  Let $F(x, y)$ be a binary form of degree at least three and non-zero
discriminant. In this article we compute the automorphism group
$\operatorname{Aut} F$ for four families of binary forms. The first two
families that we are interested in are homogenizations of minimal polynomials
of $2\cos\left(\frac{2\pi}{n}\right)$ and $2\sin\left(\frac{2\pi}{n}\right)$,
which we denote by $\Psi_n(x, y)$ and $\Pi_n(x, y)$, respectively. The
remaining two forms that we consider are homogenizations of Chebyshev
polynomials of first and second kinds, denoted $T_n(x, y)$ and $U_n(x, y)$,
respectively.
