The relation between emf and mutual inductance is as follows:
which basically means:
Emf of 2 = - Mutual inductance of 1 on 2 * change in current of 1 divided by time
Since we are given I(t), we need to take the derivative with respsect to t to get dI/dt
I(t) = 15.0 sin(1.25 103t)
dI/dt = 15*1.25*10^3 * cos(1.25*10^3 t)
which has a max value when t = 0, so cos goes to 1
since we now know both dI/dt an d the mutual inductance, the Emf can be calculated form the first equation.