If theta is a standard position angle and cot theta=1.85, in which quadrant(s) could theta lie?
I or III
Thank you. (I actually ended up figuring this out a few minutes after posting this. Go figure, right?)
To determine in which quadrant(s) theta could lie, we need to analyze the given information cot theta = 1.85.
Cotangent (cot) is defined as the ratio of the adjacent side to the opposite side of a right triangle. In the context of a standard position angle, cot theta represents the x-coordinate (adjacent side) divided by the y-coordinate (opposite side) of a point on the unit circle.
Since cot theta is positive (1.85 is positive), the x-coordinate and the y-coordinate must have the same sign. This means that theta could lie in either the first quadrant or the third quadrant.
In the first quadrant, both the x-coordinate and the y-coordinate are positive. Thus, the value of cot theta will be positive.
In the third quadrant, the x-coordinate is negative, and the y-coordinate is positive. However, the sign of cot theta remains positive because the negative x-coordinate is divided by the positive y-coordinate, resulting in a positive ratio.
Hence, theta could lie in both the first quadrant and the third quadrant.