Welcome to Bytelearn!

Let’s check out your problem:

Consider the graph of the polar function $\newline$$p=f(\theta)$, where $\newline$$f(\theta)=2=4\cos \theta$, in the polar coordinate system for $\newline$$0 \leq \theta \leq 2\pi$. Which of the following statements is true about the distance between the point with polar coordinates $\newline$$(f(\theta),\theta)$ and the origin?$\newline$(A) The distance is increasing for $\newline$$\pi < \theta < \frac{5\pi}{3}$, because $\newline$$f(\theta)$ is positive and increasing on the interval.$\newline$(B) The distance is increasing for $\newline$$\frac{5\pi}{3} < \theta < 2\pi$, because $\newline$$f(\theta)$ is negative and increasing on the interval.$\newline$(C) The distance is decreasing for $\newline$$\pi < \theta < \frac{5\pi}{3}$, because $\newline$$f(\theta)$ is positive and decreasing on the interval.$\newline$(D) The distance is decreasing for $\newline$$\frac{5\pi}{3} < \theta < 2\pi$, because $\newline$$f(\theta)$ is negative and decreasing on the interval.