{"id":7665,"date":"2022-09-16T06:58:54","date_gmt":"2022-09-16T06:58:54","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7665"},"modified":"2022-09-16T06:58:54","modified_gmt":"2022-09-16T06:58:54","slug":"finding-the-quadrant-in-which-an-angle-lies","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/finding-the-quadrant-in-which-an-angle-lies\/","title":{"rendered":"Finding the Quadrant in Which an Angle Lies"},"content":{"rendered":"\n<p>An angle is said to be in standard position if its vertex is at the origin and its initial side is along the positive x-axis.<\/p>\n\n\n\n<p>An angle is said to be in the first quadrant, if in the standard position, its terminal side falls in the first quadrant.<\/p>\n\n\n\n<p>Similarly, we can define for the other three quadrants. Angles in standard position having their terminal sides along the x-axis or y-axis are called quadrantal angles.<\/p>\n\n\n\n<p>Thus, 0\u00b0, 90\u00b0, 180\u00b0, 270\u00b0&nbsp;and 360\u00b0&nbsp;are quadrantal angles.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemath4all.com\/images\/quandrantsandangles.png\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Counter Clockwise Rotation<\/h2>\n\n\n\n<p>One complete rotation of a ray in the anticlockwise direction results in an angle measuring of 360\u00b0.<\/p>\n\n\n\n<p>By continuing the counter clockwise rotation, angles larger than 360<sup>\u25e6<\/sup>&nbsp;can be produced.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Clock Wise Rotation<\/h2>\n\n\n\n<p>If we rotate in clockwise direction, negative angles are produced.<\/p>\n\n\n\n<p><strong>Example :<\/strong><\/p>\n\n\n\n<p>Identify the quadrant in which each of the following&nbsp; angles lies.&nbsp;<\/p>\n\n\n\n<p>(i) 25\u00b0&nbsp;(ii) 825\u00b0&nbsp;(iii) -55\u00b0&nbsp;(iv) 328\u00b0&nbsp;(v) -230\u00b0<\/p>\n\n\n\n<p><strong>Solution :<\/strong><\/p>\n\n\n\n<p>(i) 25\u00b0<\/p>\n\n\n\n<p>Since 25\u00b0 is&nbsp;between 0 and 90, it is in quadrant I.<\/p>\n\n\n\n<p>(ii) 825\u00b0<\/p>\n\n\n\n<p>825\u00b0 is greater than&nbsp;360\u00b0.&nbsp;<\/p>\n\n\n\n<p>When 825\u00b0&nbsp;is divided by 360\u00b0, the remainder is 105\u00b0.&nbsp;<\/p>\n\n\n\n<p>Since 105\u00b0 is between 90\u00b0 and 180\u00b0, it is in quadrant II.&nbsp;<\/p>\n\n\n\n<p>That is, 825\u00b0 is in quadrant II.&nbsp;<\/p>\n\n\n\n<p>(iii) -55\u00b0<\/p>\n\n\n\n<p>Since it is negative angle, we have to do counter clock rotation.<\/p>\n\n\n\n<p>The difference between 360\u00b0&nbsp;and 55\u00b0&nbsp;is 305\u00b0.<\/p>\n\n\n\n<p>Since 305\u00b0&nbsp;is between 270\u00b0 and 360\u00b0, it is in quadrant IV.&nbsp;<\/p>\n\n\n\n<p>So -55\u00b0 is in quadrant&nbsp;IV.&nbsp;<\/p>\n\n\n\n<p>(iv) 328\u00b0<\/p>\n\n\n\n<p>Since 328\u00b0 is&nbsp;between 270\u00b0&nbsp;and 360\u00b0, it is in quadrant IV.<\/p>\n\n\n\n<p>(v) -230\u00b0<\/p>\n\n\n\n<p>Since it is negative angle, we have to do counter clockwise rotation.&nbsp;<\/p>\n\n\n\n<p>The difference between 360\u00b0&nbsp;and 230\u00b0&nbsp;is 130\u00b0.<\/p>\n\n\n\n<p>Since 130\u00b0 is between 90\u00b0 and 180\u00b0, it is in quadrant II.<\/p>\n\n\n\n<p>So -230\u00b0&nbsp;is in quadrant II.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An angle is said to be in standard position if its vertex is at the origin and its initial side is along the positive x-axis. An angle is said to be in the first quadrant, if in the standard position, its terminal side falls in the first quadrant. Similarly, we can define for the other [&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\/7665"}],"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=7665"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7665\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7665"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7665"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7665"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}