Lenz Law - sinusoidal current
The current in the loop being sinusoidal creates a magnetic field that is in-phase with current. 

Using V = N\$\dfrac{d\Phi}{dt}\$ we can predict what the phase angle is of the driving voltage that is induced into the loop by the changing magnetic field.

This means that \$V_{INDUCED}\$ is leading the sinewave current by 90 degrees.

However, the current produced in the loop is dependant on this voltage and the load resistors plus one other factor that your question omits. This other factor is the loop inductance of the secondary. It will form a complex impedance with the two resistors. Please note that I am now going to ignore the loop inductance.

So, the induced voltage generated by the sinusoidal current leads by 90 degrees and this causes a current to flow that is in phase with the induced voltage (ignoring loop inductance).