Consider the curveCwith parametric equationsx(t)=cos(2t),y(t)=sin(t), where−2π​≤t≤2π​. a) Find a Cartesian equation forC. Then make a rough sketch of the curve. b) The curvatureκof a curveCat a given point is a measure of how quickly the curve changes direction at that point. For example, a straight line has curvatureκ=0at every point. At any point, the curvature can be calculated byκ(t)=(1+(dxdy​)2)23​∣∣​dx2d2y​∣∣​​.Show that the curvature of the curveCis:κ(t)=(1+16sin2t)23​4​.

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