OK what you're asking is a difficult question to answer, but I'll give you the outline anyway.
OK, I'll answer your first question first - it's probably not ideal to use

, just use

Now, how can current be induced in the BC part of the coil? Well, what you see here is a coil - you can't consider each of the wires in the coil separately but look at the coil as a whole. You'll see that when the coil is rotated, there will be a change in flux - because flux is the number of magnetic field lines caught by the area. This means that when the
coil is parallel to the field, there will be no flux, when the coil is perpendicular to the field, there will be a flux.
So what happens when you turn the coil? Well there will be a change in flux, purely because the angle will be changing. Mathematically, we can describe this as:

)
So essentially this is why the circular function relationship exists - but this is an aside.
The way to answer your question is to use Lenz's law - which is an application of conservation of energy, when you rotate your coil, the coil will attempt to retard your rotation (otherwise you would be getting free energy) - this is just the concept of work.
So what it happens is that it will attempt to generate a force in the opposite direction to your own force, which means that it will be trying to oppose the change in flux. So essentially, if your rotation is reducing the flux, what it will do is induce current within itself in order to increase the amount of flux.
So you can use either the right hand grip rule or the right hand slap rule to find the direction of the current.