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Math Help - sketch the curve.

  1. #1
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    sketch the curve.

    sketch the curve x = 3cost+2cos4t, y = 3sint+2sin4t, -pi<=t<=pi

    please help me with this problem, not sure how to set it up and solve this.

    need an idea of what the graph will look like, i do know that cos or sin both stay close to -1 or 1.

    and the interval is between pi, so could i just use -3 and 3 inclusive for x and y inputs for t?

    thanks.
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  2. #2
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    parametric graph
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  3. #3
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    Alright thanks for the graph. Now where do i start to be able to draw the graph.
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  4. #4
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    pick some values for t and evaluate x and y.

    -pi, -3pi/4, -pi/2, -pi/4, 0 , pi/4, pi/2, 3pi/4. and pi would be some good choices of values of t to start with ... there are more values from the unit circle between -pi and pi that I left out.
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  5. #5
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    okay, so i have values for t:

    t x y
    -pi -1 0
    -3pi/4 -4 -2
    -pi/2 2 -3
    -pi/4 .12 0
    0 5 0
    pi/4 .12 2.12

    and if i plot those on a cartesian graph, they all look like they hit the graph that you have drawn. But how do i know that any of those points were actually on the polar graph? just those between pi and -pi are guaranteed? and what do i do with the points now?
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