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Consider a particle following the parametric equations

 

\(\begin{align*} x &= 1 + \sin (\pi t),\\ y &= 3 \sin (\pi t). \end{align*}\)

 

a) Give a precise description of the graph of these parametric equations if we allow  to be any real number.

b) Describe the path the particle takes from time  to .

c) Find a parametrization such that the graph of this parametrization from  to  matches our graph above, but the motion of the particle is different.

 May 7, 2021
 #2
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The path is an ellipse centered at (1,0), with the semi-minor axis (in the x-direction) of 1, and the semi-major axis (in the y-direction) of 3.

 May 8, 2021

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