Answer
$a_n= cos(n)$ is bounded and not monotonic.
Work Step by Step
A sequence is monotonic if it is either increasing ($a_n >a_{n+1}$ for all $n\geq 1$) or decreasing ($a_n< a_{n+1}$ for all $n\geq 1$). We see that $ cos( 2) > cos (3) < cos (4)$ . Thus, the sequence is not monotonic.
Since $-1 \leq cos(n) \leq1 $, $a_n$ is bounded both from above and from below, respectively by 1 and -1. Therefore, $a_n$ is bounded.
