函数f（x）=sin x^2+√3 sinx cosx在区间【π/4,π/2】上有最小值是___
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函数f（x）=sin x^2+√3 sinx cosx在区间【π/4,π/2】上有最小值是___
函数f（x）=sin x^2+√3 sinx cosx在区间【π/4,π/2】上有最小值是___
函数f（x）=sin x^2+√3 sinx cosx在区间【π/4,π/2】上有最小值是___
=sin²x+√3sinxcosx
=(1-cos(2x))/2+√3/2*sin(2x)
=√3/2*sin(2x) -cos(2x)/2+1/2
= sin(2x-π/6) +1/2
X∈[π/4,π/2],
2x-π/6∈[π/3,5π/6],
当2x-π/6=5π/6时,函数取到最小值1/2+1/2=1.
f(x)=sin^2x+√3 sinxcosx
f(x)=(1-cos2x)/2+√3 sin2x/2
f(x)=1/2-((1/2)*cos2x-(√3/2)*sin2x)
f(x)=1/2-(sinπ/6*cos2x-cosπ/6*sin2x)
f(x)=1/2-sin(π/6-2x)
x在R上的f(x)最小值f(π/2+2kπ)=1/2-1=-1/2<...
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f(x)=sin^2x+√3 sinxcosx
f(x)=(1-cos2x)/2+√3 sin2x/2
f(x)=1/2-((1/2)*cos2x-(√3/2)*sin2x)
f(x)=1/2-(sinπ/6*cos2x-cosπ/6*sin2x)
f(x)=1/2-sin(π/6-2x)
x在R上的f(x)最小值f(π/2+2kπ)=1/2-1=-1/2
π/6-2x=π/2+2kπ
x=-π/6-kπ不在区间【,π/2】
讨论区间两端点
f(π/4)=1/2-sin(π/6-2π/4)=1/2-sin(-π/6)=(1+√3)/2
f(π/2)=1/2-sin(π/6-2π/2)=1/2-sin(-5π/6)=1
f(π/4)>f(π/2)
f(x)=sin x^2+√3 sinx cosx在区间【π/4,π/2】上有最小值是1
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