# Intersection Points of Polar Equations

## Main Question or Discussion Point

I've been having a problem finding the intersection points of the following polar equations.

r=1+3sin(theta)

and

r=1-3cos(theta)

Now I've set the equations equal to each other to obtain those points. I've set each equation equal to zero. The problem I'm having is that when graphed, there are intersection points that can't be found due to each graph passing through the respective point at a different angle. I was wondering if anyone could tell me how I would go about finding those intersection points; I need these points in order to find certain areas of the graph.

It would be of MASSIVE help if anyone could provide me with information. Thank you.

Maybe I am missing something but don't you just do
1+3sin(theta) = 1-3cos(theta)
Sin[x]/Cos[x]=-1

Tan[x]=-1
x= 3Pi/4 or -Pi/4
then plug this into r equation to find the corresponding r coordinate

I said in my first post, first line of the first paragraph.

"I've been having a problem finding the intersection points of the following polar equations.

r=1+3sin(theta)

and

r=1-3cos(theta)

Now I've set the equations equal to each other to obtain those points. I've set each equation equal to zero. The problem I'm having is that when graphed, there are intersection points that can't be found due to each graph passing through the respective point at a different angle. I was wondering if anyone could tell me how I would go about finding those intersection points; I need these points in order to find certain areas of the graph.

It would be of MASSIVE help if anyone could provide me with information. Thank you."

I have those points. I need the other points. Its easier to understand if you have a graphing calculator handy and plug them into it. The points are when each limacon passes through the inner loop of the other limacon. Those are what I can't find.

And I'm sorry if I came across as testy. Its just I've been working on this problem for the past 3 days. I've expended every possible resource that I know of; no one in my class knows how to mathematically obtain those points. It's just really bothersome that I can't figure it out.

Tan[-Pi/4+Pi]=-1
Tan[3Pi/4+Pi]=-1
Tan[3Pi/4+Pi+Pi]=-1
Tan[-Pi/4+Pi+Pi]=-1
etc etc. there are an infinite amount of answers.

epenguin
Homework Helper
Gold Member
Well this seems to be revealing something about polar plots I never thought of before. :surprised Just do your graphs Cartesian-wise and see whether you don't see something unexpected! Then you may be able to see what it is that is causing you this pain.