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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 ≤ θ < 2 π . a) ( − 2 , 2) Solution: We have r = radicalbig ( − 2) 2 + 2 2 = √ 8 and tan θ = 2 2 = − 1. Since the point is in quadrant 2 we get θ = 3 π 4 . Hence the point in polar coordinates is ( √ 8 , 3 π 4 ). b) ( √ 3 , − 1) Solution: We have r = radicalBig ( √ 3) 2 + ( − 1) 2 = 2 and tan θ = 1 √ 3 . Since the point is in quadrant 4 we get θ = 11 π 6 . Hence the point in polar coordinates is (2 , 11 π 6 ). 2. Convert the following points from polar coordinates to Cartesian coordinates. a) (2 , π/ 3) Solution: We get x = 2 cos π 3 = 1 and y = 2 sin π 3 = √ 3, hence the point is (1 , √ 3) in Cartesian coordinates. b) (3 , 5 π/ 6) Solution: We have x = 3 cos 5 π 6 = 3 √ 3 2 and y = 3 sin 5 π 6 = 3 2 , hence the point is ( − 3 √ 3 2 , 3 2 ) in Cartesian coordinates. 2 3. For each of the indicated regions in polar coordinates, sketch the region and find the area.For each of the indicated regions in polar coordinates, sketch the region and find the area....
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 Fall '08
 WOLCZUK
 Polar Coordinates, Sin, Polar coordinate system

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