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Unformatted text preview: patino (mp25752) Assignment2 luecke (57510) 1 This printout should have 15 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Locate the points given in polar coordinates by P parenleftBig 2 , 1 6 parenrightBig , Q parenleftBig 1 , 1 2 parenrightBig R parenleftBig 2 , 2 3 parenrightBig , among 2 4 2 4 2 4 2 4 b u b c r u t r s 1. b u t b c P : Q : R : 2. b u t b c P : Q : R : correct 3. b u t b c P : Q : R : 4. b u t b c P : Q : R : 5. b u t b c P : Q : R : 6. b u t b c P : Q : R : Explanation: To convert from polar coordinates to Carte sian coordinates we use x = r cos , y = r sin . For then the points P parenleftBig 2 , 1 6 parenrightBig , Q parenleftBig 1 , 1 2 parenrightBig R parenleftBig 2 , 2 3 parenrightBig , correspond to b u t b c P : Q : R : in Cartesian coordinates. keywords: polar coordinates, Cartesian coor dinates, change of coordinates, 002 10.0 points Which, if any, of A. (4 , / 3) , B. ( 4 , 7 / 6) , C. (4 , 13 / 6) , are polar coordinates for the point given in Cartesian coordinates by P (2 , 2 3)? 1. all of them 2. A only correct 3. C only 4. A and B only 5. A and C only 6. B only 7. none of them 8. B and C only Explanation: To convert from Cartesian coordinates to polar coordinates we use the relations: x = r cos , y = r sin , so that r 2 = x 2 + y 2 , tan = y x . For the point P (2 , 2 3) in Cartesian co ordinates, therefore, one choice of r and is patino (mp25752) Assignment2 luecke (57510) 2 r = 4 and = / 3, but there are equivalent solutions for r < 0 as well as values of dif fering by integer multiples of . For the given choices we thus see that A. TRUE: solution noted already. B. FALSE: incorrect. C. FALSE: differs from / 6 by 2 . 003 10.0 points Which, if any, of A. (2 , 5 / 6) , B. (2 , 17 / 6) , C. ( 2 , 5 / 6) , are polar coordinates for the point given in Cartesian coordinates by P ( 3 , 1)? 1. none of them 2. C only 3. B and C only 4. A only 5. all of them 6. A and C only 7. B only 8. A and B only correct Explanation: To convert from Cartesian coordinates to polar coordinates we use the relations: x = r cos , y = r sin , so that r 2 = x 2 + y 2 , tan = y x . For the point P ( 3 , 1) in Cartesian co ordinates, therefore, one choice of r and is r = 2 and = 5 / 6, but there are equivalent solutions for r < 0 as well as values of dif fering by integer multiples of . For the given choices we thus see that A. TRUE: solution noted already. B. TRUE: differs from 5 / 6 by 2 . C. FALSE: incorrect. 004 10.0 points A point P is given in Cartesian coordinates by P (1 , 1). Find polar coordinates ( r, ) of this point with r < 0 and 0 < 2 ....
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This note was uploaded on 10/21/2009 for the course M 53215 taught by Professor Lueke during the Spring '09 term at University of Texas at Austin.
 Spring '09
 Lueke

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