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Math Help - Finding a parametric Equation for a Cycloid

  1. #1
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    Finding a parametric Equation for a Cycloid

    "We suppose that the wheel rolls to the right. P being at the origin when the turn angle t equals 0. The figure shows the wheel after it has turned t radians. The base of the wheel is at distance at from the origin. The wheel's center is at (at,a), and the coordinates of P are

    x = at + a\cos\theta, y = a + a\sin\theta.

    To express \theta in terms of t, we absorve that t + \theta = 3\pi/2 + 2k\pi for some integer k, so

     \theta = 3\pi/2 - t + 2k\pi

    Thus,

     \cos\theta = \cos(\frac{3\pi}{2} - t + 2k\pi)  = -\sin t

    I get everything up to the prior line. How does that equal -sint?
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  2. #2
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    cos(x-\frac{\pi }{2})=sin(x)

    Your equation is of the form cos(\frac{\pi }{2}-x)=-sin(x).

    Assuming k is an integer. This \frac{3\pi }{2}+2k\pi always yields a \frac{-\pi }{2}
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