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Write vectors in R2 as (x,y). Define the relation on R2 by writing (x1,y1) ∼ (x2,y2)...

Write vectors in R2 as (x,y). Define the relation on R2 by writing (x1,y1) ∼ (x2,y2) iff y1 − sin x1 = y2 − sin x2 . Prove that ∼ is an equivalence relation.

Find the classes [(0, 0)], [(2, π/2)] and draw them on the plane. Describe the sets which are the equivalence classes for this relation.

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