Question

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

Answer 1

Lines `t=+-kpi`, k = 1, 2, 3, 4,..., parallel to s-axis.

Explanation:

As `t to0_(+-), sto8`.
Here, `0_+-` indicate the approaches for limit, from either side.

As `t to+-kpi_(+-), sto+-oo`, k = 1, 2, 3,...
Here, `kpi_(+-)` indicate the approaches for limit, from either side.

So, the asymptotes are the lines `t=+-kpi`, 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.