{"id":20125,"date":"2022-12-17T09:10:36","date_gmt":"2022-12-17T09:10:36","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=10429"},"modified":"2022-12-17T09:10:36","modified_gmt":"2022-12-17T09:10:36","slug":"trig-functions-in-four-quadrants","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/12\/17\/trig-functions-in-four-quadrants\/","title":{"rendered":"Trig Functions in Four Quadrants"},"content":{"rendered":"\n<p>The angle \u03b8 is an acute angle (\u03b8 &lt; 90\u00b0) and is measured with reference to the positive x-axis, in the anticlockwise direction. Further, these trig functions have different numeric signs (+ or -) in the different quadrants, which are based on the positive or negative axis of the quadrant. The trigonometric functions of Sin\u03b8, Cosec\u03b8 are positive in quadrants I and II, and are negative in quadrants III and IV. All the trigonometric functions have a positive range in the first quadrant. The trigonometric functions Tan\u03b8, Cot\u03b8 are positive only in Quadrants I and III, and the trigonometric ratios of Cos\u03b8, Sec\u03b8 are positive only in quadrants I and IV.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/12\/amar-trigonometric-functions-01-1623323124.png\" alt=\"\" class=\"wp-image-10430\"\/><\/figure>\n\n\n\n<p>The trigonometric functions have values of \u03b8, (90\u00b0 &#8211; \u03b8) in the first quadrant. The cofunction identities provide the interrelationship between the different complementary trigonometric functions for the angle (90\u00b0 &#8211; \u03b8).<\/p>\n\n\n\n<ul>\n<li>sin(90\u00b0\u2212\u03b8) = cos \u03b8<\/li>\n\n\n\n<li>cos(90\u00b0\u2212\u03b8) = sin \u03b8<\/li>\n\n\n\n<li>tan(90\u00b0\u2212\u03b8) = cot \u03b8<\/li>\n\n\n\n<li>cot(90\u00b0\u2212\u03b8) = tan \u03b8<\/li>\n\n\n\n<li>sec(90\u00b0\u2212\u03b8) = cosec \u03b8<\/li>\n\n\n\n<li>cosec(90\u00b0\u2212\u03b8) = sec \u03b8<\/li>\n<\/ul>\n\n\n\n<p>The domain \u03b8 value for different trigonometric function in the second quadrant is (\u03c0\/2 + \u03b8, \u03c0 &#8211; \u03b8), in the third quadrant is (\u03c0 + \u03b8, 3\u03c0\/2 &#8211; \u03b8), and in the fourth quadrant is (3\u03c0\/2 + \u03b8, 2\u03c0 &#8211; \u03b8). For \u03c0\/2, 3\u03c0\/2 the trigonometric values changes as their complementary ratios such as Sin\u03b8\u21d4Cos\u03b8, Tan\u03b8\u21d4Cot\u03b8, Sec\u03b8\u21d4Cosec\u03b8. For \u03c0, 2\u03c0 the trigonometric values remain the same. The changing trigonometric ratios in different quadrants and angles can be understood from the below table.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><thead><tr><th scope=\"col\">Trigonometric Ratio<\/th><th scope=\"col\">I &#8211; Quadrant<\/th><th scope=\"col\">II &#8211; Quadrant<\/th><th scope=\"col\">III-Quadrant<\/th><th scope=\"col\">IV-Quadrant<\/th><\/tr><\/thead><tbody><tr><td>\u03b8<\/td><td>\u03c0\/2 &#8211; \u03b8<\/td><td>\u03c0\/2 + \u03b8<\/td><td>\u03c0 &#8211; \u03b8<\/td><td>\u03c0 + \u03b8<\/td><td>3\u03c0\/2 &#8211; \u03b8<\/td><td>3\u03c0\/2 + \u03b8<\/td><td>2\u03c0 &#8211; \u03b8<\/td><\/tr><tr><td>Sin\u03b8<\/td><td>Cos\u03b8<\/td><td>Cos\u03b8<\/td><td>Sin\u03b8<\/td><td>-Sin\u03b8<\/td><td>-Cos\u03b8<\/td><td>-Cos\u03b8<\/td><td>-Sin\u03b8<\/td><\/tr><tr><td>Cos\u03b8<\/td><td>Sin\u03b8<\/td><td>-Sin\u03b8<\/td><td>-Cos\u03b8<\/td><td>-Cos\u03b8<\/td><td>-Sin\u03b8<\/td><td>Sin\u03b8<\/td><td>Cos\u03b8<\/td><\/tr><tr><td>Tan\u03b8<\/td><td>Cot\u03b8<\/td><td>-Cot\u03b8<\/td><td>-Tan\u03b8<\/td><td>Tan\u03b8<\/td><td>Cot\u03b8<\/td><td>-Cot\u03b8<\/td><td>-Tan\u03b8<\/td><\/tr><tr><td>Cot\u03b8<\/td><td>Tan\u03b8<\/td><td>-Tan\u03b8<\/td><td>-Cot\u03b8<\/td><td>Cot\u03b8<\/td><td>Tan\u03b8<\/td><td>-Tan\u03b8<\/td><td>-Cot\u03b8<\/td><\/tr><tr><td>Sec\u03b8<\/td><td>Cosec\u03b8<\/td><td>-Cosec\u03b8<\/td><td>-Sec\u03b8<\/td><td>-Sec\u03b8<\/td><td>-Cosec\u03b8<\/td><td>Cosec\u03b8<\/td><td>Sec\u03b8<\/td><\/tr><tr><td>Cosec\u03b8<\/td><td>Sec\u03b8<\/td><td>Sec\u03b8<\/td><td>Cosec\u03b8<\/td><td>-Cosec\u03b8<\/td><td>-Sec\u03b8<\/td><td>-Sec\u03b8<\/td><td>-Cosec\u03b8<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The angle \u03b8 is an acute angle (\u03b8 &lt; 90\u00b0) and is measured with reference to the positive x-axis, in the anticlockwise direction. Further, these trig functions have different numeric signs (+ or -) in the different quadrants, which are based on the positive or negative axis of the quadrant. The trigonometric functions of Sin\u03b8, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[451],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20125"}],"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=20125"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20125\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=20125"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=20125"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=20125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}