Parametric equations and polar coordinates

[maiad]

Homework Statement

Find the area enclosed by the inner loop of the curve r=1-3sinθ

Homework Equations

A=o.5\int r^2 dθ

The Attempt at a Solution

I found the integral but i don't 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

 

[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.

 

[maiad]

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

 

[DryRun]

You should probably follow his posts to avoid having to ask the same questions:
https://www.physicsforums.com/showthread.php?t=598155

 

[HallsofIvy]

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

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