# Consider the curve*C*with parametric equations*x*(*t*)=cos(2*t*),*y*(*t*)=sin(*t*), where−2*π*≤*t*≤2*π*. a) Find a Cartesian equation for*C*. Then make a rough sketch of the curve. b) The curvature*κ*of a curve*C*at a given point is a measure of how quickly the curve changes direction at that point. For example, a straight line has curvature*κ*=0at every point. At any point, the curvature can be calculated by*κ*(*t*)=(1+(*d**x**d**y*)2)23∣∣*d**x*2*d*2*y*∣∣.Show that the curvature of the curve*C*is:*κ*(*t*)=(1+16sin2*t*)234.

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