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Homework Help: Converting rectangular to polar

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data
    How do you convert the rectangular coordinate points (1, -2) to polar form?

    note: rectangular is (x,y) polar is (r, theta)

    2. Relevant equations
    r^2 = x^2 + y^2 , x = rcos(theta) , y = rsin(theta) , tan(theta) = y/x

    3. The attempt at a solution
    So basically, I tried getting it to polar form by first finding the radius. This part was easy since all I had to do was to plug it into the first equation.

    r^2 = (1)^2 + (-2)^2
    = sqrt(5)

    Next, I tried getting theta by getting tan(theta).

    tan(theta) = -2/1

    Here is where the problem came in. When I tried putting this onto the unit circle, I didn't get any recognizable triangles(such as the 45-45 right triangle or the 30-60-90 right triangle).

    So how would I find theta?(without using calculator)
    Last edited: Dec 11, 2011
  2. jcsd
  3. Dec 11, 2011 #2


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    You wouldn't. You could express it is Arctan(-2) since that is in the 4th quadrant but you will need a calculator or tables for a decimal answer.
  4. Dec 11, 2011 #3
    even using a calculator my answer comes out to be -63.435 as theta whereas the answer is -1.107.
  5. Dec 11, 2011 #4


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    That's because -63.435 is in degrees whereas -1.107 is in radians.
  6. Dec 11, 2011 #5
    oh ty.

    hmm, strange. professor said calculator wasn't necessary.
  7. Dec 11, 2011 #6


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    I guess you could state your answer like this:
    [itex]\left( \sqrt{5}, \arctan (-2) \right)[/itex]
    (Fortunately, we can leave arctan (-2) as it is, ie. not add a multiple of pi, because θ is in Q IV.)
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