{"id":33671,"date":"2020-03-25T14:05:00","date_gmt":"2020-03-25T18:05:00","guid":{"rendered":"https:\/\/www.myedme.com\/login\/?p=33671"},"modified":"2020-04-11T12:14:32","modified_gmt":"2020-04-11T16:14:32","slug":"polar-coordinates","status":"publish","type":"post","link":"https:\/\/myedme.com\/login\/polar-coordinates\/","title":{"rendered":"Polar Coordinates"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Introduction by Sal<\/h2>\n\n\n\n<figure class=\"wp-block-embed-youtube is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><div  id=\"_ytid_52488\"  width=\"980\" height=\"551\"  data-origwidth=\"980\" data-origheight=\"551\" data-facadesrc=\"https:\/\/www.youtube.com\/embed\/8RasCV_Lggg?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=1&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;disablekb=0&#038;\" class=\"__youtube_prefs__ epyt-facade epyt-is-override  no-lazyload\" data-epautoplay=\"1\" ><img data-recalc-dims=\"1\" decoding=\"async\" data-spai-excluded=\"true\" class=\"epyt-facade-poster skip-lazy\" loading=\"lazy\"  alt=\"YouTube player\"  src=\"https:\/\/i0.wp.com\/i.ytimg.com\/vi\/8RasCV_Lggg\/maxresdefault.jpg?w=980&#038;ssl=1\"  \/><button class=\"epyt-facade-play\" aria-label=\"Play\"><svg data-no-lazy=\"1\" height=\"100%\" version=\"1.1\" viewBox=\"0 0 68 48\" width=\"100%\"><path class=\"ytp-large-play-button-bg\" d=\"M66.52,7.74c-0.78-2.93-2.49-5.41-5.42-6.19C55.79,.13,34,0,34,0S12.21,.13,6.9,1.55 C3.97,2.33,2.27,4.81,1.48,7.74C0.06,13.05,0,24,0,24s0.06,10.95,1.48,16.26c0.78,2.93,2.49,5.41,5.42,6.19 C12.21,47.87,34,48,34,48s21.79-0.13,27.1-1.55c2.93-0.78,4.64-3.26,5.42-6.19C67.94,34.95,68,24,68,24S67.94,13.05,66.52,7.74z\" fill=\"#f00\"><\/path><path d=\"M 45,24 27,14 27,34\" fill=\"#fff\"><\/path><\/svg><\/button><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Reading Learning Objectives from <a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/10-3-polar-coordinates\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"OpenStax Algebra &amp; Trigonometry (opens in a new tab)\">OpenStax <em>Algebra &amp; Trigonometry<\/em><\/a><\/h3>\n\n\n\n<p>In this section, you will:\n<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Plot points using polar coordinates.<\/li><li>Convert from polar coordinates to rectangular coordinates.<\/li><li>Convert from rectangular coordinates to polar coordinates.<\/li><li>Transform equations between polar and rectangular forms.<\/li><li>Identify and graph polar equations by converting to rectangular equations.<\/li><\/ul>\n\n\n\n<p>Over 12 kilometers from port, a sailboat encounters rough weather and is blown off course by a 16-knot wind (see <a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/10-3-polar-coordinates#Figure_08_03_001\">Figure 1<\/a>).\n How can the sailor indicate his location to the Coast Guard? In this \nsection, we will investigate a method of representing location that is \ndifferent from a standard coordinate grid.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/openstax.org\/resources\/e64a7f3b0943a529836ab148781ad2ded1e04599\" alt=\"An illustration of a boat on the polar grid.\"\/><\/figure><\/div>\n\n\n\n<p>Figure 1  <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Plotting Points Using Polar Coordinates<\/h3>\n\n\n\n<p>When we think about plotting points in the plane, we usually think of rectangular coordinates(<em>\ud835\udc65<\/em>,<em>\ud835\udc66<\/em>)in  the Cartesian coordinate plane. However, there are other ways of  writing a coordinate pair and other types of grid systems. In this  section, we introduce to polar coordinates, which are points labeled (<em>\ud835\udc5f<\/em>, <em>\ud835\udf03<\/em>) and plotted on a polar grid. The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane.