函数=3sinxcosx-√3cos^2x,x属于[π/3,π/2]的值域是 ________

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函数=3sinxcosx-√3cos^2x,x属于[π/3,π/2]的值域是 ________

函数=3sinxcosx-√3cos^2x,x属于[π/3,π/2]的值域是 ________
函数=3sinxcosx-√3cos^2x,x属于[π/3,π/2]的值域是 ________

函数=3sinxcosx-√3cos^2x,x属于[π/3,π/2]的值域是 ________
f(x)=3sinxcosx-√3cos^2x
=(3sin2x)/2-√3(1+cos2x)/2
=(3/2)sin2x-(√3/2)cos2x-√3/2
=√3[sin2x*cos(π/6)-cos(2x)sin(π/6)]-√3/2
=√3sin(2x-π/6)-√3/2
x ∈[π/3,π/2]
2x-π/6∈[-π/6,5π/6]
当2x-π/6=-π/6时,f(x)有最小值-(√3/2)-√3/2=-√3
当2x-π/6=π/2时,f(x)有最大值√3-√3/2=√3/2
值域为[-√3,√3/2]