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Romania NMO 2023 Grade 10 P2

Source: Romania National Olympiad 2023

April 14, 2023
algebratrigonometry

Problem Statement

Determine the largest natural number kk such that there exists a natural number nn satisfying:
sin⁡(n+1)<sin⁡(n+2)<sin⁡(n+3)<…<sin⁡(n+k). \sin(n + 1) < \sin(n + 2) < \sin(n + 3) < \ldots < \sin(n + k).
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