Consider the graph of the polar fimetion p=f(θ), where f(θ)=2=4cosθ, in the polar coordinate system for 0≤θ≤2π. Which of the following statements is true about the distance between the point with polar coordinates (f(θ),θ) and the origin?(A) The distance is increasing for \pi<\theta<\frac{5 \pi}{3} , because f(θ) is positive and increasing on the interval.(B) The distance is increasing for \frac{5 \pi}{3}<\theta<2 \pi , because f(θ) is negative and increasing on the interval.(C) The distance is decreasing for \pi<\theta<\frac{5 \pi}{3} , because f(θ) is positive and decreasing on the interval,(D) The distance is decreasing for \frac{5 \pi}{3}<\theta<2 \pi , because f(θ) is negative and deereasing on the interval.
Q. Consider the graph of the polar fimetion p=f(θ), where f(θ)=2=4cosθ, in the polar coordinate system for 0≤θ≤2π. Which of the following statements is true about the distance between the point with polar coordinates (f(θ),θ) and the origin?(A) The distance is increasing for π<θ<35π, because f(θ) is positive and increasing on the interval.(B) The distance is increasing for 35π<θ<2π, because f(θ) is negative and increasing on the interval.(C) The distance is decreasing for π<θ<35π, because f(θ) is positive and decreasing on the interval,(D) The distance is decreasing for 35π<θ<2π, because f(θ) is negative and deereasing on the interval.
Analyze Function Behavior: Analyze the function f(θ)=2−4cos(θ) to understand its behavior over the interval 0≤θ≤2π.
Determine Increasing/Decreasing Intervals: Determine the intervals where f(θ) is increasing or decreasing.
Match Behavior with Statements: Match the behavior of f(θ) with the given statements.