#### Answer

$r=\dfrac{1}{\pi} \sin \pi \theta +1$

#### Work Step by Step

We need to find the anti-derivative for $\dfrac{dr}{d \theta}= \cos \pi \theta $
Thus, we have $r=\dfrac{1}{\pi} \sin \pi \theta +C$
Apply the initial condition $r(0)=1$ in the above equation to solve for $C$.
we get $0+C=1 \implies C=1$
Hence, $r=\dfrac{1}{\pi} \sin \pi \theta +1$