Verified answer

Since secθ = 1/cosθ, consider the sign of cosθ (since secθ and cosθ will have the same sign).

Recall that a point on the unit circle in terms of θ, the angle made with the positive x-axis, is:

(cosθ, sinθ).

In Quadrant I, we know that the x and y-coordinates of any point are positive, so:

cosθ > 0 and sinθ > 0 in Quadrant I.

In Quadrant II, the x-coordinate is negative and the y-coordinate is positive, so:

cosθ < 0 and sinθ > 0 in Quadrant II.

In Quadrant III, both the x and y-coordinates are negative, so:

cosθ < 0 and sinθ > 0 in Quadrant III.

The x-coordinate is positive and the y-coordinate is negative in Quadrant IV, so:

cosθ > 0 and sinθ < 0 in Quadrant IV.

Since cosθ < 0 in Quadrants II and III, secθ < 0 in Quadrants II and III as well.

I hope this helps!