How to determine which of the trig functions have horizontal and vertical asymptotes?

Question

1. Do any of the trigonometric functions $\sin x, \cos x, \tan x, \cot x, \sec x$, and $\csc x$ have horizontal asymptotes?
2. Do any of the trigonometric functions have vertical asymptotes? Where?

The answer for Q1 is 'No' whereas for Q2, it is 'Yes, $\tan x \space$ and $\space \sec x \space$ at $\space x = nπ + π/2 \space$ and $\space \cot x$ and $\space \csc x \space$ at $\space x = nπ, \space n = 0, ±1, ±2$, ...'

What formula and techniques should I use to prove that the two answers above are correct? Any suggestion will be helpful!