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Math Help - Rectangular to polar coordinate conversion

  1. #1
    TWN
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    Rectangular to polar coordinate conversion

    Rectangular coordinates: (0,-6)

    Show me how to find the polar coordinates for this please.
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    Re: Rectangular to polar coordinate conversion

    Well you have not moved across at all, and gone down 6 units. Surely you can read off what the magnitude is. As for the angle, if you started from the positive x axis and went anticlockwise, what angle is swept out?
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    TWN
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    Re: Rectangular to polar coordinate conversion

    Quote Originally Posted by Prove It View Post
    Well you have not moved across at all, and gone down 6 units. Surely you can read off what the magnitude is. As for the angle, if you started from the positive x axis and went anticlockwise, what angle is swept out?
    Here's what is giving me trouble:

    tan(theta) = y/x

    Therefore, theta = arctan(y/x)

    Plugging in x and y, we get

    theta = arctan(-6/0)

    Negative six over zero is undefined...so now what?
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    Re: Rectangular to polar coordinate conversion

    Quote Originally Posted by TWN View Post
    Here's what is giving me trouble:

    tan(theta) = y/x

    Therefore, theta = arctan(y/x)

    Plugging in x and y, we get

    theta = arctan(-6/0)

    Negative six over zero is undefined...so now what?
    Don't apply a formula if you don't understand what it means. Draw a diagram. Surely you can read off your answers from the diagram, if you try it...
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  5. #5
    TWN
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    Re: Rectangular to polar coordinate conversion

    Quote Originally Posted by Prove It View Post
    Don't apply a formula if you don't understand what it means. Draw a diagram. Surely you can read off your answers from the diagram, if you try it...
    Would theta be -pi/2 ? Or -3pi/2 ? Or am I still not looking at it right?
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    Re: Rectangular to polar coordinate conversion

    It's either \displaystyle \begin{align*} \frac{3\pi}{2} \end{align*} if you move anticlockwise, or \displaystyle \begin{align*} -\frac{\pi}{2} \end{align*} if you move clockwise. Generally we define \displaystyle \begin{align*} \theta \in (-\pi, \pi]  \end{align*}, so choose \displaystyle \begin{align*} -\frac{\pi}{2} \end{align*}.

    Now what is r?
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  7. #7
    TWN
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    Re: Rectangular to polar coordinate conversion

    Would it be 6 or -6?
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    Re: Rectangular to polar coordinate conversion

    r represents the magnitude, magnitudes can never be negative.
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