Question

let θ be an angle in standard position. name the quadrant in which θ lies. sin θ>0, cot θ>0 the angle θ lies in which quadrant? iii i ii iv

Explanation:

Step1: Recall sine - quadrant relationship

The sine function $\sin\theta=\frac{y}{r}$, where $r = \sqrt{x^{2}+y^{2}}>0$. If $\sin\theta>0$, then $y>0$. This means the angle $\theta$ lies in either the first or second quadrant since in the first quadrant $(x > 0,y>0)$ and in the second quadrant $(x<0,y > 0)$.

Step2: Recall cotangent - quadrant relationship

The cotangent function $\cot\theta=\frac{x}{y}$. If $\cot\theta>0$, then $x$ and $y$ have the same sign. Since we know from Step 1 that $y>0$, for $\cot\theta>0$, we must have $x>0$ as well.

Step3: Determine the quadrant

The quadrant where $x>0$ and $y>0$ is the first quadrant.

Answer:

B. I