# How do you find the asymptotes for  s(t)=(8t)/sin(t)?

Apr 12, 2016

Lines $t = \pm k \pi$, k = 1, 2, 3, 4,..., parallel to s-axis.

#### Explanation:

As $t \to {0}_{\pm} , s \to 8$.
Here, ${0}_{\pm}$ indicate the approaches for limit, from either side.

As $t \to \pm k {\pi}_{\pm} , s \to \pm \infty$, k = 1, 2, 3,...
Here, $k {\pi}_{\pm}$ indicate the approaches for limit, from either side.

So, the asymptotes are the lines $t = \pm k \pi$, k = 1, 2, 3, 4,..., parallel to s-axis

To understand the approaches fpr limits and limits better, recall that sine is positive in the first two quadrants and negative in the third and fourth.