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Unformatted text preview: Math 237 Assignment 6 Solutions 1. Convert the following points from Cartesian coordinates to polar coordinates with 0 < 2 . a) ( 1 , 3). Solution: We have r = radicalBig ( 1) 2 + ( 3) 2 = 2 and tan = 3 1 = 3. Since the point is in quadrant 3 we get = 4 3 . Hence the point in polar coordinates is (2 , 4 3 ). b) (2 , 1). Solution: We have r = 2 2 + 1 2 = 5 and tan = 1 2 . Since the point is in quadrant 1 we get = arctan(1 / 2). Hence the point in polar coordinates is ( 5 , arctan(1 / 2)). 2. Convert the following points from polar coordinates to Cartesian coordinates. a) (3 , 2 / 3). Solution: We get x = 3 cos 2 3 = 1 2 and y = 3 sin 2 3 = 3 3 2 , hence the point is parenleftBig 1 2 , 3 3 2 parenrightBig in Cartesian coordinates. b) (2 , / 6). Solution: We get x = 2 cos 6 = 3 and y = 2 sin 6 = 1, hence the point is ( 3 , 1) in Cartesian coordinates....
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This note was uploaded on 04/18/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.
 Spring '08
 WOLCZUK
 Math, Polar Coordinates

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