Question

identify all possible quadrants of an angle θ that satisfies the given conditions. sin θ>0 and cos θ>0 select all possible quadrants below. a. quadrant iv b. quadrant ii c. quadrant iii d. quadrant i

Explanation:

Step1: Recall sine - cosine signs in quadrants

In the unit - circle, the sine of an angle $\theta$ is the $y$ - coordinate of the point on the unit - circle corresponding to $\theta$ ($\sin\theta=y$), and the cosine of an angle $\theta$ is the $x$ - coordinate of the point on the unit - circle corresponding to $\theta$ ($\cos\theta = x$).

Step2: Analyze quadrants for positive sine and cosine

In Quadrant I, both $x>0$ 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:

D. Quadrant I