已知向量a=(√3,cosωx),b=(sinωx,1)(ω>0)函数f(x)=aXb,且最小正周期为4π.1.设α,β∈[π/2,π],f(2α-π/3)=6/5,f(2β+2π/3)=-24/13,求sin(α+β)的值
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![已知向量a=(√3,cosωx),b=(sinωx,1)(ω>0)函数f(x)=aXb,且最小正周期为4π.1.设α,β∈[π/2,π],f(2α-π/3)=6/5,f(2β+2π/3)=-24/13,求sin(α+β)的值](/uploads/image/z/5243054-14-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28%E2%88%9A3%2Ccos%CF%89x%29%2Cb%3D%28sin%CF%89x%2C1%29%28%CF%89%3E0%29%E5%87%BD%E6%95%B0f%28x%29%3DaXb%2C%E4%B8%94%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E4%B8%BA4%CF%80.1.%E8%AE%BE%CE%B1%2C%CE%B2%E2%88%88%5B%CF%80%2F2%2C%CF%80%5D%2Cf%282%CE%B1-%CF%80%2F3%29%3D6%2F5%2Cf%282%CE%B2%2B2%CF%80%2F3%29%3D-24%2F13%2C%E6%B1%82sin%28%CE%B1%2B%CE%B2%29%E7%9A%84%E5%80%BC)
已知向量a=(√3,cosωx),b=(sinωx,1)(ω>0)函数f(x)=aXb,且最小正周期为4π.1.设α,β∈[π/2,π],f(2α-π/3)=6/5,f(2β+2π/3)=-24/13,求sin(α+β)的值
已知向量a=(√3,cosωx),b=(sinωx,1)(ω>0)函数f(x)=aXb,且最小正周期
为4π.1.设α,β∈[π/2,π],f(2α-π/3)=6/5,f(2β+2π/3)=-24/13,求sin(α+β)的值
已知向量a=(√3,cosωx),b=(sinωx,1)(ω>0)函数f(x)=aXb,且最小正周期为4π.1.设α,β∈[π/2,π],f(2α-π/3)=6/5,f(2β+2π/3)=-24/13,求sin(α+β)的值
已知向量a=(√3,cosωx),b=(sinωx,1)(ω>0)函数f(x)=aXb,且最小正周期为4π.
1.设α,β∈[π/2,π],f(2α-π/3)=6/5,f(2β+2π/3)=-24/13,求sin(α+β)的值
解析:∵向量a=(√3,cosωx),b=(sinωx,1)(ω>0)
∴函数f(x)=a·b=√3sinωx+ cosωx=2sin(ωx+π/6)
∵最小正周期为4π
∴f(x)=2sin(1/2x+π/6)
设α,β∈[π/2,π],
f(2α-π/3)= 2sin(α)=6/5==>sinα=3/5==>cosα=-4/5,
f(2β+2π/3)=2sin(β+π/2)=-24/13==>cosβ=-12/13==>sinβ=5/13
sin(α+β)=sinαcosβ+cosαsinβ=-36/65-20/65=-56/65