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A7 - Math 128 ASSIGNMENT 7 Polar coordinates curves Winter...

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Math 128 ASSIGNMENT 7: Polar coordinates & curves Winter 2011 Due at 8:25 am on Wednesday, March 9 th in the correct drop slot across from MC4066 or in class depending on your instructor’s preference. Assignments put into the wrong drop slot will not be marked. Part A (answer only): Submit your answers using the template provided on the last page of this assignment, which you can print or hand-copy. 1. Find polar co-ordinates with r > 0 and - π < θ π for each of the following Cartesian points: i) (1 , - 1) , ii) ( - 1 , 3) iii) ( - 1 , 0) 2. Find the Cartesian co-ordinates of the following polar points: i) - 1 , π 2 , ii) 2 , 3 π 4 , iii) 1 , - π 3 3. From the text, exercise 10.3 # 56. 4. Note that the cardioid r = a (1 + cos θ ) can be represented by r = 2 a cos 2 θ 2 , 0 θ 2 π . Determine its length. Part B (full solution): All solutions must be clearly stated and fully justified. 1. Convert each of the following equations to polar form, and sketch the curve in R 2 .
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