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Equilateral Triangles "Inscribed in" a Cosine Curve

A question from Twitter: Is there an equilateral triangle with all three vertices on a cosine curve? The amplitude of the cosine curve can be changed using the red slider below. If the amplitude is high enough, it is possible to find one, two, or more equilateral triangles with a vertex along the -axis. (Having GeoGebra find more general triangles, as done with parabolas before, is harder here.)