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Math Help - parametric equations

  1. #1
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    parametric equations

    find parametric equations for the path of particle that moves along x2+(y-1)2=4 in a manner described.....

    A.) once around clockwise, starting at (2,1)
    B.) three times around counterclockwise, starting at (2,1)
    C.) halfway around counterclockwise, starting at (3,0)

    please help!!!!!
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  2. #2
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    Re: parametric equations

    Quote Originally Posted by pnfuller View Post
    find parametric equations for the path of particle that moves along x2+(y-1)2=4 in a manner described.....

    A.) once around clockwise, starting at (2,1)
    B.) three times around counterclockwise, starting at (2,1)
    C.) halfway around counterclockwise, starting at (3,0)

    please help!!!!!
    Since this is a circle, the Pythagorean Identity makes the parameterisations quite easy.
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  3. #3
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    Re: parametric equations

    Hello, pnfuller!

    Find parametric equations for the path of particle that moves along x^2 + (y-1)^2 \:=\:4 in the manner described.
    The equation represents a circle with center (0,1) and radius r =2.
    Code:
                    |
                  * * *
              *     |     *
            *       |       *
           *        |        *
                    |
          *         |         *
          *        1* - - - - o(2,1)
          *         |         *
                    |
      -----*--------+--------*-----
            *       |       *
              *     |     *
                  * * *
                    |
    The parametric equations are: . \begin{Bmatrix}x \;=\;2\cos\theta \\ y \;=\;1 + 2\sin\theta \end{Bmatrix}



    A) Once around clockwise, starting at (2,1)

    \begin{Bmatrix}x \;=\;2\cos\theta \\ y \;=\;1 + 2\sin\theta \end{Bmatrix}\quad 0 \,\le \theta \,\le\,2\pi




    B) Three times around counterclockwise, starting at (2,1)

    \begin{Bmatrix}x \;=\;2\cos\theta \\ y \;=\;1 + 2\sin\theta \end{Bmatrix}\quad 0 \,\le\,\theta\,\le\,6\pi




    C) halfway around counterclockwise, starting at (3,0)

    Is there a typo?
    The point (3,0) is not on the circle.
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  4. #4
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    Re: parametric equations

    can you explain how you got those equations please? i dont understand...
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  5. #5
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    Re: parametric equations

    can you show your work like you did before please? im not following...
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  6. #6
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    Re: parametric equations

    and for C.) the point should be (0,3)
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    Re: parametric equations

    Quote Originally Posted by pnfuller View Post
    can you explain how you got those equations please? i dont understand...
    Surely you know that \displaystyle \begin{align*} \left(r\cos{\theta}\right)^2 + \left(r\sin{\theta}\right)^2 = r^2 \end{align*} by the Pythagorean Identity...
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