{"id":7663,"date":"2022-09-16T06:56:23","date_gmt":"2022-09-16T06:56:23","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7663"},"modified":"2022-09-16T06:56:23","modified_gmt":"2022-09-16T06:56:23","slug":"trigonometric-ratios-in-4-quadrants","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/trigonometric-ratios-in-4-quadrants\/","title":{"rendered":"Trigonometric Ratios In 4 Quadrants"},"content":{"rendered":"\n<p><strong>How to remember the signs of the trigonometric functions for the four quadrants?<\/strong><br>We can use a mnemonic like&nbsp;<strong>CAST<\/strong>&nbsp;or** A**ll** S**tudents **T**ake** C**alculus to remember the signs in the 4 quadrants.<\/p>\n\n\n\n<p>The following figure shows the signs of the trigonometric functions for the four quadrants. Scroll down the page for more examples and solutions.&nbsp;<img loading=\"lazy\" decoding=\"async\" height=\"242\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-ratios5.jpg\" width=\"436\"><\/p>\n\n\n\n<p>The trigonometric ratios for 0\u02da, 90\u02da, 180\u02da, 270\u02da and 360\u02da are shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-ratios6.jpg\" alt=\"\"\/><\/figure>\n\n\n\n<p>Take note of the signs of the trigonometric ratios in the following examples.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"quadrant-1-0deg--\u03b8--90deg\">Quadrant 1 (0\u00b0 &lt;&nbsp;<em>\u03b8<\/em>&nbsp;&lt; 90\u00b0)<\/h3>\n\n\n\n<p>In the following diagram,&nbsp;<em>\u03b8<\/em>&nbsp;is in the first quadrant.<\/p>\n\n\n\n<p>Sine, cosine and tangent are all positive.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-ratios1.jpg\" alt=\"trigonometric ratios\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"quadrant-ii-90deg--\u03b8--180deg\">Quadrant II (90\u00b0 &lt;&nbsp;<em>\u03b8<\/em>&nbsp;&lt; 180\u00b0)<\/h3>\n\n\n\n<p>In the following diagram,&nbsp;<em>\u03b8<\/em>&nbsp;is in the second quadrant.<\/p>\n\n\n\n<p>The reference angle, \u03b1 = 180\u00b0 \u2013&nbsp;<em>\u03b8<\/em><\/p>\n\n\n\n<p>Sine is positive whereas cosine and tangent are negative.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-ratios2.jpg\" alt=\"signs of trigonometric ratios\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"quadrant-iii-180deg--\u03b8--270deg\">Quadrant III (180\u00b0 &lt;&nbsp;<em>\u03b8<\/em>&nbsp;&lt; 270\u00b0)<\/h3>\n\n\n\n<p>In the following diagram,&nbsp;<em>\u03b8<\/em>&nbsp;is in the third quadrant.<\/p>\n\n\n\n<p>The reference angle, \u03b1 =&nbsp;<em>\u03b8<\/em>&nbsp;\u2013 180\u00b0<\/p>\n\n\n\n<p>Tangent is positive whereas sine and cosine are negative.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-ratios3.jpg\" alt=\"trigonometric signs\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"quadrant-iv-270deg--\u03b8--360deg\">Quadrant IV (270\u00b0 &lt;&nbsp;<em>\u03b8<\/em>&nbsp;&lt; 360\u00b0)<\/h3>\n\n\n\n<p>In the following diagram, * \u03b8* is in the fourth quadrant.<\/p>\n\n\n\n<p>The reference angle, \u03b1 = 360\u00b0 \u2013&nbsp;<em>\u03b8<\/em><\/p>\n\n\n\n<p>Cosine is positive whereas sine and tangent are negative.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-ratios4.jpg\" alt=\"trigonometric signs\"\/><\/figure>\n\n\n\n<p><strong>Example:<\/strong><br>Determine the sign of each of the following values.<\/p>\n\n\n\n<p>a) cos 121\u00b0<br>b) tan 220\u00b0<\/p>\n\n\n\n<p><strong>Solution:<\/strong><br>a) cos 121\u00b0 is in quadrant II (90\u00b0 &lt; 121\u00b0 &lt; 180\u00b0)<br>In quadrant II, only sine is positive, so cos 121\u00b0 is negative.<\/p>\n\n\n\n<p>b) tan 220\u00b0 is in quadrant III (180\u00b0 &lt; 220\u00b0 &lt; 270\u00b0)<br>In quadrant III, tangent is positive, so tan 220\u00b0 is positive.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How to remember the signs of the trigonometric functions for the four quadrants?We can use a mnemonic like&nbsp;CAST&nbsp;or** A**ll** S**tudents **T**ake** C**alculus to remember the signs in the 4 quadrants. The following figure shows the signs of the trigonometric functions for the four quadrants. Scroll down the page for more examples and solutions.&nbsp; The trigonometric [&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\/7663"}],"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=7663"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7663\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7663"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7663"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}