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Area element in polar coordinates (hard question)

  1. Sep 26, 2009 #1
    1. The problem statement, all variables and given/known data

    using only trigonometric identities, derive the differential area element in polar coordinates? any help with this problem or at least a start?


    2. Relevant equations

    i found this so far
    dA=(dr)(rd θ)

    3. The attempt at a solution
    i have tried to figure this one out but i really have no clue how to start the problem, i tried taking derivatives but got no where , im not sure how to use a trigonometric identitie in this problem?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 26, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    geomtrically:

    say you have a vector given by r = (r, θ)

    think of a small "square" at the end of the vector,
    one side length is given by moving in the r dierction by dr
    the other side is swept by changing θ by dθ, the length is a circular arc so will be r.dθ

    so the "square" area elemnt is givne by
    dA = r.dθ.dr

    algebraically:

    you know for cartesian coordinates dA = dx.dy
    write x & y in terms of θ & r, then take the partial derivatives to find dx(r,θ)
     
  4. Sep 27, 2009 #3
    thank you, i haven't learned partial derivatives yet, but i will try to figure that out and im guessing i will be able to use some trig id. after i take the partial derivative.
     
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