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Parameterization of the Circle

  • Thread starter vanitymdl
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  • #1
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Homework Statement



Consider the following parameterization of the circle:
a) x1 (t) = (cost, sint)

b) x2 (t) = (cos3t, sin3t)

c) x3 (t) = (sint, cost)

How long does it take point a particle to go from (1,0) to (0,1) for each parameterization.

Homework Equations





The Attempt at a Solution


(cos,sin) of (1,0) is 2pi then (cos, sin) of (0,1) is pi/2

how would I figure out the time it takes?
 

Answers and Replies

  • #2
SammyS
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Homework Statement



Consider the following parametrization of the circle:
a) x1 (t) = (cost, sint)

b) x2 (t) = (cos3t, sin3t)

c) x3 (t) = (sint, cost)

How long does it take point a particle to go from (1,0) to (0,1) for each parametrization.

Homework Equations



The Attempt at a Solution


(cos,sin) of (1,0) is 2pi then (cos, sin) of (0,1) is pi/2

how would I figure out the time it takes?
For each parametrization find a value of t for which x(t) = (1, 0), then find the next greater value of t for which x(t) = (0, 1) .
 
  • #3
DryRun
Gold Member
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Tricky wording. :smile:
 

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