{"id":13135,"date":"2023-05-01T10:00:18","date_gmt":"2023-05-01T04:30:18","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=13135"},"modified":"2023-05-02T10:13:45","modified_gmt":"2023-05-02T04:43:45","slug":"polar-cartesian-coordinates","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/polar-cartesian-coordinates\/","title":{"rendered":"Polar and Cartesian Coordinates"},"content":{"rendered":"<h2>Polar and Cartesian Coordinates<\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/L4v98ZZft68?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h3><a href=\"https:\/\/www.aplustopper.com\/cartesian-coordinates\/\">Cartesian co-ordinates<\/a> of a point<\/h3>\n<p>This is the most popular <a href=\"https:\/\/www.aplustopper.com\/cartesian-coordinate-system\/\">co-ordinate system<\/a>.<br \/>\n<strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128614 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-1.jpg\" alt=\"Polar and Cartesian Coordinates 1\" width=\"255\" height=\"228\" \/>Axis of x:<\/strong> The line XOX&#8217; is called axis of x.<\/p>\n<p><strong>Axis of y:<\/strong> The line YOY&#8217; is called axis of y.<\/p>\n<p><strong>Co-ordinate axes:<\/strong> x axis and y axis together are called axis of co-ordinates or axes of reference.<\/p>\n<p><strong>Origin:<\/strong> The point \u2018O\u2019 is called the origin of co-ordinates or the origin.<\/p>\n<p>Let OL = x and OM = y which are respectively called the abscissa (or x-coordinate) and the ordinate (or y-coordinate). The co-ordinate of P are (<em>x, y<\/em>).<br \/>\nHere, co-ordinates of the origin is (0, 0). The y co-ordinates of every point on x-axis is zero.<br \/>\nThe x co-ordinates of every point on y-axis is zero.<\/p>\n<p><strong>Oblique axes:<\/strong> If both the axes are not perpendicular then they are called as oblique axes.<\/p>\n<h3>Polar co-ordinates<\/h3>\n<p>Let OX be any fixed line which is usually called the initial line and O be a fixed point on it. If distance of any point P from the O is &#8216;r&#8217; and <em>\u2220XOP<\/em> <em>=<\/em> <em>\u03b8<\/em>, then (<em>r, \u03b8<\/em> ) are called the polar co-ordinates of a point P.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128615 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-2.jpg\" alt=\"Polar and Cartesian Coordinates 2\" width=\"270\" height=\"263\" \/><\/p>\n<h3>To convert from Polar Coordinates (<em>r,\u03b8<\/em>) to <a href=\"https:\/\/www.aplustopper.com\/cartesian-coordinates\/\">Cartesian Coordinates<\/a> (<em>x,y<\/em>):<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128616 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-3.jpg\" alt=\"Polar and Cartesian Coordinates 3\" width=\"393\" height=\"254\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-3.jpg 393w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-3-300x194.jpg 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/>If (<em>x, y<\/em>) are the cartesian co-ordinates of a point P, then <strong><em>x = r cos\u00a0\u03b8<\/em><\/strong>; <strong><em>y = r sin\u00a0\u03b8<\/em><\/strong>; and<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128618\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-4.jpg\" alt=\"Polar and Cartesian Coordinates 4\" width=\"354\" height=\"80\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-4.jpg 354w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polar-and-Cartesian-Coordinates-4-300x68.jpg 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Polar and Cartesian Coordinates Cartesian co-ordinates of a point This is the most popular co-ordinate system. Axis of x: The line XOX&#8217; is called axis of x. Axis of y: The line YOY&#8217; is called axis of y. Co-ordinate axes: x axis and y axis together are called axis of co-ordinates or axes of reference. [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Polar and Cartesian Coordinates - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/polar-cartesian-coordinates\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Polar and Cartesian Coordinates\" \/>\n<meta property=\"og:description\" content=\"Polar and Cartesian Coordinates Cartesian co-ordinates of a point This is the most popular co-ordinate system. Axis of x: The line XOX&#8217; is called axis of x. Axis of y: The line YOY&#8217; is called axis of y. Co-ordinate axes: x axis and y axis together are called axis of co-ordinates or axes of reference. 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Axis of x: The line XOX&#8217; is called axis of x. Axis of y: The line YOY&#8217; is called axis of y. Co-ordinate axes: x axis and y axis together are called axis of co-ordinates or axes of reference. 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