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Homework Help: Polar coords - Range of theta

  1. Jun 4, 2012 #1
    1. The problem statement, all variables and given/known data
    We have the circle [itex](x - 1)^2 + (y-2)^2 = 1[/itex]. Find the boundaries of θ and r.

    2. Relevant equations
    x = h + rcosθ
    y = k + rsinθ

    3. The attempt at a solution
    This is a circle with its origin at (1,2) and a radius of 1 so r is between 0 and 1 and the circle lies in the first quadrant but touches the x and y axis so theta is between 0 and pi/2

    Is this correct? Just curious

    edit: additional question: let's say I define y = 2 + rsinθ and x = 1 + rcosθ. Would this circle go from 0 to 2pi? (point of origin (1,2))
  2. jcsd
  3. Jun 4, 2012 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Your comment in the edit is exactly how to set up the problem. You would put ##r = 1## to get the circle and ##0 \le r \le 1## to get the interior.
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