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Rectangular Form to Polar Form Saturday, October 19, 2013 1:43 PM Slides Notes Overview You can go from rectangular form to polar form. Let's look at it as an overview first. (-6, 2). Right now it is in the rectangular format (x,y). To convert that to polar, you will need to think in terms of a right triangle so that you can find the angle inside the triangle that touches (0,0). Then you will use that angle and find the total angle of rotation from the right of the x-axis. Next, you will find the length of the hypotenuse using the Pythagorean Theorem. Now that we have the overview, let's actually do one. Angle in Triangle Saxon 2_ 3rd ed Page 1 Angle in Triangle We will do that first step now of finding the interior angle in the triangle. You have the opposite and the adjacent legs of the right triangle. That combination is related to tangent. You need the angle though, so you will use the inverse tangent. Let's make sure you remember how to do this calculation on your calculator. Click the shift button and then tangent. Notice that the display is waiting for you to put the opposite over adjacent leg lengths. Type it in and end with the end parenthesis. You get a little over 18. We will record 18 degrees as the angle inside the triangle. Rotation from Right Now, we will get the total angle of rotation from the right side of the x-axis. There are a few possible ways we can do it, but an easy one would be to start from the 180 degree point and subtract back the 18 degrees. That will give us 162 degrees. Find the Vector Length Saxon 2_ 3rd ed Page 2 Find the Vector Length Now we are in the home stretch. All we have left is to use the Pythagorean Theorem to find the hypotenuse. You have done these for a while now and they are probably getting second nature now. We will plug in the side lengths. Simplify the squares then simplify by adding them. We need to get rid of the square with our variable and we can do that if we undo is by taking the square root. Whatever we do to one side we must do to the other in a transformation. That leaves us with the hypotenuse of the square root of 40. Now we have all the parts of our polar form. Congratulations Saxon 2_ 3rd ed Page 3 Congratulations Saxon 2_ 3rd ed Page 4