f(x)=sinx-cos2x x∈(π/6,5π/6] 则f(x)值域

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f(x)=sinx-cos2x x∈(π/6,5π/6] 则f(x)值域
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f(x)=sinx-cos2x x∈(π/6,5π/6] 则f(x)值域
f(x)=sinx-cos2x x∈(π/6,5π/6] 则f(x)值域

f(x)=sinx-cos2x x∈(π/6,5π/6] 则f(x)值域
f(x)=sinx-cos2x=sinx-(1-2sinx方)=2sinx方+sinx-1,因为x属于(pai/6,5pai/6],所以当sinx=1时,函数最大值为f(x)=2,当x=5pai/6时,函数最小f(x)=0,所以函数值域为[0,2].