Is sin convergent or divergent

[trumpetplaya1687]

I just have a quick question, is cos and sin divergent or convergent? I keep getting mixed results from different sources. I know that both functions oscillate so on the interval [0, infinity) they both diverge. But for some of my homework problems relating to improper integrals, the book says that both functions approach some number. I need some guidance as to when both functions approach a number and when they both are divergent. Please help.

 

[HallsofIvy]

The words "convergence" and "divergence" simply do not apply to functions- they apply go sequences or series of numbers or functions.

I think you are trying to ask if lim_{x\rightarrow \infty} sin(x) and lim_{x\rightarrow \infty} cos(x) exist. You are correct that those limits do not exist.

Could you please post the exact example your text gives?