f(x)=4sinxcos(x+π/3)+根号3 - 知识问答

f(x)=4sinxcos(x+π/3)+根号3

2个回答

f(x)=4sinxcos（x+π/3)+√3
=4sinx(1/2cosx-√3/2sinx)+√3
=2sinxcosx-2√3sin²x+√3
=sin2x+√3（1-2sin²x）
=sin2x+√3con2x
=2sin(2x+π/3)
f(x)最小正周期T=2π/2=π
-π/2+2Kπ≤2x+π/3≤π/2+2Kπ
2、
因为x∈[-π/4,π/6] 则2x+π/3∈[-π/6,2π/3]
由图像知在2x+π/3=-π/6时取得最小值=-1
2x+π/3=π/2取得最大值=2

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