Find all points where r = 1 + cos θ and r = 1 + sin θ intersect.
Answer
Graph the functions first:
If we zoom in enough we can see that there are three points of intersection. One of these is the origin, r = 0.
Set the functions equal and solve:
We didn't need to use when finding the intersection of sin θ and cos θ, but we need it now because we have morepoints of intersection.When we have , and when we have .
The points of intersection are
Example 2
Find all points where r = 1 + cos θ and r = -cos θ intersect.
Answer
First, draw the graph:
It looks like we have three points of intersection again, and one of them is r = 0.To find the other two points we need to set the functions equal and solve for θ.
At these values of θ,
The points of intersection are
Example 3
Find all points in the first quadrant where r = 2sin(3θ) and r = 1 intersect.
Answer
Graph the functions:
There are two points of intersection in the first quadrant. We set the functions equal and solve for θ.
when finding the intersection of sin θ and cos θ, but we need it now because we have more
we have 
, and when 
we have 
. 
