Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 240: 80

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

The anti-derivative for $\dfrac{dr}{d \theta}= \cos \pi \theta $ is $r=\dfrac{1}{\pi} \sin \pi \theta +C$ Apply the initial conditions $r(0)=1$. This implies $0+C=1$ or, $C=1$ Hence, $r=\dfrac{1}{\pi} \sin \pi \theta +1$