Question

In what quadrant does theta lie if sin theta > 0, and cos theta < 0?

A) Quadrant I
B) Quadrant II
C) Quadrant III
D) Quadrant IV

Answer 1

The angle lies in Quadrant II.

Step-by-step explanation:

When sin(theta) > 0, it means that the angle theta is located either in the first or second quadrant, where the y-coordinate is positive.

When cos(theta) < 0, it means that the angle theta is located either in the second or third quadrant, where the x-coordinate is negative.

Combining these conditions, theta must be located in Quadrant II as it is the only quadrant that satisfies both sin(theta) > 0 and cos(theta) < 0.