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Math 98: Adjunct for Math 53Faculty: Professor ZworkiAdjunct Instructor: Mike Wong, [email protected]Location:MWF 9-10, 182 DwinelleMWF 12-1, B5 Hearst Field AnnexWorksheet 2: Parametric Equations and Polar Coordinates(10.2-10.4)1)A curve is defined by the parametric equations!(#) = 1 − #(,)(#) = #*− #a)Find the area of the loop.b)Find the length of the loop.c)Find the concavity at the origin (you should have two answers).2)Convert each equation into polar coordinates.a)!(+ )(= 1b)(! − 3)(+ )(= 9c)!(+ () − 3)(= 9d)) = !e)) = √3!f)) = 1g)! = 13)Sketch each polar curvea)/ = 2b)1 =23c)/ = 1(d)/ = cos 1e)/ = sin 1f)/ = 2 cos 1g)/ = 2 cos 91 −2:;h)/ = 1 + cos 1i)/ = 2 + cos 1j)/ = 1 + 2 cos 1k)/ = cos 21l)/ = sin 21m)/ = sin 31n)/ = sin 921 +2(;4)Consider the polar curve/ = 1 + 2 cos 1.a)Sketch the curveb)Find the area of the inner loop.c)Find the area between the outer loop and the inner loop.5)Set up the integral for the length of the inner loop of the curve/ = 1 + 2 cos 1.Itootmaltby2ttintScccandofullareabcthereare2negsignsthatcancelbottom halfnegtx'ItsnegOoa2fttt2tatL

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Parametric equation, Conic section, Vert Mateo, B5 Hearst Field Annex
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