How to find the current's phase given the period?
I need to write the sinusoidal expression of the current if I = 2 [A], and f = 100 [Hz]. The initial phase of the current should be 1/4*T.


Somehow you have already the solution written above.

A sinusuidal current can be described by

$$ i = î \sin(\omega t + \varphi)\,. $$

In this case

$$ i = \sqrt{2} I_\mathrm{eff} \sin(2 \pi f\,  t + \frac{\pi}{2}) $$

with \$ I_\mathrm{eff} = 2\,\mathrm{A}\$, \$ f = 100\,\mathrm{Hz}\$.