{"id":7753,"date":"2022-09-18T04:47:49","date_gmt":"2022-09-18T04:47:49","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7753"},"modified":"2022-09-18T04:47:49","modified_gmt":"2022-09-18T04:47:49","slug":"sine-and-cosine-rule-trig-identities","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/18\/sine-and-cosine-rule-trig-identities\/","title":{"rendered":"Sine and Cosine Rule Trig Identities"},"content":{"rendered":"\n<p>The&nbsp;<strong>sine rule<\/strong>&nbsp;gives the relation between the angles and the corresponding sides of a triangle. For the non-right-angled triangles, we will have to use the sine rule and the cosine rule. For a triangle with sides &#8216;a&#8217;, &#8216;b&#8217;, and &#8216;c&#8217; and the respective opposite angles are A, B, and C, sine rule can be given as,<\/p>\n\n\n\n<ul><li>a\/sinA = b\/sinB = c\/sinC<\/li><li>sinA\/a = sinB\/b = sinC\/c<\/li><li>a\/b = sinA\/sinB; a\/c = sinA\/sinC; b\/c = sinB\/sinC<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/09\/cue.png\" alt=\"\" class=\"wp-image-7754\"\/><\/figure>\n\n\n\n<p>The&nbsp;<strong>cosine rule<\/strong>&nbsp;gives the relation between the angles and the sides of a triangle and is usually used when two sides and the included angle of a triangle are given. Cosine rule for a triangle with sides &#8216;a&#8217;, &#8216;b&#8217;, and &#8216;c&#8217; and the respective opposite angles are A, B, and C, sine rule can be given as,<\/p>\n\n\n\n<ul><li>a<sup>2<\/sup>&nbsp;= b<sup>2<\/sup>&nbsp;+ c<sup>2&nbsp;<\/sup>&#8211; 2bc\u00b7cosA<\/li><li>b<sup>2<\/sup>&nbsp;= c<sup>2<\/sup>&nbsp;+ a<sup>2<\/sup>&nbsp;&#8211; 2ca\u00b7cosB<\/li><li>c<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ b<sup>2<\/sup>&nbsp;&#8211; 2ab\u00b7cosC<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/09\/cosine-rule-formula-1613465537-1024x497.png\" alt=\"\" class=\"wp-image-7755\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Important Notes on Trigonometric Identities<\/strong><\/p>\n\n\n\n<ul><li>To write the trigonometric ratios of complementary angles, we consider the following as pairs: (sin, cos), (cosec, sec), and (tan, cot).<\/li><li>While writing the trigonometric ratios of supplementary angles, the trigonometric ratio won&#8217;t change. The sign can be decided using the fact that only sin and cosec are positive in the second quadrant where the angle is of the form (180-\u03b8).<\/li><li>There are 3 formulas for the cos 2x formula. Among them, you can remember just the first one because the other two can be obtained by the Pythagorean identity sin<sup>2<\/sup>x + cos<sup>2<\/sup>x = 1.<\/li><li>The half-angle formula of tan is obtained by applying the identity tan = sin\/cos and then using the half-angle formulas of sin and cos.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The&nbsp;sine rule&nbsp;gives the relation between the angles and the corresponding sides of a triangle. For the non-right-angled triangles, we will have to use the sine rule and the cosine rule. For a triangle with sides &#8216;a&#8217;, &#8216;b&#8217;, and &#8216;c&#8217; and the respective opposite angles are A, B, and C, sine rule can be given as, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[310],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7753"}],"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=7753"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7753\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}