Step 1 :The cosine of an angle is zero when the angle is \(\frac{\pi}{2}\) or \(\frac{3\pi}{2}\) (90 or 270 degrees). This means that the angle is either in Quadrant II or Quadrant III.
Step 2 :However, the tangent of an angle is negative when the angle is in Quadrant II or Quadrant IV.
Step 3 :Therefore, the only quadrant that satisfies both conditions is Quadrant II.
Step 4 :\(\boxed{\text{Quadrant II}}\)