{"id":156346,"date":"2022-03-26T01:39:17","date_gmt":"2022-03-25T20:09:17","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/polar-coordinates-formula-and-solved-examples\/"},"modified":"2024-12-11T14:29:27","modified_gmt":"2024-12-11T08:59:27","slug":"polar-coordinates-formula-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/polar-coordinates\/","title":{"rendered":"Polar Coordinates \u2013 Formula and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polar-coordinates\/#What_are_Polar_Coordinates\" title=\"What are Polar Coordinates?\">What are Polar Coordinates?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polar-coordinates\/#Polar_Coordinates_Formula\" title=\"Polar Coordinates Formula\">Polar Coordinates Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polar-coordinates\/#Plotting_Points_in_Polar_Coordinate_System\" title=\"Plotting Points in Polar Coordinate System\">Plotting Points in Polar Coordinate System<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polar-coordinates\/#Converting_Cartesian_Coordinate_System_to_Polar_Coordinate_System\" title=\"Converting Cartesian Coordinate System to Polar Coordinate System\">Converting Cartesian Coordinate System to Polar Coordinate System<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polar-coordinates\/#Converting_Polar_Coordinate_System_to_Cartesian_coordinate_System\" title=\"Converting Polar Coordinate System to Cartesian coordinate System\">Converting Polar Coordinate System to Cartesian coordinate System<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Polar_Coordinates\"><\/span>What are Polar Coordinates?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Polar coordinates are a system of coordinates that uses a radial distance and an angle to identify a point in two-dimensional space. In polar coordinates, the point (x, y) is represented as (r, \u03b8), where r is the radial distance from the origin and \u03b8 is the angle measured from the positive x-axis.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156345 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polar-coordinates-formula-and-solved-examples.jpg\" alt=\"Polar Coordinates \u2013 Formula and Solved Examples\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polar-coordinates-formula-and-solved-examples.jpg?v=1648238955 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polar-coordinates-formula-and-solved-examples-300x212.jpg?v=1648238955 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Polar_Coordinates_Formula\"><\/span>Polar Coordinates Formula<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>In mathematics, polar coordinates are a coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. The fixed point is called the pole, and the direction is called the polar axis.<\/li>\n<li>The coordinate system is defined by the equation<\/li>\n<li>where is the distance from the pole to the point, is the angle from the polar axis to the point, and is the signed distance from the origin to the point.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Plotting_Points_in_Polar_Coordinate_System\"><\/span>Plotting Points in Polar Coordinate System<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>A point in polar coordinate system is specified by its distance from the origin and the angle from the positive x-axis. The distance from the origin is always a positive number, while the angle can be any number between 0 and 360 degrees.<\/li>\n<li>To plot a point in polar coordinate system, first find the distance from the origin and the angle. Then, use a compass to draw a circle with the given distance from the origin as the radius. Finally, draw an arrow from the origin to the point on the circle, and mark the angle.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Converting_Cartesian_Coordinate_System_to_Polar_Coordinate_System\"><\/span>Converting Cartesian Coordinate System to Polar Coordinate System<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>In a Cartesian coordinate system, points are located by their x- and y-coordinates. The x-coordinate is the point&#8217;s distance from the origin along the x-axis, and the y-coordinate is the point&#8217;s distance from the origin along the y-axis.<\/li>\n<li>In a polar coordinate system, points are located by their radius and angle. The radius is the point&#8217;s distance from the origin, and the angle is the point&#8217;s location around the origin.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Converting_Polar_Coordinate_System_to_Cartesian_coordinate_System\"><\/span>Converting Polar Coordinate System to Cartesian coordinate System<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert a polar coordinate system to a Cartesian coordinate system, we use the following formula:<\/p>\n<p>x = r cos\u03b8<br \/>\ny = r sin\u03b8<\/p>\n<p>where r is the radius and \u03b8 is the angle.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What are Polar Coordinates? Polar coordinates are a system of coordinates that uses a radial distance and an angle to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Polar Coordinates","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Polar Coordinates topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online session.","custom_permalink":"maths\/polar-coordinates\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Polar Coordinates \u2013 Formula and Solved Examples - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Polar Coordinates topic of Maths in details explained by subject experts on infinitylearn.com. 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