已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域速求!
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![已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域速求!](/uploads/image/z/11561258-2-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28CosX%2C%E6%A0%B9%E5%8F%B73SinX%EF%BC%89%2Cb%3D%EF%BC%88CosX%2CCosX%EF%BC%89%2C%E5%87%BD%E6%95%B0f%EF%BC%88X%29%3Da%E4%B9%98b%2C%E6%B1%82%E5%87%BD%E6%95%B0f%EF%BC%88X%29%E5%9C%A8%E3%80%90-%CF%80%2F2%2C0%E3%80%91%E7%9A%84%E5%80%BC%E5%9F%9F%E9%80%9F%E6%B1%82%21)
已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域速求!
已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域
速求!
已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域速求!
f(x)
=cos²x+√3sinxcosx
=1/2(2cos²x-1)+√3sinxcosx+1/2
=1/2cos2x+√3/2sin2x+1/2
=cos(2x-π/3)+1/2
当x∈[-π/2,0]时,(2x-π/3)∈[-4π/3,-π/3]
2x-π/3=-π/3时,f(x)取最大为1;2x-π/3=-π时,f(x)取最小为-1/2
故f(x)的值域为[-1/2,1]
已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域
解析:f(x)=(cosx)^2+√3sinxcosx=1/2+cos2x/2+√3/2sin2x=sin(2x+π/6)+1/2
f(-π/2)=sin(-π+π/6)+1/2=0
f(-π/3)=sin(-2π/3+π/6)+1/2=-1/...
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已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域
解析:f(x)=(cosx)^2+√3sinxcosx=1/2+cos2x/2+√3/2sin2x=sin(2x+π/6)+1/2
f(-π/2)=sin(-π+π/6)+1/2=0
f(-π/3)=sin(-2π/3+π/6)+1/2=-1/2
f(0)=sin(0+π/6)+1/2=1
所以f(X)在【-π/2,0】的值域【-1/2,1】
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已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域
解析:f(x)=(cosx)^2+√3sinxcosx=1/2+cos2x/2+√3/2sin2x=sin(2x+π/6)+1/2
f(-π/2)=sin(-π+π/6)+1/2=0
f(-π/3)=sin(-2π/3+π/6)+1/2=-1/...
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已知向量a=(CosX,根号3SinX),b=(CosX,CosX),函数f(X)=a乘b,求函数f(X)在【-π/2,0】的值域
解析:f(x)=(cosx)^2+√3sinxcosx=1/2+cos2x/2+√3/2sin2x=sin(2x+π/6)+1/2
f(-π/2)=sin(-π+π/6)+1/2=0
f(-π/3)=sin(-2π/3+π/6)+1/2=-1/2
f(0)=sin(0+π/6)+1/2=1
所以f(X)在【-π/2,0】的值域【-1/2,1】(x)
=cos²x+√3sinxcosx
=1/2(2cos²x-1)+√3sinxcosx+1/2
=1/2cos2x+√3/2sin2x+1/2
=cos(2x-π/3)+1/2
当x∈[-π/2,0]时,(2x-π/3)∈[-4π/3,-π/3]
2x-π/3=-π/3时,f(x)取最大为1;2x-π/3=-π时,f(x)取最小为-1/2
故f(x)的值域为[-1/2,1]
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