Question

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

Explanation:

Step1: Recall sine - cosine signs in quadrants

In a unit - circle, $\sin\theta$ represents the $y$ - coordinate and $\cos\theta$ represents the $x$ - coordinate of a point $(x,y)$ on the unit - circle corresponding to the angle $\theta$.

Step2: Analyze the given conditions

We know that $\sin\theta>0$ means the $y$ - coordinate is positive, and $\cos\theta < 0$ means the $x$ - coordinate is negative.

Step3: Determine the quadrant

In Quadrant I, $x>0$ and $y > 0$ (so $\sin\theta>0$ and $\cos\theta>0$). In Quadrant II, $x<0$ and $y>0$ (so $\sin\theta>0$ and $\cos\theta<0$). In Quadrant III, $x < 0$ and $y<0$ (so $\sin\theta<0$ and $\cos\theta<0$). In Quadrant IV, $x>0$ and $y<0$ (so $\sin\theta<0$ and $\cos\theta>0$).

Answer:

Quadrant II