The number λq=2cosπ/q, q ∈ N, q ≥ 3, appears in the study of Hecke groups which are Fuchsian groups, and in the study of regular polyhedra. There are many results about the minimal polynomial of this algebraic number and in some of these methods, the minimal polynomials of several algebraic numbers are used. Here we obtain the minimal polynomial of one of those numbers, cos(2π/n), over the field of rationals by means of the better known Chebycheff polynomials for odd q and give some of their properties. We calculated this minimal polynomial for n ∈ N by using the Maple language and classifying the numbers n ∈ N into different classes. © 2012 American Institute of Physics.