MathDB

13

Part of 2015 AIME Problems

Problems(2)

Product of Cosecants

Source: 2015 AIME I Problem 13

3/20/2015
With all angles measured in degrees, the product ∏k=145csc⁡2(2k−1)∘=mn\prod_{k=1}^{45} \csc^2(2k-1)^\circ=m^n, where mm and nn are integers greater than 1. Find m+nm+n.
AMCAIMEAIME I
Summation of Trig Function: Sequence

Source: 2015 AIME 2 Problem 13

3/26/2015
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.
trigonometryfunction