Find $\cot \frac{3 \pi}{2}.$
Converting to degrees,
\[\frac{3 \pi}{2} = \frac{180^\circ}{\pi} \cdot \frac{3 \pi}{2} = 270^\circ.\]Since the cotangent function has period $180^\circ,$ $\cot 270^\circ = \cot (270^\circ - 180^\circ) = \cot 90^\circ = \frac{\cos 90^\circ}{\sin 90^\circ} = \boxed{0}.$