Question

If a vertical line is dropped from the x-axis to the point (12, –9) in the diagram below, what is the value of sec Theta?

A unit circle is shown. A ray intersects (12, negative 9) in quadrant 4. It forms angle theta with the x-axis in quadrant 1.
Negative five-thirds
Negative five-fourths
Five-fourths
Five-thirds

Answer 1

Answer: Five-thirds

Step-by-step explanation:

Given the point (12, -9) to which a line is drawn from the x-axis, we identify that we are in quadrant 4. Since we are dealing with radian measure, this forms an angle theta in the first quadrant with the x-axis. We identify that the secant of this angle is equal to the length of the adjacent side (x-displacement) divided by the length of the opposite side (y-displacement).

Therefore, sec Theta = 12/(-9) = -5/3 = Five-thirds