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: Areas and Lengths in Polar Coordinates

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region enclosed by one loop of the curve.
    r = sin(10θ)

    I can't seem to get the correct answer...I checked every step. I was not sure what to integrate from but the polar graph of sin(10θ) should be similar to polar graph of sin(2θ). From pi/2 to 0?

    2. Relevant equations
    A = integral(b to a) (1/2)r^2 dθ

    half angle formula
    (sinθ)^2 = (1/2)(1-cos2θ)dθ

    3. The attempt at a solution
    A = integral(b to a) (1/2)r^2 dθ = integral(pi/2 to 0) (1/2)r^2 dθ

    A = (1/2) integral(pi/2 to 0) (sin(10θ))^2 dθ
    A = (1/2) integral(pi/2 to 0) (1/2)(1-cos(20θ))dθ
    A = (1/4) integral(pi/2 to 0) (1-cos(20θ))dθ
    A = (1/4) [(θ-(1/20)sin(20θ)] (pi/2 to 0)
    A = (1/4) [(pi/2-(1/20)sin(20*(pi/2)) - (0 - 0)]
    A = (1/4)* (pi/2) = pi/8
     
    Last edited: May 11, 2010
  2. jcsd
  3. May 11, 2010 #2
    Nevermind. I figured it out. Integrating from pi/10 to 0. Thanks.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook