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Consider the parameterization of the unit circle given by [tex]x=cos(3t^{2}-t)[/tex], [tex]y=sin(3t^{2}-t)[/tex] fortin [tex](-\infty,\infty)[/tex].

In which intervals oftis the parameterization tracing the circle out in a clockwise direction?

In which intervals oftis the parameterization tracing the circle out in a counter-clockwise direction?

The attempt at a solution

I know this can't be too difficult. I'm just really struggling to understand the intervals in terms of the direction of motion. So far I've been able to conclude that the entire unit circle is in fact traced out by this parameterization and that whent=0, the point being traced out on the circle is at (1,0). I can see that initially fort>0, the motion is counter-clockwise but can't determine when the motion changes direction again. The same applies for the other direction. I see that initially fort<0, the motion is clockwise but am struggling to see when motion in that direction changes and begins going the other direction.

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# Homework Help: Parametric Equations and direction

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