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Equilateral Triangle on Sine Curve

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August 8, 2024
trigonometry2022

Problem Statement

The graph of y=Csin⁡xy=C\sin x, where C>0C>0 is a constant, is drawn on the interval [0,π][0,\pi]. Suppose that there exists a point PP on the graph such that the triangle with vertices (0,0)(0,0), (π,0)(\pi,0), and PP is equilateral. Find C2C^2.
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