Question

How do I find the vertical asymptotes for
f(x)=4 tan (pi(x))

Answer 1

ok, I dont have to turn tan into sin/cos?

Answer 2

vertical asymptotes for tan(x) = \( n \pi - {\pi \over 2} \) where \( n \in \mathbf{Z} \)
for tan(pi x), asymptotes, the frequency is multiplied by \( \pi \) so divide it by \( \pi \)

If you want to change it into sin/cos, then \( \cos ( \pi x ) = 0 = \cos (\frac{( 2n + 1) \pi} 2) \)

Answer 3

How did you get 0=cos((2n+)∏/2)?

Answer 4

(2n+1)*

Answer 5

I understand that cos is 0 at ∏/2, how did you get that period of (2n+1) though?

Answer 6

2n+1 gives the odd values, at odd multiple of pi/2 , the value of cosine is zero.

Answer 7

ohhh I see, do I have to do anything with the 4?

Answer 8

no ... that doesn't make any difference

Answer 9

Ok, thank you, you've been a huge help. I've been stuck on this one for awhile.

Answer 10

yw