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Math Help - cartesian and polar

  1. #1
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    Post cartesian and polar

    Hello,

    I need help with this question,

    a) express in polar co-cordinates the cartesian co-ordinates (2, -6)

    b) express in cartesian co-ordinates the polar co-cordinates (3, 150degrees)

    Thank you.
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  2. #2
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    Quote Originally Posted by simon
    Hello,

    I need help with this question,

    a) express in polar co-cordinates the cartesian co-ordinates (2, -6)

    b) express in cartesian co-ordinates the polar co-cordinates (3, 150degrees)

    Thank you.
    For these types of problems you need to recall that:
    x = r cos\theta
    y = r sin\theta

    Inverting these relations gives:
    r = \sqrt{x^2+y^2}
    \theta = tan^{-1} \left ( \frac{y}{x} \right )

    So for question a)
    (2,-6) => x = 2, y = -6
    r = \sqrt{2^2+(-6)^2}=\sqrt{40}=2 \sqrt{10}
    \theta = tan^{-1} \left ( \frac{-6}{2} \right ) = tan^{-1}(-3) \approx -71.5651^o

    \theta is a reference angle. The point (2,-6) is in the 4th quadrant, so your angle measured from the +x axis is 360 - 71.5651 = 288.435 degrees.

    Thus: (2,-6) => (2sqrt(10), 288.435 degrees).

    For question b)
    (3, 150 degrees) => r = 3, \theta = 150 degrees
    x = 3 cos(150) \approx -2.59808
    y = 3 sin(150) = 1.5

    Thus: (3, 150 degrees) => (-2.59808, 1.5).
    (And note that it is, in fact, in the second quadrant as the original coordinates state.)

    -Dan
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