The position of a particle is given by the parametric equations, x = 1 + sin(at)...

 

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The position of a particle is given by the parametric equations, x = 1 + sin(at) cos(nt) and y = 3 sin(t) + 2cos(πt) Answer the following, (a) Describe the graph of these parametric equations as t ranges over all real numbers. (In other words, find all possible positions of the particle.) (b) Describe the motion of the particle as t ranges from 0 to 2. (c) Find a parametrization such that the overall graph of this parametrization from t = 0 tot = 2 matches the graph of part (b), but the motion of the particle is different. The position of a particle is given by the parametric equations, x = 1 + sin(at) cos(nt) and y = 3 sin(t) + 2cos(πt) Answer the following, (a) Describe the graph of these parametric equations as t ranges over all real numbers. (In other words, find all possible positions of the particle.) (b) Describe the motion of the particle as t ranges from 0 to 2. (c) Find a parametrization such that the overall graph of this parametrization from t = 0 tot = 2 matches the graph of part (b), but the motion of the particle is different.