MathDB
Trig Sum

Source: AIME 2008II Problem 8

April 3, 2008
trigonometrymodular arithmeticAMC

Problem Statement

Let a\equal{}\pi/2008. Find the smallest positive integer n n such that 2[\cos(a)\sin(a)\plus{}\cos(4a)\sin(2a)\plus{}\cos(9a)\sin(3a)\plus{}\cdots\plus{}\cos(n^2a)\sin(na)] is an integer.