Consider the parameterization of the unit circle given by $x =\cos( t^{2}-t )$, $y = \sin( t^{2}-t )$ for $t$ in $(-\infty,\infty)$. Describe in words and sketch how the circle is traced out, and use this to answer the following questions.

(a) When is the parameterization tracing the circle out in a clockwise direction?

(Give your answer as a comma-separated list of intervals, for example, (0,1), (3,Inf)). Enter the word None if there are no such intervals.

(b) When is the parameterization tracing the circle out in a counter-clockwise direction?

(Give your answer as a comma-separated list of intervals, for example, (0,1), (3,Inf)). Enter the word None if there are no such intervals.

(c) Does the entire unit circle get traced by this parameterization?

(d) Give a time $t$ at which the point being traced out on the circle is at $(1,0)$:
$t =$