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Ratio of Trig Sums

Source:

December 20, 2005
ratiotrigonometryfloor functionintegrationcalculuscomplex numbersgeometric series

Problem Statement

Let x=∑n=144cos⁡n∘∑n=144sin⁡n∘.x=\frac{\displaystyle\sum_{n=1}^{44} \cos n^\circ}{\displaystyle \sum_{n=1}^{44} \sin n^\circ}. What is the greatest integer that does not exceed 100x100x?
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