Hey everyone. Let's plot these points in polar coordinates together. Now we've first looked at polar coordinates using angle measures given in radians, but you might also see angles given in degrees like we see here with point a at 5, 60 degrees. Now here I have an r value of 5 and a θ value of 60 degrees. Remember when plotting polar coordinates, we want to locate our angle first. So coming over here to my polar coordinate system, I'm going to first locate my angle 60 degrees or π3 radians. Then I'm going to count out on that line using that r value, in this case, 5, so 1, 2, 3, 4, 5, out to this point, point a. Now looking at point b, this is located at 390 degrees. So I have an r value of 3 and a θ value of 90 degrees. So, remember locating that angle first, which in this case is right here at 90 degrees or π2 radians, and then counting out using that r value 1, 2, 3, here is my point b. Now let's move on to point c. Now point c is 0 -5π3 radians. So I have an r value of 0 and a θ value of negative 5π3. Remember when we're dealing with a negative value of θ, that just tells us that we need to measure our angle clockwise rather than counterclockwise. So here I'm going to locate my angle first, of course, going around clockwise to 5π3 radians, which will land me right back along this line. But here our r value is 0, so I'm actually going to stay right there at the pole or what we think of as our origin on an x y coordinate system and this is my point c. Now moving on to our final point here at 27π3. So I have an r value of 2 and a θ value of 7π3. Now here if I measure around 7π3 radians, I actually do a complete rotation and then go another π3 radians to land me right back at this same line that point a is located on. Now here using my radius value counting out to 2, I end up right here at point d. So here we've plotted these 4 points in polar coordinates. Let's continue practicing together. Thanks for watching, and let me know if you have questions.
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9. Polar Equations
Polar Coordinate System
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