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Math Help - Horizontal Asymptote of a Polar Equation

  1. #1
    Junior Member freestar's Avatar
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    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.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Horizontal Asymptote of a Polar Equation

    Quote Originally Posted by freestar View Post
    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?
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  3. #3
    Junior Member freestar's Avatar
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    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
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: Horizontal Asymptote of a Polar Equation

    At which values of θ is cot(θ) undefined?
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  5. #5
    Junior Member freestar's Avatar
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    Re: Horizontal Asymptote of a Polar Equation

    0, pi, 2pi, 3pi, etc..
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  6. #6
    Super Member ILikeSerena's Avatar
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    Re: Horizontal Asymptote of a Polar Equation

    Quote Originally Posted by freestar View Post
    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)?
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  7. #7
    Junior Member freestar's Avatar
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    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.
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  8. #8
    Super Member ILikeSerena's Avatar
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    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.
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  9. #9
    Junior Member freestar's Avatar
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    Re: Horizontal Asymptote of a Polar Equation

    Thank you!
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