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Math Help - 2 polar graph questions

  1. #1
    Junior Member
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    2 polar graph questions

    1.Identify all values of theta for which r=0, and find a range of values of theta that produce one copy of the graph
    a) r=2+4cos3\theta
    my work
    0=2+4cos3\theta
    \theta= \frac{2\pi}{9}
    \theta= \frac{4\pi}{9}
    -however, i have no idea to do to find the range to make a copy? can someone tell me the procedure.

    2.find a corresponding rectangular equation.
    a) r=3sin\theta
    my work
    none
    -i understand there are some equations that relate cartesian equations to polar ones. but none of the ones listed in my book list any relevant ones that relate to solving this problem.

    All help is appreciated.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Detroit, MI
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    Quote Originally Posted by dandaman View Post
    1.Identify all values of theta for which r=0, and find a range of values of theta that produce one copy of the graph
    a) r=2+4cos3\theta
    my work
    0=2+4cos3\theta
    \theta= \frac{2\pi}{9}
    \theta= \frac{4\pi}{9}
    -however, i have no idea to do to find the range to make a copy? can someone tell me the procedure.

    2.find a corresponding rectangular equation.
    a) r=3sin\theta
    my work
    none
    -i understand there are some equations that relate cartesian equations to polar ones. but none of the ones listed in my book list any relevant ones that relate to solving this problem.

    All help is appreciated.
    For 2.

    Note that \sin\theta=\frac{y}{r} from the definition of the sine function, so

    r=3\sin\theta=3\frac{y}{r}

    Which implies that

    r^2=3y

    But, isn't it the case that r^2=x^2+y^2 ?
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