Induced emf in AC generator

The induced emf in a coil in AC generator is given as:

E = NABwsin@

Now, when the angle between the normal of plane and magnetic field is zero degrees, the induced emf is zero i.e.

E = NABwsin0 = 0

But we also define emf as the time rate of change of magnetic flux so, why do we get zero emf in the above case, magnetic flux is still changing with time?

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The magnetic flux as a function of time is $$\Phi(t) = \mathbf B \cdot \mathbf A(t) = BA\cos(\omega t)$$ where $\mathbf B$ is the magnetic field and $\mathbf A(t)$ is the area vector as a function of time and $\omega t$ is the angle between the field and the area vector as a function of time. Then the rate of change of the flux as a function of time is $$\Phi'(t) = -BA\omega\sin(\omega t)$$ Notice that if the angle between the area vector vector and the magnetic field is zero, then the flux is nonzero and equal to $AB$, its maximum, but the rate of change of the flux vanishes because $\sin(0) = 0$.
Muhammad Rafique the induced EMF in a AC generator also depend's on the rate change of magnetic flux linked with the coil, that is $\Delta\phi =\phi(f)$ - $\phi(i)$ and rate change of magnetic flux $\frac{\Delta\phi}{\Delta(t)}$ = $\frac{BASin(\theta(f)- \theta(i))}{\Delta(t)}$ so it can go zero for some values of $\theta$ but we are taking an average value in this case but the induced $EMF$ in an AC generator which generate alternating current which mean's it change's it's value from positive to negative in which it also become's zero we cannot take an average value for a complete cycle because it will result in zero EMF so we take the average for a half cycle. Hope it cleared your doubt if not you can notify me