...and now it is an island...

Calculus Level 5

Consider an island of the shape formed by the one of the areas between the curves \(\sin x+ \cos x\) and \(\sin x- \cos x\)

You must construct a park for the island residents. The park is a parallelogram, and must be completely inside the island. If you want to create the largest park possible, the ratio of the area of the park to the area of the beaches is \(R\). Find \(\lfloor 10R \rfloor\)

Assume that the residents don't have houses which take up any area. The island consists of only the park and beaches.

This is part of the Sinusoidal, Cosinusoidal series

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