What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase?
Why With two elements, the pattern depends on the combination of physical spacing and feed phasing. Along the array axis (end-fire direction), the half-wavelength of extra travel adds another 180 degrees of phase, which cancels the 180-degree feed offset, so the signals arrive in phase and add. Broadside (perpendicular to the axis), the path lengths are equal, so the 180-degree feed difference cancels the signals completely. The result is a figure-eight with its lobes pointing along the line joining the two antennas.
Watch out A figure-eight broadside to the axis is what you get from half-wave spacing fed in phase, the opposite phasing; a cardioid comes from quarter-wave spacing with 90 degrees of phase difference.
Half-wave spacing: in phase = broadside, out of phase = end-fire. Quarter-wave and 90 degrees = cardioid.