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求函数f(x)=sin(x+π/3)+2sin(x-π/3)的最大值和最小值 明白,立刻就给分.我着急要.所以以最快的为标准
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求函数f(x)=sin(x+π/3)+2sin(x-π/3)的最大值和最小值 明白,立刻就给分.我着急要.所以以最快的为标准
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答案和解析
f(x)=sin(x+π/3)+2sin(x-π/3)
=sinxcosπ/3+cosxsinπ/3+2sinxcosπ/3-2cosxsinπ/3
=3/2*sinx-√3/2*cosx
=√3(sinx*√3/2-cosx*1/2)
=√3(sinxcosπ/6-cosxsinπ/6)
=√3sin(x-π/6)
所以最大值=√3,最小值=-√3
=sinxcosπ/3+cosxsinπ/3+2sinxcosπ/3-2cosxsinπ/3
=3/2*sinx-√3/2*cosx
=√3(sinx*√3/2-cosx*1/2)
=√3(sinxcosπ/6-cosxsinπ/6)
=√3sin(x-π/6)
所以最大值=√3,最小值=-√3
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