# Parametric equations and polar coordinates

1. Apr 19, 2012

1. The problem statement, all variables and given/known data
Find the area enclosed by the inner loop of the curve r=1-3sinθ

2. Relevant equations
A=o.5$\int r^2$ dθ

3. The attempt at a solution
I found the integral but i dont know how to find the interval at which i will be integrating from. I tried finding when r=0 and it turns out to be sin^-1(1/3) but it's not a special angle so it would be messy if i plugged that interval in cos(θ).Any hints will be appreciated

2. Apr 19, 2012

### hamsterman

$\sin \theta = \frac{1}{3}$
$\cos^2 \theta = 1 - \sin^2 \theta = \frac {8}{9}$
$\cos \theta = \pm \frac {2 \sqrt 2}{3}$
So it's not a problem. You have to figure out whether it's + or -, depending on theta.

3. Apr 19, 2012

the answer had a sin(1/3)^-1 so i think you have to use that as one of your intervals im assuming

4. Apr 19, 2012

### sharks

5. Apr 19, 2012

### HallsofIvy

Staff Emeritus
Do you mean $(sin(1/3))^{-1}= 1/sin(1/3))$ or $sin^{-1}(1/3)= arcsin(1/3)$?

Last edited: Apr 19, 2012