{"id":68,"date":"2018-06-27T13:38:59","date_gmt":"2018-06-27T17:38:59","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/?post_type=chapter&#038;p=68"},"modified":"2019-01-28T13:09:30","modified_gmt":"2019-01-28T18:09:30","slug":"polar-form-vs-rectangular-form","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/chapter\/polar-form-vs-rectangular-form\/","title":{"raw":"Polar vs. Rectangular Form","rendered":"Polar vs. Rectangular Form"},"content":{"raw":"<h1>Polar form<\/h1>\r\nWhen dealing with vectors, there are two ways of expressing them.\u00a0\u00a0Up to this point, we have used a magnitude and a direction such as 30 V @ 67\u00b0.\u00a0 This is what is known as the <strong>polar form<\/strong>.\u00a0 It is more often the form that we like to express vectors in.\r\n<h1>Rectangular form<\/h1>\r\n<strong>Rectangular form<\/strong> breaks a vector down into X and Y coordinates.\u00a0\u00a0In the example below, we have a vector that, when expressed as polar, is 50 V @ 55 degrees.\u00a0\u00a0The first step to finding this expression is using the 50 V as the hypotenuse and the direction as the angle.\u00a0\u00a0Next, we draw a line straight down from the arrowhead to the X axis.\u00a0\u00a0What does this look like to you? If you said right triangle, give yourself a pat on the back.\u00a0\u00a0We then can use the angle and the hypotenuse to determine the X axis with these equations:\r\n<ul>\r\n \t<li>cos 55\u00b0\u00d750 = 28.7 for the X axis<\/li>\r\n \t<li>sin 55\u00b0\u00d750 = 41 for the Y axis<\/li>\r\n<\/ul>\r\nThis is accomplished just by transposing the ratios from what we learned previously in trigonometry.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_436\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-32-226x300.jpg\" alt=\"\" class=\"wp-image-436 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 31. Quadrant 1<\/strong>[\/caption]\r\n\r\n&nbsp;\r\n\r\nWe then can express the same vector as 28.7,\u00a0 j 41.\r\n<h1>Where did that j come from?<\/h1>\r\nThe letter j is put in front of the y component to indicate the difference between the X and the Y.\u00a0\u00a0The reason j is used is this.\r\n\r\nAs a way of telling the difference between X and Y, it was decided that a letter should be put in front of the Y.\u00a0\u00a0The X and Y components don't really exist, and are referred to as <strong>imaginary numbers<\/strong>.\u00a0 Because each is an <em>imaginary<\/em> number, the letter <em>i<\/em> was suggested.\u00a0 However, the letter i is also used as a symbol for current, so it was decided to go with the letter j instead.\r\n<h1>Why polarity is important<\/h1>\r\nLet's look at another example.\u00a0 The polar form is 60 V @ 140 degrees.\u00a0 This puts the vector in the second quadrant.\r\n\r\nIn the second quadrant, X is - (negative) and Y is + (positive).\u00a0\u00a0The angle of 140 degrees is used from the 0-degree point.\u00a0\u00a0To use trigonometry, we need to determine what the angle is in reference to the X axis. \u00a0In this example, it is 40 degrees (the supplement of 140 degrees).\u00a0\u00a0After that, we can use trigonometry to determine the X and Y components.\r\n<ul>\r\n \t<li>cos 40\u00b0\u00d760 = 46 for the X axis<\/li>\r\n \t<li>sin 40\u00b0\u00d760 = 39 for the Y axis<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n[caption id=\"attachment_437\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-33-226x300.png\" alt=\"\" class=\"wp-image-437 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 32. Quadrant 2<\/strong>[\/caption]\r\n\r\nIf we are going to express it in rectangular form, use -46, j39.\u00a0\u00a0Remember that the X component is negative and the Y component is positive as they are in the second quadrant.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\" style=\"text-align: center\"><strong>Video!<\/strong><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p style=\"text-align: center\">This video walks through how to convert from polar form to rectangular form.<\/p>\r\n\r\n<div class=\"video-container\">\r\n\r\n[embed]https:\/\/youtu.be\/9QX36MdH9ik[\/embed]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Rectangular to polar<\/h1>\r\nUp to this point, we have been converting the polar form to rectangular. \u00a0It is possible--and even important--to convert from rectangular to the polar form.\u00a0\u00a0If you have been given the rectangular coordinates, the best thing you can do is chart them out.\r\n\r\nFor instance, if you are given the coordinates 50, j80, then:\r\n\r\n<strong>Step 1.<\/strong>\u00a0 Draw them out on an X-Y chart.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_438\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-34-226x300.jpg\" alt=\"\" class=\"wp-image-438 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 33. Quadrant X\u00a0and Y (step 1)<\/strong>[\/caption]\r\n\r\n<strong>Step 2.<\/strong>\u00a0 Draw in the resultant and use Pythagoras' theorem to determine its size.\r\n\r\n[caption id=\"attachment_439\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-35-226x300.jpg\" alt=\"\" class=\"wp-image-439 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 34. Quadrant X\u00a0and Y (step 2)<\/strong>[\/caption]\r\n\r\n<strong>Step 3.\u00a0 <\/strong>Use trigonometry to determine the angle.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_440\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-36-226x300.jpg\" alt=\"\" class=\"wp-image-440 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 35. Quadrant resultant (step 3)<\/strong>[\/caption]\r\n\r\n<strong>Step 4.<\/strong>\u00a0 Using the resultant and the angle, go ahead and express it in polar form:\u00a0 94 @ 58\u00b0\r\n\r\nCongrats, you did it!\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\" style=\"text-align: center\"><strong>Video!<\/strong><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\" style=\"text-align: center\">\r\n\r\nThis video walks through how to convert from rectangular form to polar form.\r\n<div class=\"video-container\">\r\n\r\n[embed] https:\/\/youtu.be\/UCsovkGv24A [\/embed]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Heed the quadrant!<\/h1>\r\nThere is one thing you need to watch. \u00a0You need to be aware of what quadrant you are in.\u00a0\u00a0This is especially important when dealing with the direction (angle).\u00a0\u00a0When we work out the angle using the Pythagoras' theorem, we use the angle in relation to the X axis but not the direction of the vector.\u00a0\u00a0Confused? \u00a0Look at the example below where the coordinates -36,\u00a0 j29 are given.\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_433\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-37-226x300.jpg\" alt=\"\" class=\"wp-image-433 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 36. Quadrant 2 angle<\/strong>[\/caption]\r\n\r\nUsing Pythagoras and trigonometry, we worked out that the resultant was 46 and the angle, in reference to the X axis, was 38.4 degrees. \u00a0However, the polar form would <em>not<\/em> be 46 @ 38.4 degrees.\u00a0\u00a0We have to take into account that it is in the second quadrant. \u00a0That means the direction must be somewhere between 90 and 180 degrees.\u00a0\u00a0In order to work out the actual direction in this example, we take 180 degrees and subtract 38.4 degrees from it to get 141.6 degrees.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_432\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-38-226x300.jpg\" alt=\"\" class=\"wp-image-432 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 37. Quadrant 2 resultant angle<\/strong>[\/caption]\r\n\r\nIn the third quadrant, we calculate the angle in reference to the X axis and add 180 degrees to it.\u00a0\u00a0In the fourth quadrant, we calculate the angle and subtract it from 360 degrees.\r\n<h1>Something cool about the fourth quadrant<\/h1>\r\nWhen we are dealing with the fourth quadrant, there are two ways we can express the direction.\u00a0\u00a0We can work out the angle relative to the X axis and subtract it from 360 degrees as previously stated.\u00a0 Or, another way to express it is to work out the angle and then throw a negative sign in front of it. \u00a0Mathematically it is the same thing. \u00a0In this example, it can be expressed as 80 V @ 340\u00b0 or 80 V @ \u221220\u00b0.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_431\" align=\"aligncenter\" width=\"226\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-39-226x300.jpg\" alt=\"\" class=\"wp-image-431 size-medium\" width=\"226\" height=\"300\" \/> <strong>Figure 38. Quadrant 4 angle<\/strong>[\/caption]\r\n\r\nDidn't someone mention something about adding vectors?\r\n<h1>Attributions<\/h1>\r\n<a href=\"https:\/\/youtu.be\/9QX36MdH9ik\">Converting Polar to Rectangular<\/a>.\u00a0video by <a href=\"https:\/\/www.youtube.com\/channel\/UCRm79BcxKhOWRj6CQAB_Cqg\">The Electric Academy<\/a> is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">Creative Commons Attribution Licence<\/a>.\r\n\r\n<a href=\"https:\/\/youtu.be\/UCsovkGv24A\">Converting Rectangular to Polar form<\/a>.\u00a0video by <a href=\"https:\/\/www.youtube.com\/channel\/UCRm79BcxKhOWRj6CQAB_Cqg\">The Electric Academy<\/a> is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">Creative Commons Attribution Licence<\/a>.","rendered":"<h1>Polar form<\/h1>\n<p>When dealing with vectors, there are two ways of expressing them.\u00a0\u00a0Up to this point, we have used a magnitude and a direction such as 30 V @ 67\u00b0.\u00a0 This is what is known as the <strong>polar form<\/strong>.\u00a0 It is more often the form that we like to express vectors in.<\/p>\n<h1>Rectangular form<\/h1>\n<p><strong>Rectangular form<\/strong> breaks a vector down into X and Y coordinates.\u00a0\u00a0In the example below, we have a vector that, when expressed as polar, is 50 V @ 55 degrees.\u00a0\u00a0The first step to finding this expression is using the 50 V as the hypotenuse and the direction as the angle.\u00a0\u00a0Next, we draw a line straight down from the arrowhead to the X axis.\u00a0\u00a0What does this look like to you? If you said right triangle, give yourself a pat on the back.\u00a0\u00a0We then can use the angle and the hypotenuse to determine the X axis with these equations:<\/p>\n<ul>\n<li>cos 55\u00b0\u00d750 = 28.7 for the X axis<\/li>\n<li>sin 55\u00b0\u00d750 = 41 for the Y axis<\/li>\n<\/ul>\n<p>This is accomplished just by transposing the ratios from what we learned previously in trigonometry.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_436\" aria-describedby=\"caption-attachment-436\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-32-226x300.jpg\" alt=\"\" class=\"wp-image-436 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-32-226x300.jpg 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-32-65x86.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-32-225x298.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-32-350x464.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-32.jpg 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-436\" class=\"wp-caption-text\"><strong>Figure 31. Quadrant 1<\/strong><\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p>We then can express the same vector as 28.7,\u00a0 j 41.<\/p>\n<h1>Where did that j come from?<\/h1>\n<p>The letter j is put in front of the y component to indicate the difference between the X and the Y.\u00a0\u00a0The reason j is used is this.<\/p>\n<p>As a way of telling the difference between X and Y, it was decided that a letter should be put in front of the Y.\u00a0\u00a0The X and Y components don&#8217;t really exist, and are referred to as <strong>imaginary numbers<\/strong>.\u00a0 Because each is an <em>imaginary<\/em> number, the letter <em>i<\/em> was suggested.\u00a0 However, the letter i is also used as a symbol for current, so it was decided to go with the letter j instead.<\/p>\n<h1>Why polarity is important<\/h1>\n<p>Let&#8217;s look at another example.\u00a0 The polar form is 60 V @ 140 degrees.\u00a0 This puts the vector in the second quadrant.<\/p>\n<p>In the second quadrant, X is &#8211; (negative) and Y is + (positive).\u00a0\u00a0The angle of 140 degrees is used from the 0-degree point.\u00a0\u00a0To use trigonometry, we need to determine what the angle is in reference to the X axis. \u00a0In this example, it is 40 degrees (the supplement of 140 degrees).\u00a0\u00a0After that, we can use trigonometry to determine the X and Y components.<\/p>\n<ul>\n<li>cos 40\u00b0\u00d760 = 46 for the X axis<\/li>\n<li>sin 40\u00b0\u00d760 = 39 for the Y axis<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_437\" aria-describedby=\"caption-attachment-437\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-33-226x300.png\" alt=\"\" class=\"wp-image-437 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-33-226x300.png 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-33-65x86.png 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-33-225x298.png 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-33-350x464.png 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-33.png 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-437\" class=\"wp-caption-text\"><strong>Figure 32. Quadrant 2<\/strong><\/figcaption><\/figure>\n<p>If we are going to express it in rectangular form, use -46, j39.\u00a0\u00a0Remember that the X component is negative and the Y component is positive as they are in the second quadrant.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\" style=\"text-align: center\"><strong>Video!<\/strong><\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p style=\"text-align: center\">This video walks through how to convert from polar form to rectangular form.<\/p>\n<div class=\"video-container\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Converting Polar to Rectangular\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/9QX36MdH9ik?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<\/div>\n<\/div>\n<h1>Rectangular to polar<\/h1>\n<p>Up to this point, we have been converting the polar form to rectangular. \u00a0It is possible&#8211;and even important&#8211;to convert from rectangular to the polar form.\u00a0\u00a0If you have been given the rectangular coordinates, the best thing you can do is chart them out.<\/p>\n<p>For instance, if you are given the coordinates 50, j80, then:<\/p>\n<p><strong>Step 1.<\/strong>\u00a0 Draw them out on an X-Y chart.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_438\" aria-describedby=\"caption-attachment-438\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-34-226x300.jpg\" alt=\"\" class=\"wp-image-438 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-34-226x300.jpg 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-34-65x86.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-34-225x298.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-34-350x464.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-34.jpg 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-438\" class=\"wp-caption-text\"><strong>Figure 33. Quadrant X\u00a0and Y (step 1)<\/strong><\/figcaption><\/figure>\n<p><strong>Step 2.<\/strong>\u00a0 Draw in the resultant and use Pythagoras&#8217; theorem to determine its size.<\/p>\n<figure id=\"attachment_439\" aria-describedby=\"caption-attachment-439\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-35-226x300.jpg\" alt=\"\" class=\"wp-image-439 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-35-226x300.jpg 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-35-65x86.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-35-225x298.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-35-350x464.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-35.jpg 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-439\" class=\"wp-caption-text\"><strong>Figure 34. Quadrant X\u00a0and Y (step 2)<\/strong><\/figcaption><\/figure>\n<p><strong>Step 3.\u00a0 <\/strong>Use trigonometry to determine the angle.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_440\" aria-describedby=\"caption-attachment-440\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-36-226x300.jpg\" alt=\"\" class=\"wp-image-440 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-36-226x300.jpg 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-36-65x86.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-36-225x298.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-36-350x464.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-36.jpg 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-440\" class=\"wp-caption-text\"><strong>Figure 35. Quadrant resultant (step 3)<\/strong><\/figcaption><\/figure>\n<p><strong>Step 4.<\/strong>\u00a0 Using the resultant and the angle, go ahead and express it in polar form:\u00a0 94 @ 58\u00b0<\/p>\n<p>Congrats, you did it!<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\" style=\"text-align: center\"><strong>Video!<\/strong><\/p>\n<\/header>\n<div class=\"textbox__content\" style=\"text-align: center\">\n<p>This video walks through how to convert from rectangular form to polar form.<\/p>\n<div class=\"video-container\">\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Converting from Rectangular to Polar form\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/UCsovkGv24A?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<\/div>\n<\/div>\n<h1>Heed the quadrant!<\/h1>\n<p>There is one thing you need to watch. \u00a0You need to be aware of what quadrant you are in.\u00a0\u00a0This is especially important when dealing with the direction (angle).\u00a0\u00a0When we work out the angle using the Pythagoras&#8217; theorem, we use the angle in relation to the X axis but not the direction of the vector.\u00a0\u00a0Confused? \u00a0Look at the example below where the coordinates -36,\u00a0 j29 are given.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_433\" aria-describedby=\"caption-attachment-433\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-37-226x300.jpg\" alt=\"\" class=\"wp-image-433 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-37-226x300.jpg 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-37-65x86.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-37-225x298.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-37-350x464.