find the area enclosed by the cardioid with polar equation r=1sin(Θ)
how do I find the bounds?
I suggest showing the curve is closed and when it passes through the origin .
$\displaystyle r = \sin(\theta) $
we know $\displaystyle \sin(n\pi) = 0 , n \in \mathbb{Z} $
Suppose a particle has turned $\displaystyle \pi $ or $\displaystyle 180 $ degree . It comes back to the origin again !