= Solution
Let $\theta=\omega t+\theta_0$ be the angle between the <coil>'s area normal and the <magnetic field>. Its <magnetic flux linkage> is $\Lambda=NB\pi r^2\cos\theta$. Consequently <Faraday's law of induction> gives
$$
\boxed{\mathcal E(t)=-\frac{d\Lambda}{dt}=NB\pi r^2\omega\sin(\omega t+\theta_0).}
$$
The sign refers to the winding orientation used to define the normal. The initial <phase> $\theta_0$ depends on the chosen time origin; one can set it to zero when the normal first points along $+x$. The minimum <absolute value> is zero, attained at $\theta=m\pi$: the <coil>'s normal is parallel or antiparallel to the $x$-axis, and the plane of the <coil> is perpendicular to that axis. At this orientation the <magnetic flux> is extremal and its <derivative> with respect to time vanishes.
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