If we suppose that the magnetic poles in the AC generator are regular rectangular bar magnets, then the field lines are supposed to be straight lines as in the photo below:
And then the direction of velocity will be inclined with an angle to flux lines, so we will need to multiply by sinθ as in the following equation:
ℰ=NABωsinθ
But the poles are actually concave so I suppose that the direction of velocity will always be perpendicular to the flux lines as in the following photo:
So if the concave poles are the ones really used, why do we need sinθ in the equation?