Recent studies suggest that the half-wave rectifier model of the interaction of the Earth's magnetosphere with the IMF is insufficient to produce the observed amplitude of the semi-annual variation. However, the observed amplitude would ensue if there is additional modulation of geomagnetic activity dependent on the tilt of the dipole axis. We use an MHD model to demonstrate that the size of the region of antiparallel magnetic field is controlled by the tilt of the Earth's dipole axis, and hence the integrated reconnection rate and geomagnetic activity may be so controlled. The same zero guide field model for the onset of reconnection also predicts that the maximum reconnection rate occurs not for due southward field but at angles away from due southward by about the dipole tilt angle.