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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,Q−3,12πR4,13π,among24−2−42410.0 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(2,2√3)?5.P:Q:R:6.P:Q:R:For then the pointsP4,23π,Q−3,12πR4,13π,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(2,2√3)?
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) = 2√3.00310.0 pointsA pointPis given in Cartesian coordinatesbyP(−1,1). Find polar coordinates (r,θ) ofthis point withr <0 and 0≤θ<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 asP−√2,7π4,00410.0 pointsWhich one of the following shaded-regionsin the plane consists of all points whose polarcoordinates satisfy the inequalities3< r≤4,13π≤θ≤56π?188.8.131.52.245.246.24correct