Solution Found!
Intersection points Points at which the graphs of r = f()
Chapter 8, Problem 95E(choose chapter or problem)
Points at which the graphs of \(r=f(\theta)\ \text{and}\ r=g(\theta)\) intersect must be determined carefully. Solving \(f(\theta)=g(\theta)\) identifies some-but perhaps not all-intersection points. The reason is that the curves may pass through the same point for different values of \(\theta\). Use analytical methods and a graphing utility to find all the intersection points between the following curves.
\(r=2 \cos \theta\ \text{and}\ r=1+\cos \theta\)
Questions & Answers
QUESTION:
Points at which the graphs of \(r=f(\theta)\ \text{and}\ r=g(\theta)\) intersect must be determined carefully. Solving \(f(\theta)=g(\theta)\) identifies some-but perhaps not all-intersection points. The reason is that the curves may pass through the same point for different values of \(\theta\). Use analytical methods and a graphing utility to find all the intersection points between the following curves.
\(r=2 \cos \theta\ \text{and}\ r=1+\cos \theta\)
ANSWER:Solution 95EStep 1:If we solve the system of polar equations r = 2 cos and r = 1 + cos we find the intersection point (2, 0). Let’s try converting the equations into rectangular coordinates and then solving