1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Jacobian of polar coordinates

  1. Dec 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Change of coordinates from rectangular (x,y) to polar (r,θ). Not sure what's wrong with my working..

    2. Relevant equations

    3. The attempt at a solution

  2. jcsd
  3. Dec 21, 2012 #2


    User Avatar
    Homework Helper

    Your error is that you have differentiated [itex]y = x \tan\theta[/itex] incorrectly. You should get
    [tex]\frac{\partial y}{\partial \theta} = x\sec^2\theta + \frac{\partial x}{\partial \theta}\tan\theta[/tex]
    because [itex]x[/itex] is also a function of [itex]\theta[/itex].

    Also, to work out [itex]\partial x/\partial r[/itex], you would need to differentiate
    [tex]r^2 = x^2 + y^2[/tex]
    with respect to [itex]r[/itex] with [itex]\theta[/itex] held constant, which again gives
    [tex]2r = 2x\frac{\partial x}{\partial r} + 2y\frac{\partial y}{\partial r}[/tex]
    because y is also a function of [itex]r[/itex].

    If you're trying to find derivatives with respect to r and [itex]\theta[/itex], it's best to start from [itex]x = r\cos\theta[/itex], [itex]y = r\sin\theta[/itex].
    Last edited: Dec 21, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook