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Find the corresponding rectangular coordinates for the point.

  1. Jan 5, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the corresponding rectangular coordinates for the point. (-2, [itex]\frac{5\pi}{3}[/itex])



    x = -2cos([itex]\frac{5\pi}{3}[/itex])

    x = -2cos([itex]\frac{2\pi}{3}[/itex])

    x = -2* [itex]\frac{-1}{2}[/itex] = 1



    y = -2sin([itex]\frac{5\pi}{3}[/itex])

    y = -2sin([itex]\frac{2\pi}{3}[/itex])

    y = -2*[itex]\frac{\sqrt{3}}{2}[/itex] = -[itex]\sqrt{3}[/itex]


    So the coordinate is (1, -[itex]\sqrt{3}[/itex])

    This is my conclusion, however, the answer I found online does not agree: (1, -2)


    Am I incorrect? If so, what am I not doing correctly?
     
  2. jcsd
  3. Jan 5, 2014 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    I assume that is in polar coordinates, with negative radius.

    Are you sure those are equal?

    Same problem. Are you sure those are equal?

    That online answer is wrong. Fix your signs and you will have it.
     
  4. Jan 5, 2014 #3
    Yes, I should have mentioned the type of coordinates.




    x = -2cos([itex]\frac{5\pi}{3}[/itex])

    x = 2cos([itex]\frac{2\pi}{3}[/itex])

    x = 2* [itex]\frac{-1}{2}[/itex] = -1



    y = -2sin([itex]\frac{5\pi}{3}[/itex])

    y = 2sin([itex]\frac{2\pi}{3}[/itex])

    y = 2*[itex]\frac{\sqrt{3}}{2}[/itex] = [itex]\sqrt{3}[/itex]


    So the coordinate is (-1, [itex]\sqrt{3}[/itex])

    Like this?
     
  5. Jan 6, 2014 #4
    Yes...(-1,√3) is the correct answer .
     
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