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Math Help - Confusion of finding asymtotes from trig function

  1. #1
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    Confusion of finding asymtotes from trig function

    I am having a hard time on comprehending where the asymptotes lie on a variety of trig questions.

    y= sec(x/2) > [0,2pie]
    -the help sheet clearly states that when plotting a sec graph, the asymptotes are located in the domain of [0,2pie] at pie/2 and 3pie/2, but the answer repels this and has the asymptotes at just pie. What am i doing wrong?

    y= cot(3x) > [0,2pie]
    -the help sheet clear states that the asymptotes are located in the domain of [0,2pie] at 0,pie and 2 pie, yet the answer locates the asymptotes at pie/3, 2pie/3, pie, 4pie/3, 5pie/3 and 2pie........why are there more than the normal amount? is it because there is a number in the brackets, making there more cycles therefor more asymptotes, i am unsure. It would be very helpful if someone could provide me with a bit of detail on this.
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  2. #2
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    Quote Originally Posted by johnsy123 View Post
    I am having a hard time on comprehending where the asymptotes lie on a variety of trig questions.

    y= sec(x/2) > [0,2pie]
    -the help sheet clearly states that when plotting a sec graph, the asymptotes are located in the domain of [0,2pie] at pie/2 and 3pie/2, but the answer repels this and has the asymptotes at just pie. What am i doing wrong?

    y= cot(3x) > [0,2pie]
    -the help sheet clear states that the asymptotes are located in the domain of [0,2pie] at 0,pie and 2 pie, yet the answer locates the asymptotes at pie/3, 2pie/3, pie, 4pie/3, 5pie/3 and 2pie........why are there more than the normal amount? is it because there is a number in the brackets, making there more cycles therefor more asymptotes, i am unsure. It would be very helpful if someone could provide me with a bit of detail on this.
    Note that

    \dispalystyle \sec(x)=\frac{1}{\cos(x)} \ \ \ \cot(x)=\frac{1}{\tan(x)}

    Whenever cosine is 0, the sec graph will have an asymptote, and the same applies to tangent.

    The question you should ask yourself is where is \cos\left(\frac{x}{2}\right)= 0 in the defined interval and like wise for tangent.
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  3. #3
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    Quote Originally Posted by johnsy123 View Post
    I am having a hard time on comprehending where the asymptotes lie on a variety of trig questions.

    y= sec(x/2) > [0,2pie]
    ...
    this is pi ...



    ... and this is pie.

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