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-37.jpg 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-433\" class=\"wp-caption-text\"><strong>Figure 36. Quadrant 2 angle<\/strong><\/figcaption><\/figure>\n<p>Using Pythagoras and trigonometry, we worked out that the resultant was 46 and the angle, in reference to the X axis, was 38.4 degrees. \u00a0However, the polar form would <em>not<\/em> be 46 @ 38.4 degrees.\u00a0\u00a0We have to take into account that it is in the second quadrant. \u00a0That means the direction must be somewhere between 90 and 180 degrees.\u00a0\u00a0In order to work out the actual direction in this example, we take 180 degrees and subtract 38.4 degrees from it to get 141.6 degrees.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_432\" aria-describedby=\"caption-attachment-432\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-38-226x300.jpg\" alt=\"\" class=\"wp-image-432 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-38-226x300.jpg 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-38-65x86.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-38-225x298.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-38-350x464.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/Figure-38.jpg 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-432\" class=\"wp-caption-text\"><strong>Figure 37. Quadrant 2 resultant angle<\/strong><\/figcaption><\/figure>\n<p>In the third quadrant, we calculate the angle in reference to the X axis and add 180 degrees to it.\u00a0\u00a0In the fourth quadrant, we calculate the angle and subtract it from 360 degrees.<\/p>\n<h1>Something cool about the fourth quadrant<\/h1>\n<p>When we are dealing with the fourth quadrant, there are two ways we can express the direction.\u00a0\u00a0We can work out the angle relative to the X axis and subtract it from 360 degrees as previously stated.\u00a0 Or, another way to express it is to work out the angle and then throw a negative sign in front of it. \u00a0Mathematically it is the same thing. \u00a0In this example, it can be expressed as 80 V @ 340\u00b0 or 80 V @ \u221220\u00b0.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_431\" aria-describedby=\"caption-attachment-431\" style=\"width: 226px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-39-226x300.jpg\" alt=\"\" class=\"wp-image-431 size-medium\" width=\"226\" height=\"300\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-39-226x300.jpg 226w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-39-65x86.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-39-225x298.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-39-350x464.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/12\/figure-39.jpg 724w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><figcaption id=\"caption-attachment-431\" class=\"wp-caption-text\"><strong>Figure 38. Quadrant 4 angle<\/strong><\/figcaption><\/figure>\n<p>Didn&#8217;t someone mention something about adding vectors?<\/p>\n<h1>Attributions<\/h1>\n<p><a href=\"https:\/\/youtu.be\/9QX36MdH9ik\">Converting Polar to Rectangular<\/a>.\u00a0video by <a href=\"https:\/\/www.youtube.com\/channel\/UCRm79BcxKhOWRj6CQAB_Cqg\">The Electric Academy<\/a> is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">Creative Commons Attribution Licence<\/a>.<\/p>\n<p><a href=\"https:\/\/youtu.be\/UCsovkGv24A\">Converting Rectangular to Polar form<\/a>.\u00a0video by <a href=\"https:\/\/www.youtube.com\/channel\/UCRm79BcxKhOWRj6CQAB_Cqg\">The Electric Academy<\/a> is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">Creative Commons Attribution Licence<\/a>.<\/p>\n","protected":false},"author":422,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[47],"contributor":[],"license":[],"class_list":["post-68","chapter","type-chapter","status-publish","hentry","chapter-type-standard"],"part":57,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/68","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/users\/422"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/68\/revisions"}],"predecessor-version":[{"id":575,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/68\/revisions\/575"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/parts\/57"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/68\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/media?parent=68"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapter-type?post=68"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/contributor?post=68"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/license?post=68"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}