<sup>2<\/sup><\/p>\n\n\n\n<p><strong>Solution:<\/strong><br>a) 2 sin 30\u02da + 3 cos 60\u02da \u2013 3 tan 45\u02da<br><img loading=\"lazy\" decoding=\"async\" height=\"132\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/clip_trig27.gif\" width=\"140\"><\/p>\n\n\n\n<p>b) 3(cos 30\u02da)<sup>2<\/sup>&nbsp;+ 2 (sin 30\u02da)<sup>2<\/sup><br><img loading=\"lazy\" decoding=\"async\" height=\"189\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/clip_trig28.gif\" width=\"127\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We will first look into the trigonometric functions of the angles 30\u00b0, 45\u00b0 and 60\u00b0. Let us consider 30\u00b0 and 60\u00b0. These two angles form a 30\u00b0-60\u00b0-90\u00b0 right triangle as shown. The ratio of the sides of the triangle is1 : \u221a3 : 2 From the triangle we get the ratios as follows: Next, we [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[416],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20021"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=20021"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20021\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=20021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=20021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=20021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}