Answer
a.) $inductor$
b.) $ 328mH$
Work Step by Step
To determine which component it is, use the definition for impedance.
$Z = V/I$.
Now, find the phase offset using the phasor method to calculate the phase of the impedance.
$\frac{e^{j1.309}}{e^{ -j\pi/12}} = e^{j\pi/2} $
This is significant because it tells us which component it is.
How? Because we know from the derivation of impedance for each component that certain phase differences are keys to each component.
It works out that a $+\pi/2$ phase difference between V and I is characteristic of an Inductors impedance.
Now use the inductor equation $V = L*\frac{di}{dt} $ to solve for L
$3.5 * cos(w*t + 1.309) = -L*(0.017*628.3*sin(w*t-\pi/12)$
Convert the sin to a cos and write as phasors, then divide by the left hand side.
$\frac{3.5*e^{j1.309}}{10.6811*e^{j5\pi/12}} = L = 0.32768 = 328mH$
