Final answer:
The quadrant for the angle theta can be determined by looking at the signs of the trigonometric functions in each quadrant.
Step-by-step explanation:
The quadrant for the angle theta satisfying the given conditions can be determined by looking at the signs of the trigonometric functions in each quadrant. If Ay is positive and Ax is negative, the vector lies in Quadrant II. If both Ay and Ax are negative, the vector lies in Quadrant III. If Ay is negative and Ax is positive, the vector lies in Quadrant IV. And if both Ay and Ax are positive, the vector lies in Quadrant I.