# Thread: Horizontal Asymptote of a Polar Equation

1. ## Horizontal Asymptote of a Polar Equation

If you graph the polar function $\displaystyle r = 1 - cot(\theta)$, $\displaystyle 0\leq\theta\leq\2\pi$, $\displaystyle -10\leq x \leq\10$, $\displaystyle -2\leq y \leq\2$, 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.

2. ## Re: Horizontal Asymptote of a Polar Equation

Originally Posted by freestar
If you graph the polar function $\displaystyle r = 1 - cot(\theta)$, $\displaystyle 0\leq\theta\leq\2\pi$, $\displaystyle -10\leq x \leq\10$, $\displaystyle -2\leq y \leq\2$, 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 $\displaystyle \theta$ does r tend to infinity?

3. ## 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

4. ## Re: Horizontal Asymptote of a Polar Equation

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

5. ## Re: Horizontal Asymptote of a Polar Equation

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

6. ## Re: Horizontal Asymptote of a Polar Equation

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)?

7. ## Re: Horizontal Asymptote of a Polar Equation

Ahh!! I see that y = $\displaystyle \pm1$ are horizontal asymptotes but what about the ones that is not visible. Still unclear on what that means.

8. ## 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.

Thank you!

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