已知函数f(x0=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
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已知函数f(x0=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
(1)求函数f(x)的最小正周期和图像的对称轴方程
(2)求函数f(x)在区间(-π/12,π/2)上的值域
(1)求函数f(x)的最小正周期和图像的对称轴方程
(2)求函数f(x)在区间(-π/12,π/2)上的值域
/>(1)f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
=cos(2x-π/3)+2sin(x-π/4)cos[π/2-(x+π/4)]
=cos(2x-π/3)+2sin(x-π/4)cos(π/4-x)
=cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)
=cos(2x-π/3)+sin(2x-π/2)
=cos2x*(1/2)+sin2x*(√3/2)-cos2x
=(√3/2)*sin2x-(1/2)*cos2x
=sin(2x-π/6)
∴T=2π/w=π
对称轴:2x-π/6=π/2+kπ,即x=π/3+kπ/2,k∈z
﹙2﹚∵x∈(-π/12,π/2)
∴2x-π/6∈(-π/3,5π/6)
∴函数值域为(-√3/2,1]
【满意请采纳】
=cos(2x-π/3)+2sin(x-π/4)cos[π/2-(x+π/4)]
=cos(2x-π/3)+2sin(x-π/4)cos(π/4-x)
=cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)
=cos(2x-π/3)+sin(2x-π/2)
=cos2x*(1/2)+sin2x*(√3/2)-cos2x
=(√3/2)*sin2x-(1/2)*cos2x
=sin(2x-π/6)
∴T=2π/w=π
对称轴:2x-π/6=π/2+kπ,即x=π/3+kπ/2,k∈z
﹙2﹚∵x∈(-π/12,π/2)
∴2x-π/6∈(-π/3,5π/6)
∴函数值域为(-√3/2,1]
【满意请采纳】
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