{"id":7648,"date":"2022-09-16T06:39:31","date_gmt":"2022-09-16T06:39:31","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7648"},"modified":"2022-09-16T06:39:31","modified_gmt":"2022-09-16T06:39:31","slug":"coterminal-angles-and-reference-angles","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/coterminal-angles-and-reference-angles\/","title":{"rendered":"Coterminal Angles and Reference Angles"},"content":{"rendered":"\n<p>We already know how to find the coterminal angles of a given angle. The reference angle of any angle always lies between 0\u00b0 and 90\u00b0, It is the angle between the terminal side of the angle and the x-axis. The\u00a0reference angle\u00a0depends on the quadrant&#8217;s terminal side.<\/p>\n\n\n\n<p>The steps to find the reference angle of an angle depends on the quadrant of the terminal side:<\/p>\n\n\n\n<ul><li>We first determine its coterminal angle which lies between 0\u00b0 and 360\u00b0.<\/li><li>We then see the quadrant of the coterminal angle.<\/li><li>If the terminal side is in the first quadrant ( 0\u00b0 to 90\u00b0), then the reference angle is the same as our given angle. For example, if the given angle is 25\u00b0, then its reference angle is also 25\u00b0.<\/li><li>If the terminal side is in the second quadrant ( 90\u00b0 to 180\u00b0), then the reference angle is (180\u00b0 &#8211; given angle). For example, if the given angle is 100\u00b0, then its reference angle is 180\u00b0 \u2013 100\u00b0 = 80\u00b0.<\/li><li>If the terminal side is in the third quadrant (180\u00b0 to 270\u00b0), then the reference angle is (given angle &#8211; 180\u00b0). For example, if the given angle is 215\u00b0, then its reference angle is 215\u00b0 \u2013 180\u00b0 = 35\u00b0.<\/li><li>If the terminal side is in the fourth quadrant (270\u00b0 to 360\u00b0), then the reference angle is (360\u00b0 &#8211; given angle). For example, if the given angle is 330\u00b0, then its reference angle is 360\u00b0 \u2013 330\u00b0 = 30\u00b0.<\/li><\/ul>\n\n\n\n<p><strong>Example:<\/strong>&nbsp;Find the reference angle of 495\u00b0.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us find the coterminal angle of 495\u00b0. The coterminal angle is 495\u00b0 \u2212 360\u00b0 = 135\u00b0.<\/p>\n\n\n\n<p>The terminal side lies in the second quadrant. Thus the reference angle is 180\u00b0 -135\u00b0 = 45\u00b0<\/p>\n\n\n\n<p>Therefore, the reference angle of 495\u00b0 is 45\u00b0.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We already know how to find the coterminal angles of a given angle. The reference angle of any angle always lies between 0\u00b0 and 90\u00b0, It is the angle between the terminal side of the angle and the x-axis. The\u00a0reference angle\u00a0depends on the quadrant&#8217;s terminal side. The steps to find the reference angle of an [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[263],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7648"}],"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=7648"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7648\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}