Answer
Not monotonic, Bounded
Work Step by Step
Let's calculate the value of initial terms of the sequence to get an insight.
$a_1=\:\frac{cos\left(1\right)}{1}\:=\:0.54$
$a_2=\:\frac{cos\left(2\right)}{2}\:=\:-0.208$
$a_2=\:\frac{cos\left(3\right)}{3}\:=\:-0.33$
$a_4=\:\frac{cos\left(4\right)}{4}\:=\:-0.163$
Thus, the sequence is not monotonic as the terms decrease till the third term when they start rising and it keeps changing as can be seen by the graph.
Hence, the sequence is not monotonic.
We know that cos(x) is bounded from above and below by 1 and -1 respectively, and dividing it by any positive numbers only makes it go nearer to 0.
So $\frac{cos(n)}{n}$ is bounded.
