The terahertz wave packet emission theory is constructed when an s-polarized laser pulse is incident on a semi-infinite plasma whose density is much lower than the critical value. The angular, spectral and energy characteristics of a terahertz pulse are studied as a function of the plasma density, the angle of incidence and the duration of laser radiation. It is shown that the energy of the terahertz signal has the maximum value for grazing incidence of the laser pulse, when the effect of total reflection of the laser radiation from the plasma boundary takes place.