Sine of infinity? While considering limiting problems there are some situations when we have argument tending to infinity of sine or cosine function .
My book writes it as an "OSCILLATING number between $-1$ & $1$".
How is this possible?  

What is oscilatting between $1$ and $-1$ is the sine (and the cosine). It follows from this that the limit cannot exist.
It's even worst with the tangent function: it keeps oscilatting between $-\infty$ and $+\infty$. The conclusion is the same, of course: $\lim_{x\to\pm\infty}\tan x$ does not exist.
