I think the magnetic field is assumed to be uniform B=B[sub]0[/sub].
The magnetic flux pass through the coil depends on the angle $\theta=\omega t$,
assume the coil rotate at constant angular velocity $\omega$.
i.e. $\Psi=\int \vec{B}\cdot d\vec{s}= B A cos(\theta)=B A cos(\omega t)$
From Faraday's law, induced voltage $V= -\frac{d\Psi}{dt}= BA\omega \sin(\omega t)$
So the voltage is a sine wave (without commutator).