cutiecomittee123
  • cutiecomittee123
which of the following are vertical asymptotes of y=2cot(3x)+4 x=0 x=2pi x=+-pi/2 x=pi/3
Mathematics
chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
cotangent is defined as cot(x) = cos(x)/sin(x)
jim_thompson5910
  • jim_thompson5910
so, cot(3x) = cos(3x)/sin(3x)
jim_thompson5910
  • jim_thompson5910
cot(3x) has vertical asymptotes when sin(3x) = 0 solve sin(3x) = 0 to get your answer

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cutiecomittee123
  • cutiecomittee123
how do I solve that?
cutiecomittee123
  • cutiecomittee123
and I am confused on how that will help find the asymptotes
jim_thompson5910
  • jim_thompson5910
well an alternative is to plug in the given choices to see whether they make sin(3x) equal to 0
jim_thompson5910
  • jim_thompson5910
for example, choice A has x = 0 replace x with 0 to get... sin(3x) = sin(3*0) = sin(0) = 0 so when x = 0, the value of sin(3x) is equal to 0. All of this means x = 0 is a vertical asymptote of cot(3x)
jim_thompson5910
  • jim_thompson5910
how about x = 2pi? what do you get when you plug that value in for x?

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