f(x)=2根号3sin^2x-sin(2x-π/3)若x属【-π/2,0】,求函数f(x)的最大值
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f(x)=2根号3sin^2x-sin(2x-π/3)若x属【-π/2,0】,求函数f(x)的最大值
f(x)=2根号3sin^2x-sin(2x-π/3)
若x属【-π/2,0】,求函数f(x)的最大值
f(x)=2根号3sin^2x-sin(2x-π/3)若x属【-π/2,0】,求函数f(x)的最大值
f(x)=√3*(1-cos2x)-(sin2xcosπ/3-cos2xsinπ/3)
=√3-√3cos2x-1/2sin2x+√3/2*cos2x
=√3-√3/2*cos2x-1/2*sin2x
=√3-sin(π/3+2x)
∵x∈[-π/2,0]
∴π/3+2x∈[-2π/3,π/3]
∴sin(π/3+2x)∈[-1,√3/2]
∴f(x)∈[√3/2,1+√3]
∴f(x)的最大值为1+√3
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