True or false

Question

true or false:

the graph of y=cot(x) has asymptotes where the cos(x)=1

Answer 1

cotagent is the reciprocal of tangent.

tangent = sine/cosine ... so cotangent = cosine/sine

Vertical asymptotes occur where theur is division by 0.
sin(x) = 0 when cos(x) = 1 or -1 

The statement is true, but note that it does not contain ALL the asymptotes.

Answer 2

y = cot x

y = cos x / sin x

 

If cos x = 1, x = 0 + 2kπ

sin (0 + kπ) = 0

 

Therefore when cos x = 1

y = 1 / 0

 

Yes, there is a vertical asymptote.