assignment 2-solutions-2

assignment 2-solutions-2 - Mirzoyeva (tim89) assignment 2...

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Mirzoyeva (tim89) – assignment 2 – luecke – (58600) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Locate the points given in polar coordinates by P p 4 , 2 3 π P , Q p 3 , 1 2 π P R p 2 , 1 6 π P , 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 : 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 : correct 6. b u t b c P : Q : R : Explanation: To convert From polar coordinates to Carte- sian coordinates we use x = r cos θ , y = r sin θ . ±or then the points P p 4 , 2 3 π P , Q p 3 , 1 2 π P R p 2 , 1 6 π P , 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 , 13 π/ 6) , B. (4 , π/ 3) , C. ( - 4 , 4 π/ 3) , are polar coordinates For the point given in Cartesian coordinates by P (2 , 2 3)? 1. A and B only 2. A only 3. B and C only correct 4. all oF them 5. A and C only 6. C only 7. B only 8. none oF them 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 . ±or the point P (2 , 2 3) in Cartesian co- ordinates, thereFore, one choice oF r and θ is
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Mirzoyeva (tim89) – assignment 2 – luecke – (58600) 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. FALSE: di±ers from π/ 6 by 2 π . B. TRUE: solution noted already. C. TRUE: - 4 cos(4 π/ 3) = 2 , - 4 sin(4 π/ 3) = 2 3 . 003 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. p - 2 , 3 π 4 P correct 2. p - 3 , 7 π 4 P 3. p - 3 , 3 π 4 P 4. p - 3 , 5 π 4 P 5. p - 2 , 5 π 4 P 6. p - 2 , 7 π 4 P 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 p - 2 , 3 π 4 P , 004 10.0 points Find a Cartesian equation for the curve given by the polar equation r + 2 cos θ = 0 . 1. x 2 + ( y - 1) 2 = 1 2. ( x - 1) 2 + y 2 + 1 = 0 3. x 2 + ( y - 1) 2 + 1 = 0 4. x 2 + ( y + 1) 2 = 1 5. ( x - 1) 2 + y 2 = 1 6. x 2 + ( y + 1) 2 + 1 = 0 7. ( x + 1) 2 + y 2 + 1 = 0 8. ( x + 1) 2 + y 2 = 1 correct Explanation: We have to replace r and θ in the polar equation r + 2 cos θ = 0 using the relations x = r cos θ , y = r sin θ .
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assignment 2-solutions-2 - Mirzoyeva (tim89) assignment 2...

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