The Kerr and Faraday effects on the interface between a topological insulator and a Sinc-functional photonic crystal are studied by using the transfer matrix method and the equivalent medium theory. The results show that as for two kinds of linearly polarized waves, the polarization planes of their reflected waves may rotate approximately ± π2 at some frequencies. Meanwhile, the equivalent permittivity of the nearby periodic structure may change abruptly. The further investigation discloses that the law for the rotation angle of transmission wave''s polarization plane versus frequency is similar to that for the equivalent permeability of a periodic structure (BAB)n versus frequency. All the above results show that the Kerr effect and Faraday effect on the interface between a topological insulator and a functional photonic crystal are closely related to the frequency of the incident wave, the dielectric constant and the permeability of a periodic structure.