Hey, I have a polar coordinate problem here that feels like it should be much easier than I am making it out to be.

So I started by setting them equal to each other to find the angles $\displaystyle \theta$ at which they intersect.Find all points of intersection of the following curves, given in Polar Coordinates. $\displaystyle r^2 = cos(2\theta) \ and \ r = 1 - sin(\theta)$

$\displaystyle cos(2\theta) = (1-sin\theta)^2$

$\displaystyle 1-2sin^2\theta = 1-2sin\theta + sin^2\theta$

$\displaystyle sin\theta = \frac{2}{3}$

$\displaystyle \theta \approx 0.729 rad$

The problem is that by graphing it appears that there is 5 points of intersection, and I only have 1 floating point approximation of theta. What did I miss? Thanks for the help!