Based on the extended Huygens-Fresnel principle, the analytical expressions for the intensity of partially coherent sinusoidal-Gaussian beams with Schell-model correlator in atmospheric turbulence along a slant path are derived, and used to study the evolution of intensity distribution of partially coherent sinusoidal-Gaussian beams, including partially coherent sin-Gaussian (SiG), cos-Gaussian (CoG), sinh-Gaussian (ShG), cosh-Gaussian (ChG) beams. It is shown that the different intensity distribution at the source plane of the four beams evolve to the same Gaussian distribution in atmospheric turbulence along a slant path. The spreading of the partially coherent sinusoidal-Gaussian beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation, and the slant path is more beneficial to the beam propagation through atmospheric turbulence in comparison with the horizontal propagation. The validity of our results is interpreted physically. Results in this paper may provide potential applications in free-space optical communications.