Find the minimum positive period of the function f (x) = 2sinxcos (x + 6 beats) - cos2x + m (1), (2) When x belongs to [negative quarter beat, quarter beat], the minimum value of F (x) is negative 3, find the value of M, | Math enthusiast | Mathematical art

Find the minimum positive period of the function f (x) = 2sinxcos (x + 6 beats) - cos2x + m (1), (2) When x belongs to [negative quarter beat, quarter beat], the minimum value of F (x) is negative 3, find the value of M,

F (x) = 2sinxcos (x + 6 beats) - cos2x + M
＝sin(2x+π/6)+sin(-π/6)-cos2x+m
=sin(2x+π/6)-sin(π/2-2x)-1/2+m
=sin(2x-π/6)+m-1/2
∴T＝2π/2=π
When x = - π / 6, the function value is the smallest
Let - 1 + m - 12 = - 3, then M = 10

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