The phase sensitivity of the atomic ionization by intense one-cycle linearly polarized laser pulses has been discussed within the analytic Landau-Dykhne approximation. The generalized Keldysh parameter has been introduced for analysis of two regimes of ionization. In the case of super-intense laser field we found that ionization by cosine waveform pulse is much more effective than that by sine waveform pulse with the same energy in the pulse. This is pure quantum destructive interference effect. Electron energy spectra and effective electron temperatures are also derived analytically for both waveform pulses.