8
Part of 2008 AIME Problems
Problems(2)
Arctangent Sum
Source: AIME 2008I Problem 8
3/23/2008
Find the positive integer such that \arctan\frac{1}{3}\plus{}\arctan\frac{1}{4}\plus{}\arctan\frac{1}{5}\plus{}\arctan\frac{1}{n}\equal{}\frac{\pi}{4}.
trigonometryAMCAIMEanalytic geometryUSAMTSfunctionLaTeX
Trig Sum
Source: AIME 2008II Problem 8
4/3/2008
Let a\equal{}\pi/2008. Find the smallest positive integer 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.
trigonometrymodular arithmeticAMC