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Maximum Value of Trigonometric Functions

Source: 1983 National High School Mathematics League, Exam Two, Problem 5

February 22, 2020
function

Problem Statement

Function F(x)=∣cos⁡2x+2sin⁡xcos⁡x−sin⁡2x+Ax+B∣F(x)=|\cos^2x+2\sin x\cos x-\sin^2x+Ax+B|, where A,BA,B are two real numbers, x∈[0,32π]x\in[0,\frac{3}{2}\pi]. MM is the maximun value of F(x)F(x). Find the minumum value of MM.
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