MathDB

Let f(x) \equal{} a \sin^2x \plus{} b \sin x \plus{} c, where

a, b,

and

c

are real numbers. Find all values of

a, b

and

c

such that the following three conditions are satisfied simultaneously: (i) f(x) \equal{} 381 if \sin x \equal{} \frac{1}{2}. (ii) The absolute maximum of

f(x)

444.

(iii) The absolute minimum of

f(x)

364.

Problem Statement