Can the phase shift be less than $-\pi/2$ or greater than $\pi/2$ at $t=0$?

For (passive) reactive elements such as the inductors and capactors we've seen so far, the phase shift between voltage and current is always $-\pi/2 \le \theta \le \pi/2$. (We will see later that with active circuit elements, i.e., components that add energy to the circuit, this need not be true.)