Question

Which of the following are vertical asymptotes of the function y=2cot (3x) +4? Check all that applies (also attached below).

A. x=0
B. x=+-pi/2
C. x=2pi
D. x=pi/3

Please explain. Thank you!

Answer 1

cotagent is cosine over sine
it will have a vertical asymptote where sine is equal to zero

Answer 2

wouldn't one be a. because x=0

Answer 3

\(x=0\) is one of them for sure

Answer 4

but there may be more here

Answer 5

for example if \(x=2\pi\) then \(3x=6\pi\) and \(\sin(6\pi)=0\) too

Answer 6

also check D since if \(x=\frac{\pi}{3}\) then \(3x=\pi\) and again \(\sin(\pi)=0\)

Answer 7

but what about c.

Answer 8

If cot(3x)=cos(3x)/sin(3x) and it is undefined if x=0, pi, pi/3,...

Therefore, there are three vertical asymptotes:
x=0
x=2pi
and x=pi/3

Would the answers be A. C. and D. then?

Answer 9

yes

Answer 10

even c. x=2pi also? @satellite73

Answer 11

Well thank you for your help and time @satellite73