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$f(x)=\frac{6+6\cos x}{\sin x}$ is continuous on the interval $(n\pi,(n+1)\pi)$ where $n$ is an integer.

I understand the continuous interval concept, but I don't understand why that specific interval. What is the thought process behind it? If I'm looking at the unit circle, what should I be thinking to determine the interval? Can someone walk me through it?

Thomas Andrews
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Monica
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  • Well, it is not even defined at $x=n\pi$ for any integer $n$. (Although it can be defined when $n$ is odd...) – Thomas Andrews Mar 15 '14 at 16:58
  • @monica thus is a function from the real numbers into the real numbers... The unit circle does not really come into play. – rschwieb Mar 15 '14 at 17:03
  • @rschwieb: After reading both wckronholm's answer and then your comment, I understand why. Thank you! – Monica Mar 15 '14 at 17:38

1 Answers1

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Your function is an elementary function, and so is continuous on any interval on which it is defined. The only discontinuities occur when $\sin(x) = 0$.

And you are not really looking at one specific interval. You are considering $(n \pi, (n+1)\pi)$ for all integers $n$, so you have one interval for each integer.

wckronholm
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