{"id":7763,"date":"2022-09-18T05:14:09","date_gmt":"2022-09-18T05:14:09","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7763"},"modified":"2022-09-18T05:14:09","modified_gmt":"2022-09-18T05:14:09","slug":"trigonometric-equations","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/18\/trigonometric-equations\/","title":{"rendered":"Trigonometric Equations"},"content":{"rendered":"\n<p>The&nbsp;<strong>trigonometric equations<\/strong>&nbsp;involve trigonometric functions of angles as variables. The angle of \u03b8 trigonometric functions such as Sin\u03b8, Cos\u03b8, Tan\u03b8 is used as a variable in trigonometric equations. Similar to general polynomial equations, the trigonometric equations also have solutions, which are referred to as principal solutions, and general solutions.<\/p>\n\n\n\n<p>We will use the fact that the period of sin x and cos x is 2\u03c0 and the period of tan x is \u03c0 to find the solutions of the trigonometric equations. Let us learn more about trigonometric equations, the method to solve them, and find their solutions with the help of a few solved examples of trigonometric equations for a better understanding of the concept.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What are Trigonometric Equations?<\/h2>\n\n\n\n<p>The trigonometric equations are similar to\u00a0algebraic equations\u00a0and can be linear equations, quadratic equations, or polynomial equations. In trigonometric equations, the trigonometric ratios of Sin\u03b8, Cos\u03b8, Tan\u03b8 are represented in place of the variables, as in a normal polynomial equation. The\u00a0trigonometric ratios\u00a0used in trigonometric equations are Sin\u03b8, Cos\u03b8, or Tan\u03b8.<\/p>\n\n\n\n<p>The linear equation ax + b = 0 can be written as a trigonometry equation as aSin\u03b8 + b = 0, which is also sometimes written as Sin\u03b8 = Sin\u03b1. The\u00a0quadratic equation\u00a0ax<sup>2<\/sup>\u00a0+ bx + c = 0 is as an example of trigonometric equation is written as aCos<sup>2<\/sup>\u03b8 + bCos\u03b8 + c = 0. But unlike normal solutions of equations with the number of solutions based on the\u00a0degree\u00a0of the variable, in trigonometric equations, the same value of solution exists for different values of \u03b8. For example, we have Sin\u03b8 = 1\/2 = Sin\u03c0\/6 = Sin5\u03c0\/6 = Sin13\u03c0\/6, and so on as the values of the\u00a0sine function\u00a0repeat after every 2\u03c0 radians.<\/p>\n\n\n\n<p>Some of the examples of trigonometric equations are as follows.<\/p>\n\n\n\n<ul><li>Sin2x &#8211; Sin4x + Sin6x = 0<\/li><li>2Cos<sup>2<\/sup>x + 3Sinx = 0<\/li><li>Cos4x = Cos2x<\/li><li>Sin2x + Cosx = 0<\/li><li>Sec<sup>2<\/sup>2x = 1 &#8211; Tan2x<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The&nbsp;trigonometric equations&nbsp;involve trigonometric functions of angles as variables. The angle of \u03b8 trigonometric functions such as Sin\u03b8, Cos\u03b8, Tan\u03b8 is used as a variable in trigonometric equations. Similar to general polynomial equations, the trigonometric equations also have solutions, which are referred to as principal solutions, and general solutions. We will use the fact that the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[384],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7763"}],"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=7763"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7763\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}