Pls help..question: discuss the behaviour of sequence a(n)= sin(n). does it converge, why or why not?

No, it doesn't converge. If you look at the graph of y = sin(x), you'll see that it keeps on waving up and down. It never actually settles to a limit, even if you only take integer values of x. There is no special value of n (call it "N") where you can say "For any values of n > N, the value of a(n) gets closer to a particular limit".