已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n (1) 求函数f(x)的解析式 (2)求f(x)的单调递增区间 (3)如果三角形ABC的三边abc
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![已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n (1) 求函数f(x)的解析式 (2)求f(x)的单调递增区间 (3)如果三角形ABC的三边abc](/uploads/image/z/3741924-12-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fm%3D%28cos+x%2F3%2C%E6%A0%B9%E5%8F%B73cos+x+%2F3%29+n%28sin+x%2F3+%2Ccosx%2F3%29+%E5%87%BD%E6%95%B0f%28x%29%3Dm%2An%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fm%3D%28cos+x%2F3%2C%E6%A0%B9%E5%8F%B73cos+x+%2F3%29+n%28sin+x%2F3+%2Ccosx%2F3%29+%E5%87%BD%E6%95%B0f%28x%29%3Dm%2An+%281%29+%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F+%EF%BC%882%EF%BC%89%E6%B1%82f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4+%EF%BC%883%EF%BC%89%E5%A6%82%E6%9E%9C%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E4%B8%89%E8%BE%B9abc)
已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n (1) 求函数f(x)的解析式 (2)求f(x)的单调递增区间 (3)如果三角形ABC的三边abc
已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n
已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n (1) 求函数f(x)的解析式 (2)求f(x)的单调递增区间 (3)如果三角形ABC的三边abc 满足b^2=ac 且边b所对的角为x 试求x的范围及此函数f(x)的值域
已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n已知向量m=(cos x/3,根号3cos x /3) n(sin x/3 ,cosx/3) 函数f(x)=m*n (1) 求函数f(x)的解析式 (2)求f(x)的单调递增区间 (3)如果三角形ABC的三边abc
(1)f(x)=m*n=sin(x/3)cos(x/3)+√3cos²(x/3)
=1/2sin(2x/3)+√3/2cos(2x/3)+√3/2
=sin(2x/3+π/3)+√3/2.
(2)由2kπ-π/2≤2x/3+π/3≤2kπ+π/2(k∈Z),
得3kπ-5π/4≤x≤3kπ+π/4(k∈Z),
所以f(x)的单调递增区间是[3kπ-5π/4,3kπ+π/4](k∈Z).
(3)因为b²=ac,
所以由余弦定理,得cosx=(a²+c²-b²)/2ac=(a²+c²-ac)/2ac≥(2ac-ac)/2ac=1/2,
上式当且仅当a=c时等号成立.
因为x是三角形的内角,所以0