Question

name the quadrant in which the angle θ lies. sin θ > 0, cos θ < 0 choose the correct answer below. ○ quadrant i ○ quadrant iv ○ quadrant iii ○ quadrant ii

Explanation:

Step1: Recall sign rules in quadrants

In Quadrant I: $\sin\theta>0$, $\cos\theta>0$; Quadrant II: $\sin\theta>0$, $\cos\theta<0$; Quadrant III: $\sin\theta<0$, $\cos\theta<0$; Quadrant IV: $\sin\theta<0$, $\cos\theta>0$.

Step2: Match given conditions

Given $\sin\theta>0$ (so possible Quadrants I, II) and $\cos\theta<0$ (so possible Quadrants II, III). The intersection is Quadrant II.

Answer:

Quadrant II