{"id":7659,"date":"2022-09-16T06:51:47","date_gmt":"2022-09-16T06:51:47","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7659"},"modified":"2022-09-16T06:51:47","modified_gmt":"2022-09-16T06:51:47","slug":"how-to-find-reference-angles","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/how-to-find-reference-angles\/","title":{"rendered":"How to Find Reference Angles?"},"content":{"rendered":"\n<p>In the previous section, we learned that we could find the reference angles using the set of rules mentioned in the table. That table works only when the given angle lies between 0\u00b0 and 360\u00b0. But what if the given angle does not lie in this range? Let&#8217;s see how we can find the reference angles when the given angle is greater than 360\u00b0.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Steps to Find Reference Angles<\/h3>\n\n\n\n<p>The steps to find the reference angle of an angle are explained with an example. Let us find the reference angle of 480\u00b0.<\/p>\n\n\n\n<p><strong>Step 1: Find the\u00a0coterminal angle\u00a0of the given angle that lies between 0<\/strong>\u00b0<strong>\u00a0and 360<\/strong>\u00b0<strong>.<\/strong><\/p>\n\n\n\n<p>The coterminal angle can be found either by adding or subtracting 360\u00b0 from the given angle as many times as required. Let&#8217;s find the coterminal angle of 480\u00b0 that lies between 0\u00b0 and 360\u00b0. We will subtract 360\u00b0 from 480\u00b0 to find its coterminal angle.<\/p>\n\n\n\n<p>480\u00b0 &#8211; 360\u00b0 = 120\u00b0<\/p>\n\n\n\n<p><strong>Step 2: If the angle from step 1 lies between 0<\/strong>\u00b0<strong>&nbsp;and 90<\/strong>\u00b0<strong>, then that angle itself is the reference angle of the given angle. If not, then we have to check whether it is closest to 180\u00b0 or 360\u00b0 and by how much.<\/strong><\/p>\n\n\n\n<p>Here, 120\u00b0 does not lie between 0\u00b0 and 90\u00b0 and it is closest to 180\u00b0 by 60\u00b0. i.e.,<\/p>\n\n\n\n<p>180\u00b0 &#8211; 120\u00b0 = 60\u00b0<\/p>\n\n\n\n<p><strong>Step 3:&nbsp;<\/strong><strong>The angle from step 2 is the reference angle of the given angle.<\/strong><\/p>\n\n\n\n<p>Thus, the reference angle of 480\u00b0 is&nbsp;<strong>60<\/strong>\u00b0<strong>.<\/strong><\/p>\n\n\n\n<p>This is how we can find reference angles of any given angle.<\/p>\n\n\n\n<p><strong>\u25ba Important Notes:<\/strong><\/p>\n\n\n\n<ul><li>The reference angle of an angle is always non-negative i.e., a negative reference angle doesn&#8217;t exist.<\/li><li>The reference angle of any angle always lies between 0 and \u03c0\/2 (both inclusive).<\/li><\/ul>\n\n\n\n<p><strong>Tricks to Find Reference Angles:<\/strong><\/p>\n\n\n\n<ul><li>We use the reference angle to find the values of trigonometric functions at an angle that is beyond 90\u00b0. For example, we can see that the coterminal angle and reference angle of 495\u00b0 are 135\u00b0 and 45\u00b0 respectively.<\/li><\/ul>\n\n\n\n<p>sin 495\u00b0 = sin 135\u00b0 = +sin 45\u00b0.<\/p>\n\n\n\n<p>We have included the + sign because 135\u00b0 is in quadrant II, where sine is positive.<\/p>\n\n\n\n<p>sin 495\u00b0 = \u221a2\/2 [Using unit circle]<\/p>\n\n\n\n<ul><li>If we use reference angles, we don&#8217;t need to remember the complete unit circle, instead we can just remember the first quadrant values of the unit circle.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous section, we learned that we could find the reference angles using the set of rules mentioned in the table. That table works only when the given angle lies between 0\u00b0 and 360\u00b0. But what if the given angle does not lie in this range? Let&#8217;s see how we can find the reference [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[383],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7659"}],"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=7659"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7659\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7659"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7659"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}