Sum of sines is greater than 1.
Source: Vietnam MO 1980 P1
March 17, 2011
trigonometryvectorabsolute valueinequalities unsolvedinequalities
Problem Statement
Let \alpha_{1}, \alpha_{2}, \cdots , \alpha_{ n} be numbers in the interval [0, 2\pi] such that the number \displaystyle\sum_{i=1}^n (1 + \cos \alpha_{ i}) is an odd integer. Prove that
\displaystyle\sum_{i=1}^n \sin \alpha_i \ge 1