I need to find the Big-O of $f(n) = n^{\sin^2n} \cdot \sqrt{n}$. I know that the value of $\sin(n)$ oscillates between -1 and 1, and so does the value of $\sin^2(n) = \sin ( \sin(n))$. Now, if I am required to be as accurate as possible, should I say that $f(n) = O(n^{1.5})$ and $f(n) = \Omega(\dfrac{1}{\sqrt{n}})$. Maybe as a more general side question, should I always provide both the $O$ and $\Omega$ notation, if the I cannot express it with $\Theta$?
For me, this feels both correct and accurate. This is not strictly homework, but yes, I am practicing for an exam.