a8_soln

# a8_soln - Math 237 Assignment 8 Solutions 1 Convert the...

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Unformatted text preview: Math 237 Assignment 8 Solutions 1. Convert the following points from Cartesian coordinates to polar coordinates with ≤ θ < 2 π . a) (- 3 , 3) Solution: We have r = p (- 3) 2 + 3 2 = √ 18 and tan θ = 3- 3 =- 1 . Since the point is in quadrant 2 we get θ = 3 π 4 . Hence the point in polar coordinates is ( √ 18 , 3 π 4 ) . b) (1 ,- 1 / √ 3) . Solution: We have r = q 1 2 + (- 1 / √ 3) 2 = p 4 / 3 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 ( p 4 / 3 , 11 π 6 ) . 2. Convert the following points from polar coordinates to Cartesian coordinates. a) (3 ,- π/ 6) . Solution: We get x = 3 cos- π 6 = 3 √ 3 2 and y = 3 sin- π 6 =- 3 2 , hence the point is ( 3 √ 3 2 ,- 3 2 ) in Cartesian coordinates. b) (1 ,π/ 5) . Solution: We get x = cos π 5 and y = sin π 5 , hence the point is (cos π 5 , sin π 5 ) in Cartesian coordinates....
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## This note was uploaded on 11/18/2010 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.

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a8_soln - Math 237 Assignment 8 Solutions 1 Convert the...

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