{"id":20120,"date":"2022-12-17T08:56:16","date_gmt":"2022-12-17T08:56:16","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=10418"},"modified":"2022-12-17T08:56:16","modified_gmt":"2022-12-17T08:56:16","slug":"repeating-pattern","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/12\/17\/repeating-pattern\/","title":{"rendered":"Repeating Pattern"},"content":{"rendered":"\n<p>Because the angle is\u00a0<strong>rotating around and around the circle<\/strong>\u00a0the Sine, Cosine and Tangent functions\u00a0<strong>repeat once every full rotation<\/strong>\u00a0(see\u00a0Amplitude, Period, Phase Shift and Frequency).<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.mathsisfun.com\/algebra\/images\/cosine-repeating.svg\" alt=\"cosine repeates every 360 degrees\"\/><\/figure>\n\n\n\n<p>When we want to calculate the function for an angle larger than a full rotation of 360\u00b0 (2<strong>\u03c0<\/strong>&nbsp;radians) we subtract as many full rotations as needed to bring it back below 360\u00b0 (2<strong>\u03c0<\/strong>&nbsp;radians):<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example: what is the cosine of 370\u00b0?<\/h3>\n\n\n\n<p>370\u00b0 is greater than 360\u00b0 so let us subtract 360\u00b0<\/p>\n\n\n\n<p>370\u00b0 \u2212 360\u00b0 = 10\u00b0<\/p>\n\n\n\n<p>cos(370\u00b0) = cos(10\u00b0) =&nbsp;<strong>0.985<\/strong>&nbsp;(to 3 decimal places)<\/p>\n\n\n\n<p>And when the angle is less than zero, just add full rotations.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example: what is the sine of \u22123 radians?<\/h3>\n\n\n\n<p>\u22123 is less than 0<strong><\/strong>&nbsp;so let us add 2<strong>\u03c0<\/strong>&nbsp;radians<\/p>\n\n\n\n<p>\u22123 + 2<strong>\u03c0<\/strong>&nbsp;= \u22123 + 6.283&#8230; = 3.283&#8230; rad<strong><\/strong>ians<\/p>\n\n\n\n<p>sin(\u22123) = sin(3.283&#8230;) =&nbsp;<strong>\u22120.141<\/strong>&nbsp;(to 3 decimal places)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Because the angle is\u00a0rotating around and around the circle\u00a0the Sine, Cosine and Tangent functions\u00a0repeat once every full rotation\u00a0(see\u00a0Amplitude, Period, Phase Shift and Frequency). When we want to calculate the function for an angle larger than a full rotation of 360\u00b0 (2\u03c0&nbsp;radians) we subtract as many full rotations as needed to bring it back below 360\u00b0 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[333],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20120"}],"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=20120"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20120\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=20120"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=20120"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=20120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}