Question

which of the following are vertical asymptotes of y=2cot(3x)+4
x=0
x=2pi
x=+-pi/2
x=pi/3

Answer 1

cotangent is defined as

cot(x) = cos(x)/sin(x)

Answer 2

so,

cot(3x) = cos(3x)/sin(3x)

Answer 3

cot(3x) has vertical asymptotes when sin(3x) = 0

solve sin(3x) = 0 to get your answer

Answer 4

how do I solve that?

Answer 5

and I am confused on how that will help find the asymptotes

Answer 6

well an alternative is to plug in the given choices to see whether they make sin(3x) equal to 0

Answer 7

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)

Answer 8

how about x = 2pi? what do you get when you plug that value in for x?