# Graphing y = csc x

• Sep 18th 2008, 02:57 PM
D. Martin
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)$\displaystyle \pi$, 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 $\displaystyle \pi$ would get you to a member of the $\displaystyle \pi$ family.

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

Thank you
• Sep 18th 2008, 03:03 PM
skeeter
$\displaystyle y = \csc{x} = \frac{1}{\sin{x}}$

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

vertical asymptotes occur at values of x where $\displaystyle sin{x} = 0$ ...
that would be at all integer multiples of $\displaystyle \pi$... $\displaystyle x = k\pi$
• Sep 18th 2008, 04:16 PM
D. Martin
Thank you, once again, for your help. It was really useful.