已知sinα=3/5,α∈(0,π/2),cosβ=-12/13,β∈(π/2,π).求sin(α+β)的值.求详解,
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![已知sinα=3/5,α∈(0,π/2),cosβ=-12/13,β∈(π/2,π).求sin(α+β)的值.求详解,](/uploads/image/z/11466141-69-1.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B1%3D3%2F5%2C%CE%B1%E2%88%88%280%2C%CF%80%2F2%29%2Ccos%CE%B2%3D-12%2F13%2C%CE%B2%E2%88%88%28%CF%80%2F2%2C%CF%80%29.%E6%B1%82sin%28%CE%B1%2B%CE%B2%29%E7%9A%84%E5%80%BC.%E6%B1%82%E8%AF%A6%E8%A7%A3%2C)
已知sinα=3/5,α∈(0,π/2),cosβ=-12/13,β∈(π/2,π).求sin(α+β)的值.求详解,
已知sinα=3/5,α∈(0,π/2),cosβ=-12/13,β∈(π/2,π).求sin(α+β)的值.求详解,
已知sinα=3/5,α∈(0,π/2),cosβ=-12/13,β∈(π/2,π).求sin(α+β)的值.求详解,
利用sin²x+cos²x=1
sinα=3/5,α∈(0,π/2),
∴cosα=4/5
cosβ=-12/13,β∈(π/2,π)
sinβ=5/13
sin(α+β)
=sinαcosβ+cosαsinβ
=3/5*(-12/13)+4/5*5/13
=-16/65