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Math Help - asymptotes of a cot function.

  1. #1
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    Question asymptotes of a cot function.

    I had a question similar to this yesterday but I cant figure this one out.
    what are the equations of the asymptotes for the function
    y=(3)(cot)(3)(pi)(x)

    y=
    3 sin 3 pi x
    3 cos 3pi x

    one of the asympotes is found by making the bottom = 0

    so I get

    x cannot be apx. = .1667

    but how can I find the equation for the asymptotes from that?
    answer is either

    x=n
    x=n/2
    x=n/3
    x=2n
    x=3n
    thanks for any help.
    Last edited by brentwoodbc; April 26th 2009 at 08:26 PM.
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  2. #2
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    Quote Originally Posted by brentwoodbc View Post
    I had a question similar to this yesterday but I cant figure this one out.
    what are the equations of the asymptotes for the function
    y=(3)(cot)(3)(pi)(x)

    y=
    3 sin 3 pi x
    3 cos 3pi x

    one of the asympotes is found by making the bottom = 0

    so I get

    x cannot be apx. = .1667

    but how can I find the equation for the asymptotes from that?
    answer is either

    x=n
    x=n/2
    x=n/3
    x=2n
    x=3n
    thanks for any help.
    cot A = cos A/sin A. NOT sin A/cos A. So you've started with the wrong expression.

    Solve 3 sin (3pi x) = 0 => sin (3pi x) = 0

    => 3pi x = n pi where n is any integer.

    Solve for x.
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  3. #3
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    Quote Originally Posted by The Second Solution View Post
    cot A = cos A/sin A. NOT sin A/cos A. So you've started with the wrong expression.

    Solve 3 sin (3pi x) = 0 => sin (3pi x) = 0

    => 3pi x = n pi where n is any integer.

    Solve for x.
    Im a little confused.
    how do you get 3pi x = n pi?
    Just from the period?

    and how come you divided out the 3sin? I mean cant you divide out the whole thing other than the x?

    anyways I get x = n/3,
    Last edited by brentwoodbc; April 27th 2009 at 09:17 AM.
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  4. #4
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    Quote Originally Posted by brentwoodbc View Post
    Im a little confused.
    how do you get 3pi x = n pi?
    Just from the period?

    and how come you divided out the 3sin? I mean cant you divide out the whole thing other than the x?

    anyways I get x = n/3,
    Both sides of the equation were divided by 3.

    The basic fact that if sin(A) = 0 then A = n pi has been used.
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