anonymous
  • anonymous
find limx→π+ csc(2x) is it positive or a negative limit?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[\lim_{x \rightarrow \pi} \csc(2x)\] written like this ?
anonymous
  • anonymous
yup
anonymous
  • anonymous
now you know the relationship between csc and sin ?

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anonymous
  • anonymous
yeah reciprocals right?
anonymous
  • anonymous
it's called inverse actually : csc(x)=1/sin(x)
anonymous
  • anonymous
my bad
anonymous
  • anonymous
now csc(2x)=1/sin(2x)
anonymous
  • anonymous
now sin(2x)=sin(x+x) which is....
anonymous
  • anonymous
sin(a+b)=...
anonymous
  • anonymous
continue
anonymous
  • anonymous
yeah I'm lost
anonymous
  • anonymous
sin(a+b)=?
anonymous
  • anonymous
you have a formula for this
anonymous
  • anonymous
sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
anonymous
  • anonymous
now sin(x+x)=...
anonymous
  • anonymous
sin(2x)
anonymous
  • anonymous
use the formula mate
anonymous
  • anonymous
replace x with a and x with b and add that sum
anonymous
  • anonymous
sin(a+b) ??
anonymous
  • anonymous
what?
anonymous
  • anonymous
sin(2x)=2sinxcosx
anonymous
  • anonymous
now
anonymous
  • anonymous
your limit can be written in this form \[\lim_{x \rightarrow \pi}\frac{ 1 }{ 2\sin x \cos x }\]
anonymous
  • anonymous
now replace x with pi and do the math...
anonymous
  • anonymous
.027 ?
anonymous
  • anonymous
thank you i got it

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