Consider the parameterization of the unit circle given by z = cos(3t2 – t), y = sin(3t2 – t) for t in (-00, o0). 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? OA. yes OB. no (d) Give a timet at which the point being traced out on the circle is at (1, 0): t =
Consider the parameterization of the unit circle given by z = cos(3t2 – t), y = sin(3t2 – t) for t in (-00, o0). 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? OA. yes OB. no (d) Give a timet at which the point being traced out on the circle is at (1, 0): t =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the parameterization of the unit circle given by a = cos(3t2 – t), y = sin(3t2 – t) for t in (-o, 00). 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?
OA. yes
OB. no
(d) Give a time t at which the point being traced out on the circle is at (1, 0):
t 3D
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