Cheap sensor for angular rotation (not rotation rate)

Thanks. Accuracy isn't important, but I want to know the absolute angle (angular position), not just the amount of angular displacement (by counting the lines). E.g. if the disc is rotated when the device is off (so it's no longer in its last known position) I want to detect this. I think I need some reference point (or points) on the disc, so that, when the device is back on, I can re-establish a specific, fixed angular reference