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Determining max and min pts of a polar curve

  1. Sep 28, 2005 #1
    Determine the maximum and minimum values of the curvature at points of the polar curve r = 3 + sin q.

    I know that the polar curve, r = 3 + sin q is sort of similar to an upside down heart when graphed. However, I am not sure what to do when finding the maximum and minimum values of the curvature at points of r = 3 + sin q.

    Thanks in advance.
     
    Last edited: Sep 29, 2005
  2. jcsd
  3. Sep 29, 2005 #2

    Fermat

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    You want to find the max and min values of the curve, rather than the curvature, yes?
    The curvature is the rate at which the slope is changing.

    Sorry, but the polar curve you gave is just a circle, sitting on top of the x-axis with the y-axis passing through the middle of it.
    What you described sounds like an epi-cycloid.

    There are a couple of ways of doing this problem. You can just sketch, and label, the graph of the curve and simply state that, by inspection, from the Figure/sketch, the max and min points are such-and-such.

    Or, you can use this formula.
    Set dy/dx equal to zero and solve for the angle.
     

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    Last edited: Sep 29, 2005
  4. Sep 29, 2005 #3
    Thanks. btw, how did you plot those graphs in graphmatica?

    edit - I also realized I made a typo with the equation. It's suppose to be r = 3 + sin q and not r = 3 sin q.
     
    Last edited: Sep 29, 2005
  5. Sep 29, 2005 #4

    Fermat

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    for the circle, just type in at the "function" window,

    r = 3 + sin(t)

    for the epi-cycloid, just type in at the "function" window,

    x = 2sin(t) - sin(2t); y = -2cos(t) + cos(2t) {-pi,pi}

    where the {-pi,pi}is the range.

    If you hit F1 then type "parametric" in the index, then click on "Display", you'll get full info.
     
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