i forgot to mention that y>=0 and theta is from 0 to pi
But you give one equation, $\displaystyle x^2+ y^2= 1$, in Cartesian coordinates! In polar coordinates, that is r= 1. That should be easy to draw. As for $\displaystyle r= 1+ cos(\theta)$, that is what is called a "cardioid". Look it up. As far as graphing is concerned, you could just use the "old fashioned" way- calculate r for a number of $\displaystyle \theta$ values. The are beween them will be the integral of $\displaystyle f_1(\theta)- f_2(\theta)= (1+ cos(\theta))- 1= cos(\theta)$. And the integration will be between values of $\displaystyle \theta$ where the graphs cross: solve $\displaystyle 1+ cos(\theta)= 1$.