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Math Help - Finding Period of polar graph

  1. #1
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    Finding Period of polar graph

    How come the polar graph of r=a cos\Theta or r=a sin\Theta only has a period of a pi?
    To find the period I would use \frac{2\pi}{b}, so why wouldnt the period of both these polar circles be  2\pi
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  2. #2
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    Re: Finding Period of polar graph

    Quote Originally Posted by delgeezee View Post
    How come the polar graph of r=a cos\Theta or r=a sin\Theta only has a period of a pi?
    To find the period I would use \frac{2\pi}{b}, so why wouldnt the period of both these polar circles be  2\pi
    Consider r = a\cos(\theta), which is a circle of radius a/2, centered at a/2. From 0 to pi/2 , \cos(\theta) is positive, so r is positive. From pi/2 to pi, \cos(\theta) is negative, which makes r negative as well. On a graph, a negative r implies that the line starts from the origin and proceeds in the direction opposite to that which the corresponding angle points to.

    So at theta=0, r = a, and theta=pi, r = -a, which are the same point.
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