已知函数f(x)=sinx+根号3cosx,x属于R(1)求函数f(x)的最小正周期(2)若f(a-π/3)=6/5,a属于(0,π/2),求f(2a-π/3)的值
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![已知函数f(x)=sinx+根号3cosx,x属于R(1)求函数f(x)的最小正周期(2)若f(a-π/3)=6/5,a属于(0,π/2),求f(2a-π/3)的值](/uploads/image/z/616367-47-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsinx%2B%E6%A0%B9%E5%8F%B73cosx%2Cx%E5%B1%9E%E4%BA%8ER%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%282%29%E8%8B%A5f%28a-%CF%80%2F3%29%3D6%2F5%2Ca%E5%B1%9E%E4%BA%8E%EF%BC%880%2C%CF%80%2F2%EF%BC%89%2C%E6%B1%82f%282a-%CF%80%2F3%29%E7%9A%84%E5%80%BC)
已知函数f(x)=sinx+根号3cosx,x属于R(1)求函数f(x)的最小正周期(2)若f(a-π/3)=6/5,a属于(0,π/2),求f(2a-π/3)的值
已知函数f(x)=sinx+根号3cosx,x属于R
(1)求函数f(x)的最小正周期
(2)若f(a-π/3)=6/5,a属于(0,π/2),求f(2a-π/3)的值
已知函数f(x)=sinx+根号3cosx,x属于R(1)求函数f(x)的最小正周期(2)若f(a-π/3)=6/5,a属于(0,π/2),求f(2a-π/3)的值
f(x)=2sin(x+π/3); 所以最小正周期为2π;
(2)f(a-π/3)=2sina=6/5; sina=3/5;cosa=4/5;
f(2a-π/3)=2sin2a=4sinacosa=4×(3/5)(4/5)=48/25
已知函数f(x)=sinx+(√3)cosx,x∈R;(1)求函数f(x)的最小正周期;(2)若f(α-π/3)=6/5,
α∈(0,π/2),求f(2α-π/3)的值;
(1)。f(x)=2[(1/2)sinx+(√3/2)cosx]=2[sinxcos(π/3)+cosxsin(π/3)]=2sin(x+π/3)
故最小正周期T=2π;
(2)。若f(α-π/3...
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已知函数f(x)=sinx+(√3)cosx,x∈R;(1)求函数f(x)的最小正周期;(2)若f(α-π/3)=6/5,
α∈(0,π/2),求f(2α-π/3)的值;
(1)。f(x)=2[(1/2)sinx+(√3/2)cosx]=2[sinxcos(π/3)+cosxsin(π/3)]=2sin(x+π/3)
故最小正周期T=2π;
(2)。若f(α-π/3)=2sin[(α-π/3)+π/3)]=2sinα=6/5,则sinα=3/5,α是锐角,故cosα=√(1-9/25)=4/5;
故f(2α-π/3)=2sin(2α-π/3+π/3)=2sin2α=4sinαcosα=4×(3/5)×(4/5)=48/25
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