Consider the parameterization of the unit circle given by x=cos(3t^2-t), y=sin(3t^2-t) for t in (-infinity, infinity). 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)). Put 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)). Put the word None if there are no such intervals.
(c) Does the entire unit circle get traced by this parameterization?
A. yes
B. no
(d) Give a time t at which the point being traced out on the circle is at (10):
t= ___________?
(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)). Put 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)). Put the word None if there are no such intervals.
(c) Does the entire unit circle get traced by this parameterization?
A. yes
B. no
(d) Give a time t at which the point being traced out on the circle is at (10):
t= ___________?
1 answer:
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Hey there :)
Let us translate each one separately
{ Using w for unknown }
The difference of a number divided by 3 and 5 is 2
'is' is the key-word, meaning you apply the = sign
Difference is subtraction
→ a number divided by 3 - 5 = 2
This is your equation:
→
Solving for w
Take 5 to the other side
[ When you see subtraction you do addition on the opposite side ]
→
Take 3 to the other side
[ When you see division you do multiplication on the opposite side ]
w = 3 x 7
w = 21
Let us translate each one separately
{ Using w for unknown }
The difference of a number divided by 3 and 5 is 2
'is' is the key-word, meaning you apply the = sign
Difference is subtraction
→ a number divided by 3 - 5 = 2
This is your equation:
→
Solving for w
Take 5 to the other side
[ When you see subtraction you do addition on the opposite side ]
→
Take 3 to the other side
[ When you see division you do multiplication on the opposite side ]
w = 3 x 7
w = 21