  We study some properties of the Askey-Wilson polynomials (AWP) when q is a
primitive N-th root of unity. For general four-parameter AWP, zeros of the N-th
polynomial and the orthogonality measure are found explicitly. Special
subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi
polynomials, are considered in detail. A set of discrete weight functions
positive on a real interval is described. Some new trigonometric identities
related to the AWP are obtained. Normalization conditions of some polynomials
are expressed in terms of the Gauss sums.
