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Summation of Trig Function: Sequence

Source: 2015 AIME 2 Problem 13

March 26, 2015
trigonometryfunction

Problem Statement

Define the sequence a1,a2,a3,…a_1,a_2,a_3,\ldots by an=∑k=1nsin⁡(k)a_n=\sum_{k=1}^n\sin(k), where kk represents radian measure. Find the index of the 100100th term for which an<0a_n<0.
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