If \(\cos \theta = 0\), this occurs when \(\theta\) is an odd multiple of \(\frac{\pi}{2}\) (90 degrees). The angles are typically:
- \(\frac{\pi}{2}\) (90°)
- \(\frac{3\pi}{2}\) (270°)
Since you specified that \(\theta\) is a reflex angle, we are looking for the angle that is greater than \(180^\circ\) but less than \(360^\circ\). Therefore, we consider:
\[ \theta = \frac{3\pi}{2} \quad (\text{which is } 270^\circ) \]
At this angle, the coordinates of the point where the terminal side of \(\theta\) intersects the unit circle are given by:
\[ (\cos(\frac{3\pi}{2}), \sin(\frac{3\pi}{2})) = (0, -1) \]
Thus, the coordinates of the point are:
\[ \boxed{(0, -1)} \]