Question

name the quadrant in which the angle θ lies. cos θ>0, sec θ<0 choose the correct answer below. a. the angle θ lies in quadrant iii. b. the angle θ lies in quadrant i or iv. c. the angle θ does not exist. d. the angle θ lies in quadrant i.

Explanation:

Step1: Recall the relationship between cosine and secant

We know that $\sec\theta=\frac{1}{\cos\theta}$. If $\cos\theta> 0$, then $\frac{1}{\cos\theta}>0$ (since a positive - number's reciprocal is positive).

Step2: Analyze the given conditions

We are given that $\cos\theta>0$ and $\sec\theta < 0$. But from the identity $\sec\theta=\frac{1}{\cos\theta}$, when $\cos\theta>0$, $\sec\theta$ must be positive. So, a situation where $\cos\theta>0$ and $\sec\theta < 0$ is impossible.

Answer:

C. The angle $\theta$ does not exist.