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Math Help - help with these two world problems please

  1. #1
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    help with these two world problems please

    1. A circle C1 of radius 1 rolls counterclockwise along the outside of a circle C2 of radius 4 which is centered at the origin. Assume that there is a point P on the circumference of the circle C1 that sits intially at the point (4,0). Find a parametric curve describing the way that P traces in the plane.

    My idea of whats going on: imgur: the simple image sharer

    2. For a<0 show that the polar curves r=asin(t) and r=acos(t) intersect at right angles.
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  2. #2
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    Re: help with these two world problems please

    Quote Originally Posted by smoez View Post
    1. A circle C1 of radius 1 rolls counterclockwise along the outside of a circle C2 of radius 4 which is centered at the origin. Assume that there is a point P on the circumference of the circle C1 that sits intially at the point (4,0). Find a parametric curve describing the way that P traces in the plane.

    My idea of whats going on: imgur: the simple image sharer

    2. For a<0 show that the polar curves r=asin(t) and r=acos(t) intersect at right angles.
    What have you tried so far?

    -Dan
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  3. #3
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    Re: help with these two world problems please

    I figured out #2. As for number one I know it is an Epicycloid and looking at the wiki page I just dont understand how to show in the notation.
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  4. #4
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    Re: help with these two world problems please

    The wiki page does a pretty good job of explaining how they got the equation (see "Proof"). Do you see why the center of the small circle is (5\cos\theta,5\sin\theta)? And do you see that \alpha=4\theta? From there, it's just a matter of figuring out the coordinates of p.

    - Hollywood
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