A6_soln - Math 237 Assignment 6 Due: Friday, July 4th 1....

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Unformatted text preview: Math 237 Assignment 6 Due: Friday, July 4th 1. Convert the following points from Cartesian coordinates to polar coordinates with ≤ θ < 2 π . a) (1 ,- 1) Solution: We have r = radicalbig (1) 2 + (- 1) 2 = √ 2 and tan θ =- 1 1 . Since the point is in the fourth quadrant we get θ = 7 π 4 hence we have the point ( √ 2 , 7 π 4 ). b) (- 1 , √ 3) Solution: We have r = radicalBig (- 1) 2 + ( √ 3) 2 = 2 and tan θ = √ 3- 1 . Since the point is in second quadrant we get θ = 2 π 3 and hence have the point (2 , 2 π 3 ). 2. Convert the following points from polar coordinates to Cartesian coordinates. a) (2 , π/ 4) Solution: We have x = r cos θ = 2 cos π 4 = √ 2 and y = r sin θ = 2 sin π 4 = √ 2. Hence, we have the point ( √ 2 , √ 2). b) (6 ,- π/ 6) Solution: We have x = r cos θ = 6 cos(- π 6 ) = 3 √ 3 and y = r sin θ = 6 sin(- π 6 ) =- 3. Hence, we have the point (3 √ 3 ,- 3)....
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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.

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A6_soln - Math 237 Assignment 6 Due: Friday, July 4th 1....

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