已知向量a=(2sinx,根号2cosx+1),向量b=(根号3cosx,根号2cosx-1)函数f(x)=向量a乘向量b求函数最小正周期和在区间【0,π/2】上最大最小值若f(a)=8/5,a属于【π/4,π/2】,求sinx值
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![已知向量a=(2sinx,根号2cosx+1),向量b=(根号3cosx,根号2cosx-1)函数f(x)=向量a乘向量b求函数最小正周期和在区间【0,π/2】上最大最小值若f(a)=8/5,a属于【π/4,π/2】,求sinx值](/uploads/image/z/2626310-38-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%282sinx%2C%E6%A0%B9%E5%8F%B72cosx%2B1%29%2C%E5%90%91%E9%87%8Fb%3D%28%E6%A0%B9%E5%8F%B73cosx%2C%E6%A0%B9%E5%8F%B72cosx-1%29%E5%87%BD%E6%95%B0f%28x%29%3D%E5%90%91%E9%87%8Fa%E4%B9%98%E5%90%91%E9%87%8Fb%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%92%8C%E5%9C%A8%E5%8C%BA%E9%97%B4%E3%80%900%2C%CF%80%2F2%E3%80%91%E4%B8%8A%E6%9C%80%E5%A4%A7%E6%9C%80%E5%B0%8F%E5%80%BC%E8%8B%A5f%EF%BC%88a%29%3D8%2F5%2Ca%E5%B1%9E%E4%BA%8E%E3%80%90%CF%80%2F4%2C%CF%80%2F2%E3%80%91%2C%E6%B1%82sinx%E5%80%BC)
已知向量a=(2sinx,根号2cosx+1),向量b=(根号3cosx,根号2cosx-1)函数f(x)=向量a乘向量b求函数最小正周期和在区间【0,π/2】上最大最小值若f(a)=8/5,a属于【π/4,π/2】,求sinx值
已知向量a=(2sinx,根号2cosx+1),向量b=(根号3cosx,根号2cosx-1)函数f(x)=向量a乘向量b
求函数最小正周期和在区间【0,π/2】上最大最小值
若f(a)=8/5,a属于【π/4,π/2】,求sinx值
已知向量a=(2sinx,根号2cosx+1),向量b=(根号3cosx,根号2cosx-1)函数f(x)=向量a乘向量b求函数最小正周期和在区间【0,π/2】上最大最小值若f(a)=8/5,a属于【π/4,π/2】,求sinx值
f(x)=向量a乘向量b
=2sinx*√3cosx+(√2cosx+1)(√2cosx-1)
=√3sin2x+2(cosx)²-1
=√3sin2x+cos2x
=2sin(2x+π/6)
∴T=π.x属于[0,π/2] 2x+π/6属于[π/6,7π/6]
f(x)属于[-1,2].∴f(x)max=2 f(x)min=-1.
f(a)=8/5
2sin(2a+π/6)=8/5
sin(2a+π/6)=4/5.
sin(π/2-(-2a+π/3))=4/5
cos(2a-π/3)=4/5
1-2[2sin(a-π/6)]²=4/5 a属于[π/4,π/2]
sin(a-π/6)=√10/10 cos(a-π/6)=3√10/10
sina=sin(a-π/6+π/6)
=sin(a-π/6)*cosπ/6+cos(a-π/6)*sinπ/6
=√10/10*√3/2+3√10/10*1/2
=(√30+3√10)/20.