Math

Let G be the graph of the parametric equations
x = cos(4t),
y = sin(6t).

What is the length of the smallest interval P such that the graph of these equations for all t E P produces the entire graph G?

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asked by Bob
  1. if 4 t = 2 pi
    t = pi/2
    if 6 t = 2 pi
    t = pi/3
    so we need at least t = 0 to t = pi/2 or any other interval of length pi/2

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    posted by Damon
  2. In the interval -pi/4 <= t <= pi/4, the graph is traced once.

    But on 0 <= t <= pi/2, only half the curve is completed.

    Try changing the domain on this plot at

    http://www.wolframalpha.com/input/?i=plot+x%3Dcos(4t),y%3Dsin(6t),+-pi%2F4+%3C%3D+t+%3C%3D+pi%2F4

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    posted by Steve

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