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

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

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posted by Katie
3. 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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