Answer
$$c(\theta)=(\cos( \pi+\theta), \sin(\pi+ \theta)),$$
Work Step by Step
Since the parametrization $c(\theta)$ of the unit circle is given by $$c(\theta)=(\cos \theta, \sin \theta),$$then we can choose the parametrization $$c(\theta)=(\cos( \pi+\theta), \sin(\pi+ \theta)),$$
which satisfies $$c(0)=(\cos( \pi), \sin(\pi))=(-1,0).$$
