Thread: Horizontal Asymptote of a Polar Equation

If you graph the polar function , , , , you should find a horizontal asymptote. Prove there is one, and find the other, not visible horizontal asymptote

I tried converting it back to cartesian but the equation cannot be isolated for y so that I could take the limit as x approaches positive or negative infinity. Other than that, I have no idea how to approach this problem. Any help would be appreciated.

Originally Posted by freestar

If you graph the polar function , , , , you should find a horizontal asymptote. Prove there is one, and find the other, not visible horizontal asymptote

I tried converting it back to cartesian but the equation cannot be isolated for y so that I could take the limit as x approaches positive or negative infinity. Other than that, I have no idea how to approach this problem. Any help would be appreciated.

Hi freestar!

You would get an asymptote if r tends to infinity.
At which values of does r tend to infinity?

I tried to find that limit but I can't seem to find it because plugging in large numbers does not yeild one specific number. Confused. Sorry if I am being dumb.

Thanks a lot

At which values of θ is cot(θ) undefined?

0, pi, 2pi, 3pi, etc..

Originally Posted by freestar

0, pi, 2pi, 3pi, etc..

Right!
Let's stick to the ones within your domain, which are 0 and pi.
What are the x and y coordinates that correspond to those angles (or angles close to them)?

Ahh!! I see that y = are horizontal asymptotes but what about the ones that is not visible. Still unclear on what that means.

You can approach 0 and pi both from different sides.
This leads to 4 asymptotic relations.
In 2 of those r tends to +infinity.
In the other 2, r tends to -infinity.
I can only assume that the last 2 are considered "not visible", since in polar coordinates r should be positive.

Thank you!