函数f(x)=2sin(x-4/π)-sin2x的值域为

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函数f(x)=2sin(x-4/π)-sin2x的值域为
函数f(x)=2sin(x-4/π)-sin2x的值域为

函数f(x)=2sin(x-4/π)-sin2x的值域为
f(x)=2sin(x-π/4)-sin2x
f(x)=2sin(x-π/4)-cos(2x-π/2)
f(x)=2sin(x-π/4)-cos[2(x-π/4)]
f(x)=2sin(x-π/4)-[1-2sin²(x-π/4)]
令t=sin(x-π/4) ,t∈[-1,1]
f(t)=2t²+2t-1
所以f(x)的值域是[-1.5,3]

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