math3b_HWch10_parametric_polar - Berkeley City College...

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BerkeleyCityCollegeHW-Chapter10-ParametricEquationsandPolarCoordinatesDue:________________Name___________________________________Parametricequationsandaparameterintervalforthemotionofaparticleinthexy-planearegiven.Identifytheparticle'spathbyfindingaCartesianequationforit.GraphtheCartesianequation.Indicatetheportionofthegraphtracedbytheparticleandthedirectionofmotion.1) x=4cost,y=4sint,!t2!x-4-3-2-11234y54321-1-2-3-4-5x-4-3-2-11234y54321-1-2-3-4-52) x=2sint,y=3cost,0t2!x-4-3-2-11234y54321-1-2-3-4-5x-4-3-2-11234y54321-1-2-3-4-5Instructor K. Pernell1
3) x=25t2,y=5t,-tx-4-3-2-11234y54321-1-2-3-4-5x-4-3-2-11234y54321-1-2-3-4-5ObtaintheCartesianequationofthecurvebyeliminatingtheparameter.4) x=t,y=2t+85) x=3t-7,y=98-t6) x=t3-5t,y=t2-52
7) x=9sin2t,y=9cos2t;0t2!Finddy/dxwithouteliminatingtheparameter.8) x=5t2,y=11t3;t09) x=6tant-2,y=4sect+3,t(2n+1)!210) x=ln(2t),y=e2t11) x=1/t6,y= -3+lntFindd2y/dx2withouteliminatingtheparameter.12) x=5t2,y=10t3;t03
13) x=1-2 sint,y=1+7 cost,tn!14) x=ln(2t),y=ln(8t)3,t>015) x=t22+8t,y=t22-2t,t-8Findanequationforthelinetangenttothecurveatthepointdefinedbythegivenvalueoft.16) x=sint,y=6sint,t=!3

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Term
Spring
Professor
KellyPernell
Tags
Math, Calculus, Equations, Cartesian Coordinate System, Parametric Equations, Polar Coordinates, Polar coordinate system, Parametric equation, Conic section

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