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MAT_267_Section 12.7.pdf - Austin Cholley Assignment...

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Austin CholleyZhuMAT267ONLINEAFall2021Assignment Section12.7 due 09/26/2021 at 11:59pm MSTProblem 1.(1 point)What are the rectangular coordinates of the point whose sphericalcoordinates are(3,7π6,2π3)?x=y=z=Problem 2.(1 point)What are the spherical coordinates of the point whose rectangularcoordinates are(2,5,-1)?ρ=θ=φ=
1
Problem 3.(1 point)Express the point given in Cartesian coordinates in spherical co-ordinates(ρ,θ,φ). Note: you really only have to do the work forone, if you use a little geometry and your knowledge of the trigfunctions.A)742,742,-723=B)-742,742,-723=C)742,-742,+723=D)-742,-742,+723=Solution:SOLUTIONA)ρ2=px2+y2+z2=r7422+7422+(-723)2=72=7The point742,742is in the first quadrant of thexy-plane, soθ=arctan(yx)=arctan742/742=arctan(1) =π4cos(φ) =zρ=-7237=-123φ=5π6Thus spherical coordinates are7,π4,5π6.B)ρ2=px2+y2+z2=r-7422+7422+(-723)2=72=7The point-742,742is in the second quadrant of thexy-plane, soθ=arctan(yx)+π=arctan742/-742+π=arctan(-1)+π=-π4+π=3π4cos(φ) =zρ=-7237=-123φ=5π6Thus spherical coordinates are7,3π4,5π6.C)ρ2=px2+y2+z2=r7422+-7422+(+723)2=72=7The point742,-742is in the fourth quadrant of thexy-plane, soθ=arctan(yx)+2π=arctan-742/742+2π=arctan(-1)+2π=-π4+2π=7π4cos(φ) =zρ=+7237= +123φ=π6Thus spherical coordinates are7,7π4,π6.D)ρ2=px2+y2+z2=r-7422+-7422+(-723)2=72=7The point-742,-742is in the third quadrant of thexy-plane, soθ=arctan(yx)+π=arctan-742/-742+π=arctan(1)+π=π4+π=5π4cos(φ) =zρ=+7237= +123φ=π6Thus spherical coordinates are7,5π4,π6.Answer(s) submitted:(7,arctan(1),((7pi )/4))(7,)(7,)(7,)(incorrect)Correct Answers:(7,0.785398,2.61799)(7,2.35619,2.61799)(7,5.49779,0.523599)(7,3.92699,0.523599)Problem 4.(1 point)What are the cylindrical coordinates of the point whose sphericalcoordinates are(ρ,θ,φ) = (5,1,2π3)?r=θ=z=Solution:SOLUTIONr=ρsin(φ) =5sin(2π3)=532= (5/2)3θ=1z=ρcos(φ) =5cos(2π3)=5(-12)=-5/2Thus cylindrical coordinates are((5/2)3,1,-5/2)Answer(s) submitted:4.33011-2.5(correct)Correct Answers:4.330131-2.52

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Term
Spring
Professor
Brewer
Tags
Cartesian Coordinate System, Polar coordinate system

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