Determine the quadrant for an angle with the following characteristics: tan theta<0 and sec theta >0
If tan(theta) < 0, it means that the sine(theta) < 0 and cosine(theta) > 0. This indicates that the angle lies in either the third or the fourth quadrant.
If sec(theta) > 0, it means that cosine(theta) > 0 and therefore, the angle lies in either the first or the fourth quadrant.
Considering both conditions, we can conclude that the angle lies in the fourth quadrant.