Question

Theta is an angle of rotation corresponding to the point (x,y) on the unit circle such that sinθ<0 and cosθ>0. Which quadrant is (x,y) located in?

a. Quadrant I
b. Quadrant II
c. Quadrant III
d. Quadrant IV

Answer 1

The point (x,y) is located in the fourth quadrant of the unit circle because sinθ is negative (indicating a negative y-coordinate) and cosθ is positive (indicating a positive x-coordinate).

Step-by-step explanation:

The angle θ corresponds to the point (x,y) on the unit circle where sinθ is less than 0 and cosθ is greater than 0. Given these conditions, the point (x,y) would be located in the fourth quadrant. This is because in the unit circle, the sine represents the y-coordinate and the cosine represents the x-coordinate of the point corresponding to the angle θ. When sinθ is negative, y is negative, and when cosθ is positive, x is positive. Therefore, a point with a positive x and a negative y would be situated in the fourth quadrant.