Consider the parameterization of the unit circle given by
, for in .
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 at which the point being traced out on the circle is at
:
You can earn partial credit on this problem.