<\/p>\n\n\n\n<p>The polar grid is scaled as the unit circle with the positive <em>x-<\/em>axis now viewed as the polar axis and the origin as the pole. The first coordinate<em>\ud835\udc5f<\/em>is the radius or length of the directed line segment from the pole. The angle<em> \ud835\udf03<\/em>, measured in radians, indicates the direction of <em>\ud835\udc5f<\/em>. We move counterclockwise from the polar axis by an angle of <em>\ud835\udf03<\/em>,and measure a directed line segment the length of<em>\ud835\udc5f<\/em>in the direction of <em>\ud835\udf03<\/em>. Even though we measure <em>\ud835\udf03 <\/em>first and then <em>\ud835\udc5f<\/em>, the polar point is written with the <em>r<\/em>-coordinate first. For example, to plot the point (2,<em> \ud835\udf0b<\/em>\/4),we would move<em> \ud835\udf0b<\/em>\/4 units in the counterclockwise direction and then a length of 2 from the pole. This point is plotted on the grid in <a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/10-3-polar-coordinates#Figure_08_03_002\">Figure 2<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/openstax.org\/resources\/0b5ae055028828c87165285505847c0020038c32\" alt=\"Polar grid with point (3, pi\/2) plotted.\"\/><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example 1<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"67606\">Plotting a Point on the Polar Grid<\/h4>\n\n\n\n<p>Plot the point (3,<em> \ud835\udf0b\/<\/em>2) on the polar grid.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Solution<\/h4>\n\n\n\n<p>The angle<em>\ud835\udf0b <\/em>\/2 is  found by sweeping in a counterclockwise direction 90\u00b0 from the polar  axis. The point is located at a length of 3 units from the pole in the <em>\ud835\udf0b\/<\/em>2 direction, as shown in <a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/10-3-polar-coordinates#Figure_08_03_003\">Figure 3<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/openstax.org\/resources\/0b5ae055028828c87165285505847c0020038c32\" alt=\"Polar grid with point (3, pi\/2) plotted.\"\/><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-pullquote\"><blockquote><p>Plot the point (2,<em> \ud835\udf0b\/<\/em>3)in the polar grid.<\/p><\/blockquote><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Converting from Rectangular Coordinates to Polar Coordinates<\/h3>\n\n\n\n<p>To convert rectangular coordinates to polar coordinates,\n we will use two other familiar relationships. With this conversion, \nhowever, we need to be aware that a set of rectangular coordinates will \nyield more than one polar point.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"711\" height=\"536\" src=\"https:\/\/i0.wp.com\/www.myedme.com\/login\/wp-content\/uploads\/2020\/03\/PolarDefs.png?resize=711%2C536&#038;ssl=1\" alt=\"\" class=\"wp-image-33674\" srcset=\"https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/03\/PolarDefs.png?w=711&amp;ssl=1 711w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/03\/PolarDefs.png?resize=300%2C226&amp;ssl=1 300w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/03\/PolarDefs.png?resize=50%2C38&amp;ssl=1 50w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/03\/PolarDefs.png?resize=100%2C75&amp;ssl=1 100w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/03\/PolarDefs.png?resize=416%2C314&amp;ssl=1 416w\" sizes=\"auto, (max-width: 711px) 100vw, 711px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Review with Sal<\/h2>\n\n\n\n<figure class=\"wp-block-embed-youtube is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><div  id=\"_ytid_11571\"  width=\"980\" height=\"735\"  data-origwidth=\"980\" data-origheight=\"735\" data-facadesrc=\"https:\/\/www.youtube.com\/embed\/jexMSlSDubM?