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

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cheatham (sc36975) – HW07 – um – (53890)1Thisprint-outshouldhave20questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.00110.0 pointsLocate the points given in polar coordinatesbyP4,23π,Q3,12πR4,13π,among24242410.0 pointsWhich, if any, ofA.(4,π/3),B.(4,7π/3),C.(4,4π/3),are polar coordinates for the point given inCartesian coordinates byP(2,23)?5.P:Q:R:6.P:Q:R:For then the pointsP4,23π,Q3,12πR4,13π,correspond toP:Q:R:in Cartesian coordinates.keywords: polar coordinates, Cartesian coor-dinates, change of coordinates,00210.0 pointsWhich, if any, ofA.(4,π/3),B.(4,7π/3),C.(4,4π/3),are polar coordinates for the point given inCartesian coordinates byP(2,23)?
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 thatA.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 pointsA pointPis given in Cartesian coordinatesbyP(1,1). Find polar coordinates (r,θ) ofthis point withr <0 and 0θ<2π.1.2,5π42.2,7π4correct3.3,7π44.3,5π45.3,3π46.2,3π4Explanation:Since the relationship between Cartesiancoordinates and polar coordinates isx=rcosθ,y=rsinθ,the pointP(1,1) in Cartesian coordinatescan be given in polar coordinates asP2,7π4,00410.0 pointsWhich one of the following shaded-regionsin the plane consists of all points whose polarcoordinates satisfy the inequalities3< r4,13πθ56π?1.242.243.244.245.246.24correct