This is the circuit:

The R = 2Ω and L = 2H. Vs(t) = 12cos(50t + 30°).

I had to find the transfer function that relates iL(t) to vS(t). I did this :

I've looked through all her notes but she doesn't explain how to find and use the phase and magnitude of the "transfer function at frequency of input voltage" (second part of question).

Any guidance at all is great, just want to be able to understand how to solve this question and questions like them for the exam.

Thanks