{"id":7671,"date":"2022-09-16T07:11:45","date_gmt":"2022-09-16T07:11:45","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7671"},"modified":"2022-09-16T07:11:45","modified_gmt":"2022-09-16T07:11:45","slug":"equation-of-a-unit-circle","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/equation-of-a-unit-circle\/","title":{"rendered":"Equation of a Unit Circle"},"content":{"rendered":"\n<p>The general equation of a circle is (x &#8211; a)<sup>2<\/sup>&nbsp;+ (y &#8211; b)<sup>2<\/sup>&nbsp;= r<sup>2<\/sup>, which represents a circle having the center (a, b) and the radius r. This equation of a circle is simplified to represent the equation of a unit circle. A unit circle is formed with its center at the point(0, 0), which is the origin of the coordinate axes. and a radius of 1 unit. Hence the equation of the unit circle is (x &#8211; 0)<sup>2<\/sup>&nbsp;+ (y &#8211; 0)<sup>2<\/sup>&nbsp;= 1<sup>2<\/sup>. This is simplified to obtain the equation of a unit circle.<\/p>\n\n\n\n<p><strong>Equation of a Unit Circle:<\/strong>&nbsp;x<sup>2<\/sup>&nbsp;+ y<sup>2<\/sup>&nbsp;= 1<\/p>\n\n\n\n<p>Here for the unit circle, the center lies at (0,0) and the radius is 1 unit. The above equation satisfies all the points lying on the circle across the four quadrants.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/09\/unite-c.png\" alt=\"\" class=\"wp-image-7672\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Finding Trigonometric Functions Using a Unit Circle<\/h2>\n\n\n\n<p>We can calculate the trigonometric functions of sine, cosine, and tangent using a unit circle. Let us apply the\u00a0Pythagoras theorem\u00a0in a unit circle to understand the trigonometric functions. Consider a right triangle placed in a unit circle in the cartesian coordinate plane. The radius of the circle represents the hypotenuse of the right triangle. The radius vector makes an angle \u03b8 with the positive x-axis and the coordinates of the endpoint of the radius vector is (x, y). Here the values of x and y are the lengths of the base and the altitude of the right triangle. Now we have a right angle triangle with the sides 1, x, y. Applying this in\u00a0trigonometry, we can find the values of the trigonometric ratio, as follows:<\/p>\n\n\n\n<ul><li>sin\u03b8 = Altitude\/Hypoteuse = y\/1<\/li><li>cos\u03b8 = Base\/Hypotenuse = x\/1<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/09\/uniteee.png\" alt=\"\" class=\"wp-image-7673\"\/><\/figure>\n\n\n\n<p>We now have sin\u03b8 = y, cos\u03b8 = x, and using this we now have tan\u03b8 = y\/x. Similarly, we can obtain the values of the other trigonometric ratios using the\u00a0right-angled triangle\u00a0within the unit circle. Also by changing the \u03b8 values we can obtain the principal values of these trigonometric ratios.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The general equation of a circle is (x &#8211; a)2&nbsp;+ (y &#8211; b)2&nbsp;= r2, which represents a circle having the center (a, b) and the radius r. This equation of a circle is simplified to represent the equation of a unit circle. A unit circle is formed with its center at the point(0, 0), which [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[453],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7671"}],"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=7671"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7671\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}