Hi everyone again! My question is as follows in full:

Sketch $\displaystyle r=3-5 \cos {theta}$ and find the area of the inner curve.

Ok, this is a cardioid [according to my book], and my graphing by sketch looks like (couldn't scan so this is an actual graph courtesy of desmos.)

I'm supposed to find the area of the curve from $\displaystyle r=-2$ to $\displaystyle 0$ and when $\displaystyle \theta$ goes from ?? This is where I get stuck. To find where $\displaystyle r=0$, that is, where the curve is at O and a tangent there, $\displaystyle 3=5\cos(\theta)$ I need two values for $\displaystyle \theta$ but I can only find one, which logically makes two because both the plus and minus of the absolute value of that value should apply.

The value I found is $\displaystyle ~53.13010235$ which converting to radians I take to be $\displaystyle \pm 0.295167235 \pi $. If I apply this number backwards from [tex]\pi[\tex], I can't seem to get the correct value. I seem to be getting the whole sector. Some help here please?

Thanks in advance!