# Horizontal Asymptote of a Polar Equation

• Jan 7th 2012, 04:08 AM
freestar
Horizontal Asymptote of a Polar Equation
If you graph the polar function $r = 1 - cot(\theta)$, $0\leq\theta\leq\2\pi$, $-10\leq x \leq\10$, $-2\leq y \leq\2$, 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.
• Jan 7th 2012, 04:57 AM
ILikeSerena
Re: Horizontal Asymptote of a Polar Equation
Quote:

Originally Posted by freestar
If you graph the polar function $r = 1 - cot(\theta)$, $0\leq\theta\leq\2\pi$, $-10\leq x \leq\10$, $-2\leq y \leq\2$, 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 $\theta$ does r tend to infinity?
• Jan 7th 2012, 05:41 AM
freestar
Re: Horizontal Asymptote of a Polar Equation
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
• Jan 7th 2012, 06:17 AM
ILikeSerena
Re: Horizontal Asymptote of a Polar Equation
At which values of θ is cot(θ) undefined?
• Jan 7th 2012, 10:42 AM
freestar
Re: Horizontal Asymptote of a Polar Equation
0, pi, 2pi, 3pi, etc..
• Jan 7th 2012, 10:45 AM
ILikeSerena
Re: Horizontal Asymptote of a Polar Equation
Quote:

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)?
• Jan 7th 2012, 03:53 PM
freestar
Re: Horizontal Asymptote of a Polar Equation
Ahh!! I see that y = $\pm1$ are horizontal asymptotes but what about the ones that is not visible. Still unclear on what that means.
• Jan 7th 2012, 05:05 PM
ILikeSerena
Re: Horizontal Asymptote of a Polar Equation
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.
• Jan 7th 2012, 05:09 PM
freestar
Re: Horizontal Asymptote of a Polar Equation
Thank you! :)