limit of the sequence

Question

Find the limit of the sequence a_n={sin(n)/n}, if it exists

Answer 1

Sin (n) oscillates between -1 and 1

Therefore, Sin (n) / n oscillates between -1/n and 1/n

as n goes to infinity Sin (n) is between -1 or 1 while 1/n goes to 0

Therefore, lim n-> infinity sin(n) / n = 0