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Assignment 2

# Assignment 2 - patino(mp25752 Assignment2 luecke(57510 This...

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patino (mp25752) – Assignment2 – luecke – (57510) 1 This print-out should have 15 questions. Multiple-choice 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 π parenrightBig , Q parenleftBig - 1 , 1 2 π parenrightBig R parenleftBig 2 , 2 3 π parenrightBig , among 2 4 - 2 - 4 2 4 - 2 - 4 1. P : Q : R : 2. P : Q : R : correct 3. P : Q : R : 4. P : Q : R : 5. P : Q : R : 6. P : Q : R : Explanation: To convert from polar coordinates to Carte- sian coordinates we use x = r cos θ , y = r sin θ . For then the points P parenleftBig 2 , 1 6 π parenrightBig , Q parenleftBig - 1 , 1 2 π parenrightBig R parenleftBig 2 , 2 3 π parenrightBig , correspond to 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 , π/ 3) , B. ( - 4 , 7 π/ 6) , C. (4 , 13 π/ 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 θ , y = r sin θ , so that r 2 = x 2 + y 2 , tan θ = y x . For the point P (2 , 2 3) in Cartesian co- ordinates, therefore, one choice of r and θ is

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patino (mp25752) – Assignment2 – luecke – (57510) 2 r = 4 and θ = π/ 3, but there are equivalent solutions for r < 0 as well as values of θ dif- fering by integer multiples of π . For the given choices we thus see that A. TRUE: solution noted already. B. FALSE: θ incorrect. C. FALSE: differs from π/ 6 by 2 π . 003 10.0 points Which, if any, of A. (2 , 5 π/ 6) , B. (2 , 17 π/ 6) , C. ( - 2 , 5 π/ 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 θ , y = r sin θ , so that r 2 = x 2 + y 2 , tan θ = y x . For the point P ( - 3 , 1) in Cartesian co- ordinates, therefore, one choice of r and θ is r = 2 and θ = 5 π/ 6, but there are equivalent solutions for r < 0 as well as values of θ dif- fering by integer multiples of π . For the given choices we thus see that A. TRUE: solution noted already. B. TRUE: differs from 5 π/ 6 by 2 π . C. FALSE: θ incorrect. 004 10.0 points A point P is given in Cartesian coordinates by P (1 , 1). Find polar coordinates ( r, θ ) of this point with r < 0 and 0 θ < 2 π . 1. parenleftBig - 3 , 5 π 4 parenrightBig 2. parenleftBig - 2 , 3 π 4 parenrightBig 3. parenleftBig - 3 , 7 π 4 parenrightBig 4. parenleftBig - 2 , 5 π 4 parenrightBig correct 5. parenleftBig - 2 , 7 π 4 parenrightBig 6. parenleftBig - 3 , 3 π 4 parenrightBig Explanation: Since the relationship between Cartesian coordinates and polar coordinates is x = r cos θ , y = r sin θ , the point P (1 , 1) in Cartesian coordinates can be given in polar coordinates as P parenleftBig - 2 , 5 π 4 parenrightBig , 005 10.0 points Find a Cartesian equation for the curve given by the polar equation r
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Assignment 2 - patino(mp25752 Assignment2 luecke(57510 This...

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