IMO 1989 LL INA43

Let f(x) = a sin2 x+b sin x+c, where a, b, and c are real num-

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IMO 1989 LL INA43

Origin: INA

Problem

Let f(x) = a sin2 x+b sin x+c, where a, b, and c are real num- bers. Find all values of a, b, and c such that the following three conditions are satisfied simultaneously: (i) f(x) = 381 if sin x = 1/2. (ii) The absolute maximum of f(x) is 444. (iii) The absolute minimum of f(x) is 364.