Q:

How to find the current's phase given the period?

I asked a question earlier, and it only made me have more questions. I'll just show you a real example and maybe someone can help me with a quick answer.
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.
I know that:
T = 1/4 = 1/100
γ = 1/4 * T = 0.25 / 100
i(t) = √2I* sin(ωt+γ).
My question is the following: Is this how you find the period's value? 
T ..... 2pi
γ ......xpi , resulting γ = 0.5 pi

A:

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}\$.

