Let n ≥ 0 be an integer. Then we have for x ε (0, π) : ∑k=0 n(2n+1 n-k)sin((2k+1)x)/2k+1 ≤ 8 n-rfnet-temp!/(2n+1)!! The upper bound is best possible. This complements a result of Fejér, who proved that the sine polynomial ...