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ASU 574 Commonwealth of Independent States 91 f(x)=acos(x+1)+bcos(x+2)+ccos(x+3)

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August 15, 2019
trigonometryfunctionalgebra

Problem Statement

Let f(x)=acos⁡(x+1)+bcos⁡(x+2)+ccos⁡(x+3)f(x) = a \cos(x + 1) + b \cos(x + 2) + c \cos(x + 3), where a,b,ca, b, c are real. Given that f(x)f(x) has at least two zeros in the interval (0,π)(0, \pi), find all its real zeros.
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