$(30$ points$)$

An inductor is connected to an AC source whose emf is represented by the equation

V$=(23\mathrm{.}0$V$)$sin$(2\backslash$pi ft$-(\backslash$pi $)/(4))$ where f$=51\mathrm{.}2$Hz$.$

a$.$ Determine the first instant after t$=0,$ when the source emf reaches a positive maximum value.

b$.$ Write an expression for the current in the inductor in terms of the frequency f $,$ maximum current

I$\_($max$),$ and time t$.$ Do not use units or numerical values.

c$.$ Determine the first instant after t$=0,$ when the current reaches a positive maximum value.