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Thread: Help? Parametric and circle questions

  1. #1
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    Help? Parametric and circle questions

    1. Find two different parametric descriptions for he circle of radiu 4 centered at (-3, 2).







    2. The radius of the circumscribed circle of the triangle ABC is 15 cm. Given that B is a 49-degree angle, find the length of side AC.
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  2. #2
    MHF Contributor
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    1. A circle of radius 4 centered at (-3, 2) has the equation $\displaystyle (x + 3)^2 + (y - 2)^2 = 16$. However, you can use trigonometric functions to establish a circular path with center (h, k) and radius r:

    $\displaystyle x = h + r \sin t$
    $\displaystyle y = k + r \cos t$

    or

    $\displaystyle x = h + r \cos t$
    $\displaystyle y = k + r \sin t$.

    The first represents a clockwise path, and the second represents a counterclockwise path.
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  3. #3
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    Hello, pyrosilver!

    2. The radius of the circumscribed circle of the $\displaystyle \Delta ABC$ is 15 cm.
    Given that $\displaystyle \angle B = 49^o$, find the length of side $\displaystyle AC.$
    Code:
                    A
                  * o *
              *    /*\    *
            *     / * \     *
           *     /  *  \     *
                / 15*   \
          *    /    *    \    *
          *   /    Po 98 \   *
          *  /         *   \  *
            / 49      15 * \
         B o - - - - - - - - o C
            *               *
              *           *
                  * * *

    The center of the circle is $\displaystyle P$.

    Draw radii $\displaystyle PA = PC = 15$

    Since inscribed angle $\displaystyle ABC = 49^o$, then central angle $\displaystyle APC = 98^o$

    Use the Law of Cosines on $\displaystyle \Delta APC.$

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