Asymptotics of a sinusoid
Let us notice the following:
$$
|\sin(\pi \cdot n/2)| = \begin{cases} 1 &amp; \text{if $n$ is odd}, \\ 0 &amp; \text{if $n$ is even}. \end{cases}
$$
This implies that your function $f(n)$ alternates between $n^2$ (for odd $n$) and $0$ (for even $n$). This means, for example, that $f(n) = O(n^2)$ (since $f(n) \leq n^2$ for all $n$) but $f(n) \neq \Omega(n^2)$ (considering even $n$).