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Math Help - Graphing y = csc x

  1. #1
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    Graphing y = csc x

    I have graphed y = csc x. I do not know what the y-intercept would be. The graph doesn't cross the y-intercept, so my hunch is that there would be no y-intercept. But one of the x-intercept coordinates passes through the y-intercept, so I don't know if I should put "undefined" for the y-intercept as well.

    Additionally, I've had some troubles with finding equations for the asymptotes (x-intercepts). I think it would just be x = (2k + 1) \pi, where k is an element of integers. But I'm not certain, I practically guessed to get that equation I thought adding any number to \pi would get you to a member of the \pi family.

    I would be happy as can be if someone could offer a little clarification.

    Thank you
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  2. #2
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    y = \csc{x} = \frac{1}{\sin{x}}

    no y-intercept since the cosecant function is undefined at x = 0.

    vertical asymptotes occur at values of x where sin{x} = 0 ...
    that would be at all integer multiples of \pi ... x = k\pi
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  3. #3
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    Thank you, once again, for your help. It was really useful.
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