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=1&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;disablekb=0&#038;\" class=\"__youtube_prefs__ epyt-facade epyt-is-override  no-lazyload\" data-epautoplay=\"1\" ><img data-recalc-dims=\"1\" decoding=\"async\" data-spai-excluded=\"true\" class=\"epyt-facade-poster skip-lazy\" loading=\"lazy\"  alt=\"YouTube player\"  src=\"https:\/\/i0.wp.com\/i.ytimg.com\/vi\/jexMSlSDubM\/maxresdefault.jpg?w=980&#038;ssl=1\"  \/><button class=\"epyt-facade-play\" aria-label=\"Play\"><svg data-no-lazy=\"1\" height=\"100%\" version=\"1.1\" viewBox=\"0 0 68 48\" width=\"100%\"><path class=\"ytp-large-play-button-bg\" d=\"M66.52,7.74c-0.78-2.93-2.49-5.41-5.42-6.19C55.79,.13,34,0,34,0S12.21,.13,6.9,1.55 C3.97,2.33,2.27,4.81,1.48,7.74C0.06,13.05,0,24,0,24s0.06,10.95,1.48,16.26c0.78,2.93,2.49,5.41,5.42,6.19 C12.21,47.87,34,48,34,48s21.79-0.13,27.1-1.55c2.93-0.78,4.64-3.26,5.42-6.19C67.94,34.95,68,24,68,24S67.94,13.05,66.52,7.74z\" fill=\"#f00\"><\/path><path d=\"M 45,24 27,14 27,34\" fill=\"#fff\"><\/path><\/svg><\/button><\/div><\/div>\n<\/div><\/figure>\n<br>\n<figure class=\"wp-block-embed-youtube is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><div  id=\"_ytid_23423\"  width=\"980\" height=\"735\"  data-origwidth=\"980\" data-origheight=\"735\" data-facadesrc=\"https:\/\/www.youtube.com\/embed\/zGpbSGj_vfE?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=1&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;disablekb=0&#038;\" class=\"__youtube_prefs__ epyt-facade epyt-is-override  no-lazyload\" data-epautoplay=\"1\" ><img data-recalc-dims=\"1\" decoding=\"async\" data-spai-excluded=\"true\" class=\"epyt-facade-poster skip-lazy\" loading=\"lazy\"  alt=\"YouTube player\"  src=\"https:\/\/i0.wp.com\/i.ytimg.com\/vi\/zGpbSGj_vfE\/maxresdefault.jpg?w=980&#038;ssl=1\"  \/><button class=\"epyt-facade-play\" aria-label=\"Play\"><svg data-no-lazy=\"1\" height=\"100%\" version=\"1.1\" viewBox=\"0 0 68 48\" width=\"100%\"><path class=\"ytp-large-play-button-bg\" d=\"M66.52,7.74c-0.78-2.93-2.49-5.41-5.42-6.19C55.79,.13,34,0,34,0S12.21,.13,6.9,1.55 C3.97,2.33,2.27,4.81,1.48,7.74C0.06,13.05,0,24,0,24s0.06,10.95,1.48,16.26c0.78,2.93,2.49,5.41,5.42,6.19 C12.21,47.87,34,48,34,48s21.79-0.13,27.1-1.55c2.93-0.78,4.64-3.26,5.42-6.19C67.94,34.95,68,24,68,24S67.94,13.05,66.52,7.74z\" fill=\"#f00\"><\/path><path d=\"M 45,24 27,14 27,34\" fill=\"#fff\"><\/path><\/svg><\/button><\/div><\/div>\n<\/div><\/figure>\n<br> \n<figure class=\"wp-block-embed-youtube is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><div  id=\"_ytid_93715\"  width=\"980\" height=\"735\"  data-origwidth=\"980\" data-origheight=\"735\" data-facadesrc=\"https:\/\/www.youtube.com\/embed\/9iqN12hCn10?