Question

How do you find vertical asymptotes of cotangent functions?

Answer 1

hmm what's the identity for cotangent in terms of sine and cosine?

Answer 2

anyhow, the identity is a fraction, a fraction is undefined when the denominator is 0
so when THAT FRACTION is undefined, that's where you'd find the vertical asymptotes

Answer 3

Do you mean how cot(x)=cos(x)/sin(x)?

Answer 4

So, would it be (pi, 0), (2pi, 0), (-pi, 0), (-2pi, 0)? @jdoe0001

Answer 5

yes

Answer 6

http://www.mathipedia.com/GraphingSecant,Cosecant,andCotangent_files/image033.jpg

Answer 7

Would those stay the same when my equation is y=-2 cot(3x)? @jdoe0001

Answer 8

\(\bf y=-2 cot({\color{red}{ 3}}x)\qquad \textit{period}=\cfrac{\textit{original period}}{{\color{red}{ 3}}}\implies \cfrac{\pi}{{\color{red}{ 3}}}\)

the asymptotes will shrink in, to that position, from the original or "parent function" of cot(x)

Answer 9

So what does that do to my asymptotes?

Answer 10

Wait, that means my VA's will be (-pi/3), and (pi/3) instead? And then they are always pi apart, right? So after that, how would they look? Like, pi/6? Or would it be 2pi/3?

Answer 11

it won't move them, just will add more asymptotes to the same interval

Answer 12

Oh, so they don't change..

Answer 13

yes, the ones won't change, the period will shrink, the graph will do 3 figures on the same interval it used to do 1
so you'd end up with 2 extra VA in between the same interval

Answer 14

Awesome. Thanks. God bless you!

Answer 15

yw

Answer 16

Wait, @jdoe0001 , what would the range of that be? y=-2 cot (3x)?