Consider the parametric equations Make a table of values and sketch a graph for

Question

Consider the parametric equations Make a table of values and sketch a graph for the curve. Set up and simplify an integral for the surface area generated when the part of the curve revolved about the x-axis. In the diagram, a circle of radius OA = 2 rolls around the inside of a circle of radius OB = 4 with the half radius AP = 1 originally positioned so that P is on OB. Find a parameterization for the path that P traces out as the inner circle rolls (without slipping.) Start by choosing an appropriate parameter. Is that a familiar curve? Find the area enclosed by oue of the loops in the graph of the polar function . Use Simpson's rule with n = 6 to approximate the arc length of r = cos(4cos( theta )) on the interval

Explanation / Answer

observe that at every position,

AP = 1, Ab = 2, OP = OB -PB = OB- (PA + AB)

=>

OP = 4-1-2 =1,

=>

locus of P is a circle of radius 1 with center O

=>

P = (cos(theta), sin (theta))

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