Consider the parameterization of the unit circle given by x=cos(4t^2−t), y=sin(4t^2−t) for t in (−InF, INF). 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=_________
Ok, I graphed it in my graphing calculator, the circle seemed to be tracing itself for a while, but I still don't get how to write the intervals. Since it appeared to be just tracing itself clockwise, I typed in the first one (my homework is online)
(0,1),(1,0),(0,-1),(-1,0)
A message was shown saying that the left endpoint must be less than the right endpoint, so I'm not sure how to solve this one. I believed the answer for B was none, but that's not it, I typed Yes for the third part and 0 for the last one since it started at that point...
Can someone please explain to me how to do the first and 2nd part?
1 answer