Math: Parametric Equations

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?

(The "E" represents the symbol for "is in" that looks kind of like a rounded E)

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asked by Katie
  1. does this help?

    https://www.wolframalpha.com/input/?i=plot+x+%3D++cos(4t),+y+%3D+sin(6t)

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    posted by Reiny
  2. So would the interval be (-inf, 1] ??

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    posted by Katie
  3. But that wouldn't be the right answer since it's asking for a length.

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    posted by Katie
  4. cos(4t) has period pi/2
    sin(6t) has period pi/3

    so, you get the entire curve using the interval

    [0,pi]

    as indicated by the note next to the graph at the suggested URL.

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    posted by Steve

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