  In this paper we prove asymptotic formulas for the $L^p$ norms of
$P_n(\theta)=\prod_{k=1}^n (1-e^{ik\theta})$ and $Q_n(\theta)=\prod_{k=1}^n
(1+e^{ik\theta})$. These products can be expressed using $\prod_{k=1}^n
\sin\Big(\frac{k\theta}{2}\Big)$ and $\prod_{k=1}^n
\cos\Big(\frac{k\theta}{2}\Big)$ respectively. We prove an estimate for $P_n$
at a point near where its maximum occurs. Finally, we give an asymptotic
formula for the maximum of the Fourier coefficients of $Q_n$.
