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Cartesian to polar conversions

  1. Feb 18, 2007 #1
    1. The problem statement, all variables and given/known data

    find polar coordinates of the points whose cartesian coordinates are given.

    2. Relevant equations

    heres the point: (3sqrt(3), 3)

    3. The attempt at a solution

    well i know that r^2 = (sqrt(a^2 + b^2))
    so the answer here is : 6

    and if we use tan(theta) = o/a = 3/(3sqrt(3)
    so the answer here is: 1/sqrt(3)

    so theta is pi/6

    so how do i know its pi/6?
    how do i convert to get this answer with pi? radians?

    help please.
  2. jcsd
  3. Feb 19, 2007 #2


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    Homework Helper

    theta = arctan(1/sqrt3) = pi/6 (in radians, always radions for polar coordinates).
  4. Feb 19, 2007 #3


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    Science Advisor

    The right hand side of that equation, not the "answer" (to what question?!), is [itex]\frac{1}{\sqrt{3}}[/itex]. In general, if you know what [itex]tan(\theta)[/itex] is, you can find [itex]\theta[/itex] by using the arctan function- perhaps on a calculator. Here, you are probably expected to know that [itex]sin(\pi/6)= \frac{1}{2}[/itex] and that [itex]cos(\pi/6)= \frac{\sqrt{3}}{2}[/itex] so that [itex]tan(\pi/6)= \frac{1}{\sqrt{3}}[/itex].

    As benorin said- in polar coordinates the angle is always in radians. As a rule, the only time you use degrees is when the problem specifically involves angle that are given in degrees.
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