Question

Sec θ > 0 and cos θ < 0 means that ∠θ is located in the _____.

A. Fourth quadrant
B. Second quadrant
C. Third quadrant
D. First quadrant

Answer 1

The angle θ is located in the fourth quadrant.

Step-by-step explanation:

Sec θ > 0 and cos θ < 0 means that the cosine function is negative and the secant function is positive.

The cosine function is negative in the second and third quadrants of the unit circle. So, if cos θ < 0, the angle θ is located in the second or third quadrant.

The secant function is positive in both the first and fourth quadrants of the unit circle. So, if sec θ > 0, the angle θ is located in the first or fourth quadrant.

Combining these conditions, we find that ∠θ is located in the fourth quadrant (A).