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=1&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;disablekb=0&#038;\" class=\"__youtube_prefs__ epyt-facade epyt-is-override  no-lazyload\" data-epautoplay=\"1\" ><img data-recalc-dims=\"1\" decoding=\"async\" data-spai-excluded=\"true\" class=\"epyt-facade-poster skip-lazy\" loading=\"lazy\"  alt=\"YouTube player\"  src=\"https:\/\/i0.wp.com\/i.ytimg.com\/vi\/9iqN12hCn10\/maxresdefault.jpg?w=980&#038;ssl=1\"  \/><button class=\"epyt-facade-play\" aria-label=\"Play\"><svg data-no-lazy=\"1\" height=\"100%\" version=\"1.1\" viewBox=\"0 0 68 48\" width=\"100%\"><path class=\"ytp-large-play-button-bg\" d=\"M66.52,7.74c-0.78-2.93-2.49-5.41-5.42-6.19C55.79,.13,34,0,34,0S12.21,.13,6.9,1.55 C3.97,2.33,2.27,4.81,1.48,7.74C0.06,13.05,0,24,0,24s0.06,10.95,1.48,16.26c0.78,2.93,2.49,5.41,5.42,6.19 C12.21,47.87,34,48,34,48s21.79-0.13,27.1-1.55c2.93-0.78,4.64-3.26,5.42-6.19C67.94,34.95,68,24,68,24S67.94,13.05,66.52,7.74z\" fill=\"#f00\"><\/path><path d=\"M 45,24 27,14 27,34\" fill=\"#fff\"><\/path><\/svg><\/button><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Questions for Practicing<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">Algebraic<\/h4>\n\n\n\n<p>For the following exercises, convert the given polar coordinates to Cartesian coordinates with <em>\ud835\udc5f<\/em>&gt;0 and 0\u2264<em>\ud835\udf03<\/em>\u22642<em>\ud835\udf0b<\/em>. Remember to consider the quadrant in which the given point is located when determining <em>\ud835\udf03<\/em> for the point. <\/p>\n\n\n\n<p>6.  (7, 7<em>\ud835\udf0b<\/em>\/6) <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165134312184-solution\">7<\/a>.  (5, <em>\ud835\udf0b<\/em>)<\/p>\n\n\n\n<p>8.  (6, \u2212<em>\ud835\udf0b\/<\/em>4) <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165134196148-solution\">9<\/a>.  (\u22123,  <em>\ud835\udf0b\/<\/em>6) <\/p>\n\n\n\n<p>10.  (4, 7<em>\ud835\udf0b\/<\/em>4) <\/p>\n\n\n\n<p>For the following exercises, convert the given Cartesian coordinates to polar coordinates with <em>\ud835\udc5f<\/em>&gt;0, 0\u2264<em>\ud835\udf03<\/em>&lt;2<em>\ud835\udf0b<\/em>. Remember to consider the quadrant in which the given point is located.<\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165134312061-solution\">11<\/a>.  (4, 2) <\/p>\n\n\n\n<p>12.  (\u22124, 6) <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165134113855-solution\">13<\/a>.  (3, \u22125) <\/p>\n\n\n\n<p>14.  (\u221210,\u221213) <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165135390847-solution\">15<\/a>.  (8, 8) <\/p>\n\n\n\n<p><strong>Checking Plot-Pointing Questions. <\/strong>This calculator allows you to plot polar and rectangular coordinates on the same graph. If the points are in the same location, then your answer is correct. (You can also change the calculator from radians to degrees.)<\/p>\n\n\n\n<div class=\"wp-block-image\"><a href=\"https:\/\/www.desmos.com\/calculator\/76z7fxg9zy\"><figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"650\" height=\"286\" src=\"https:\/\/i0.wp.com\/www.myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCheck.jpg?resize=650%2C286&#038;ssl=1\" alt=\"\" class=\"wp-image-33914\" srcset=\"https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCheck.jpg?w=650&amp;ssl=1 650w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCheck.jpg?resize=300%2C132&amp;ssl=1 300w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCheck.jpg?resize=50%2C22&amp;ssl=1 50w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCheck.jpg?resize=100%2C44&amp;ssl=1 100w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCheck.jpg?resize=416%2C183&amp;ssl=1 416w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>For the following exercises, convert the given Cartesian equation to a polar equation. <\/p>\n\n\n\n<p>16.  <em>\ud835\udc65<\/em> = 3 <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165134237043-solution\">17<\/a>.  <em>\ud835\udc66<\/em>=4 <\/p>\n\n\n\n<p>18.  <em>\ud835\udc66<\/em>=4<em>\ud835\udc65<\/em><sup>2<\/sup> <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165135339520-solution\">19<\/a>.  <em>\ud835\udc66<\/em>=2<em>\ud835\udc65<\/em><sup>4<\/sup> <\/p>\n\n\n\n<p>20.  <em>\ud835\udc65<\/em><sup>2<\/sup>+<em>\ud835\udc66<\/em><sup>2<\/sup>=4<em>\ud835\udc66<\/em> <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165137694965-solution\">21<\/a>.  <em>\ud835\udc65<\/em><sup>2<\/sup>+<em>\ud835\udc66<\/em><sup>2<\/sup>=3<em>\ud835\udc65<\/em> <\/p>\n\n\n\n<p>22.  <em>\ud835\udc65<\/em><sup>2<\/sup>\u2212<em>\ud835\udc66<\/em><sup>2<\/sup>=<em>\ud835\udc65<\/em> <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165135531341-solution\">23<\/a>.  <em>\ud835\udc65<\/em><sup>2<\/sup>\u2212<em>\ud835\udc66<\/em><sup>2<\/sup>=3<em>\ud835\udc66<\/em> <\/p>\n\n\n\n<p>24.  <em>\ud835\udc65<\/em><sup>2<\/sup>+<em>\ud835\udc66<\/em><sup>2<\/sup>=9 <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165135680173-solution\">25<\/a>.  <em>\ud835\udc65<\/em><sup>2<\/sup>=9<em>\ud835\udc66<\/em><\/p>\n\n\n\n<p>26.  <em>\ud835\udc66<\/em><sup>2<\/sup>=9<em>\ud835\udc65<\/em> <\/p>\n\n\n\n<p><a href=\"https:\/\/openstax.org\/books\/algebra-and-trigonometry\/pages\/chapter-10#fs-id1165134039275-solution\">27<\/a>.  9<em>\ud835\udc65\ud835\udc66<\/em>=1 <\/p>\n\n\n\n<p><strong>Need Additional Practice? <\/strong>Click on this image of a calculator on Desmos that explores polar coordinates by changing the radius (r) or the angle (a). <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.desmos.com\/calculator\/azvxdfv1lx\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"650\" height=\"297\" src=\"https:\/\/i0.wp.com\/www.myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCalc.jpg?resize=650%2C297&#038;ssl=1\" alt=\"\" class=\"wp-image-33907\" srcset=\"https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCalc.jpg?w=650&amp;ssl=1 650w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCalc.jpg?resize=300%2C137&amp;ssl=1 300w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCalc.jpg?resize=50%2C23&amp;ssl=1 50w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCalc.jpg?resize=100%2C46&amp;ssl=1 100w, https:\/\/i0.wp.com\/myedme.com\/login\/wp-content\/uploads\/2020\/04\/KhanPolarCalc.jpg?resize=416%2C190&amp;ssl=1 416w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Introduction by Sal Reading Learning Objectives from OpenStax Algebra &amp; Trigonometry In this section, you will: Plot points using polar coordinates. Convert from polar coordinates to rectangular coordinates. Convert from rectangular coordinates to polar coordinates. Transform equations between polar and rectangular forms. Identify and graph polar equations by converting to rectangular equations. Over 12 kilometers [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-33671","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33671","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/comments?post=33671"}],"version-history":[{"count":8,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33671\/revisions"}],"predecessor-version":[{"id":33917,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33671\/revisions\/33917"}],"wp:attachment":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/media?parent=33671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/categories?post=33671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/tags?post=33671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}