M408D SPRING 2015 HOMEWORK #7 - cheatham(sc36975 HW07 um(53890 This print-out should have 20 questions Multiple-choice questions may continue on the

# M408D SPRING 2015 HOMEWORK #7 - cheatham(sc36975 HW07...

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cheatham (sc36975) – HW07 – um – (53890) 1 This print-out should have 20 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 4 , 2 3 π , Q 3 , 1 2 π R 4 , 1 3 π , among 2 4 2 4 2 4 2 4 1. P : Q : R : correct 2. P : Q : R : 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 4 , 2 3 π , Q 3 , 1 2 π R 4 , 1 3 π , 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 / 3) , C. ( 4 , 4 π / 3) , are polar coordinates for the point given in Cartesian coordinates by P (2 , 2 3)? 1. all of them correct 2. B and C only 3. B only 4. C only 5. none of them 6. A and B only 7. A only 8. A 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
cheatham (sc36975) – HW07 – um – (53890)2r= 4 andθ=π/3, but there are equivalentsolutions forr <0 as well as values ofθdif-fering by integer multiples ofπ. For the givenchoices we thus see that A.TRUE: solution noted already.B.TRUE: differs fromπ/3 by 2π.C.TRUE:4 cos(4π/3) = 2,4 sin(4π/3) = 23.00310.0 points A pointPis given in Cartesian coordinatesbyP(1,1). Find polar coordinates (r,θ) ofthis point withr <0 and 0θ<2π. Which one of the following shaded-regionsin the plane consists of all points whose polarcoordinates satisfy the inequalities3< r4,13πθ56π? 24 6.2correct 4
Explanation: