= Solution
Let $\theta=\omega t+\theta_0$ be the angle between the coil's area normal and the uniform <magnetic flux density>. The linked <magnetic flux> is $\Phi_N=NBA\cos\theta$. <Faraday's law> gives
$$
\boxed{\mathcal E(t)=-\frac{d\Phi_N}{dt}=NBA\omega\sin(\omega t+\theta_0).}
$$
The sign uses the winding direction associated with the chosen normal; reversing the terminal convention changes it. The magnitude is largest when $\cos\theta=0$: the coil's normal is perpendicular to the <magnetic field>, so the plane of the coil is parallel to it. At that orientation the instantaneous <magnetic flux> is zero but its rate of change has maximum magnitude.
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