The current through the inductor lags the applied emf by $\frac{\pi}{2}$ and the current through the capacitor leads the current by $\frac{\pi}{2}$
$\begin{aligned}
& \therefore \mathrm{i}_{\mathrm{L}}=\frac{\mathrm{e}_0}{\omega \mathrm{L}} \sin \left(\omega \mathrm{t}-\frac{\pi}{2}\right)=-\frac{\mathrm{e}_0}{\omega \mathrm{L}} \cos \omega \mathrm{t} \\
& \text { and } \mathrm{i}_{\mathrm{c}}=\mathrm{e}_0 \omega \mathrm{C} \sin \left(\omega \mathrm{t}+\frac{\pi}{2}\right)=\mathrm{e}_0 \omega \mathrm{C} \cos \omega \mathrm{t}
\end{aligned}$
.
