The algebraic numbers $\cos(2\pi/n)$ and $2\cos(\pi/n)$ play an important role in the theory of discrete groups and has many applications because of their relation with Chebycheff polynomials. There are some partial results in literature for the minimal polynomial of the latter number over rationals until 2012 when a complete solution was given in [5]. In this paper we determine the constant term of the minimal polynomial of $\cos(\frac{2\pi}n)$ over $\mathbb{Q}$ by a new method.