Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 240: 79

$r=\cos \pi \theta -1$

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