A good trick that sometimes works when sines and cosines are involved is the squeezing thm

-1/n < sin(n^2)/n < 1/n

since lim-1/n and lim 1/n converge to 0 so does sin(n^2)/n

Makes Sense since you can think of the continuous curve sin(x)/x

as a sine curve whose amplitude 1/x decays to 0