已知函数f(x)=sin(wx+π/6)(w>0)的最小正周期为π设a∈(0,π/2),β∈(π/2,π),f(a/2+π/6)=3/5,f(β/2+5π/12)=-12/13,求sin(a+β)的值
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![已知函数f(x)=sin(wx+π/6)(w>0)的最小正周期为π设a∈(0,π/2),β∈(π/2,π),f(a/2+π/6)=3/5,f(β/2+5π/12)=-12/13,求sin(a+β)的值](/uploads/image/z/10135966-22-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28wx%2B%CF%80%2F6%29%28w%EF%BC%9E0%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E4%B8%BA%CF%80%E8%AE%BEa%E2%88%88%280%2C%CF%80%2F2%29%2C%CE%B2%E2%88%88%28%CF%80%2F2%2C%CF%80%29%2Cf%28a%2F2%2B%CF%80%2F6%29%3D3%2F5%2Cf%28%CE%B2%2F2%2B5%CF%80%2F12%29%3D-12%2F13%2C%E6%B1%82sin%28a%2B%CE%B2%29%E7%9A%84%E5%80%BC)
已知函数f(x)=sin(wx+π/6)(w>0)的最小正周期为π设a∈(0,π/2),β∈(π/2,π),f(a/2+π/6)=3/5,f(β/2+5π/12)=-12/13,求sin(a+β)的值
已知函数f(x)=sin(wx+π/6)(w>0)的最小正周期为π
设a∈(0,π/2),β∈(π/2,π),f(a/2+π/6)=3/5,f(β/2+5π/12)=-12/13,求sin(a+β)的值
已知函数f(x)=sin(wx+π/6)(w>0)的最小正周期为π设a∈(0,π/2),β∈(π/2,π),f(a/2+π/6)=3/5,f(β/2+5π/12)=-12/13,求sin(a+β)的值
数理答疑团为您解答,希望对你有所帮助.
函数f(x)=sin(wx+π/6)(w>0)的最小正周期为π,则w=2
f(a/2+π/6)=3/5,即sin(a+π/3+π/6)=3/5,sin(a+π/2)=3/5,a∈(0,π/2),
则cosa=3/5,sina=4/5,
f(β/2+5π/12)= -12/13,即sin(β+5π/6+π/6)= -12/13,sin(β+π)= -12/13,β∈(π/2,π),
则sinβ= 12/13,cosβ= 5/13,
所以:sin(a+β)=sinacosβ+cosasinβ=56/65
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