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: Polar Coordinates problem area of region

  1. Jul 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region inside: r = 9 sinθ but outside: r = 1

    2. Relevant equations

    3. The attempt at a solution
    r = 9 sinθ is a circle with center at (0, 4/2) and radius 4/2 while r= 1 is a circle with center at (0, 0) and radius 1. The two curves intersect where sin(θ)= 1/9. For 0 ≤ θ ≤ π that is satified by θ=sin^-1(1/9) and θ=π-sin^-1(1/9).
    This is where i get lost setting up the differential for the area?
  2. jcsd
  3. Jul 21, 2010 #2
    r = 9 sinθ is not what you say. I don't know where you went astray in your thinking, but if polar coordinates are giving you trouble, then think of it this way:

    r = 9 sinθ is the same thing as r^2 = 9r sinθ, which is equivalent to x^2 + y^2 = 9y, or...
    x^2 + (y-9/2)^2 = (9/2)^2. That's a circle centered at (0,9/2) with a radius of 9/2 units.

    Can you finish the rest by yourself? I hope this helps.

    EDIT: There, I fixed it :D
    Last edited: Jul 21, 2010
  4. Jul 21, 2010 #3
    Also, how did you arrive at this conclusion? Using that logic, we could let n = sin^-1(1/9) - k, where k is any real number. Then, using your logic, θ would also equal k in all these cases, i.e., sin^-1(1/9) has infinitely many solutions on a quite finite interval.
  5. Jul 21, 2010 #4
    It is actually a pi sign but a really bad one sorry for the confusion
  6. Jul 22, 2010 #5


    User Avatar
    Science Advisor

    Using Latex, [itex]\theta= sin^{-1}(1/9)[/itex] and [itex]\theta= \pi- sin^{-1}(1/9)[/itex].

    Of course, for any [itex]\alpha[/itex], [itex]sin(\alpha)= sin(\pi- \alpha)[/itex].

    You should have learned when you first learned integration in polar coordinates that "dxdy" becomes "[itex]r dr d\theta[/itex]".
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook