已知函数f(x)=2sin(2wx+π/3)(w>0),T=π,g(x)=cos^2(2x+π/3)令h(x)=g(x)-f(x),x属于【0,π/2】求函数h(x)的值域

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已知函数f(x)=2sin(2wx+π/3)(w>0),T=π,g(x)=cos^2(2x+π/3)令h(x)=g(x)-f(x),x属于【0,π/2】求函数h(x)的值域
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已知函数f(x)=2sin(2wx+π/3)(w>0),T=π,g(x)=cos^2(2x+π/3)令h(x)=g(x)-f(x),x属于【0,π/2】求函数h(x)的值域
已知函数f(x)=2sin(2wx+π/3)(w>0),T=π,g(x)=cos^2(2x+π/3)
令h(x)=g(x)-f(x),x属于【0,π/2】求函数h(x)的值域

已知函数f(x)=2sin(2wx+π/3)(w>0),T=π,g(x)=cos^2(2x+π/3)令h(x)=g(x)-f(x),x属于【0,π/2】求函数h(x)的值域
f(x)=2sin(2wx+π/3)(w>0),T=2π/2w=π/w=π,w=1,f(x)=2sin(2x+π/3),
h(x)=g(x)-f(x)=cos^2(2x+π/3)-2sin(2x+π/3)=1-sin^2(2x+π/3)-2sin(2x+π/3)
=-sin^2(2x+π/3)-2sin(2x+π/3)+1=-[sin(2x+π/3)+1]^2+2,
,x属于[0,π/2],0=1-(根号3)/2=15/4-根号3=<[sin(2x+π/3)+1]^2+2<=6,
函数h(x)的值域为[15/4-根号3,6]

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