若平面向量m=(根号3,-2sinx/2),向量n=(cosx,-cosx/2)(x属于R),函数f(x)=向量m*向量n

题目

若平面向量m=(根号3,-2sinx/2),向量n=(cosx,-cosx/2)(x属于R),函数f(x)=向量m*向量n
(1)求函数f(x)的值域.
(2)记三角形ABC的内角A,B,C的对边长分别为a,b,c,若f(A)=根号3,且b=2c,求角C的值.

答案

(1)m=(√3,-2sinx/2), n=(cosx,-cosx/2)f(x) =m.n=√3cosx+2(sinx/2)cosx/2=√3cosx+sinx= 2sin(x+π/6)值域 = [-2,2](2)f(A)= √3=> 2sin(A+π/6)= √3A+π/6 = π/3A = π/6b/sinB = c/sinC2c/sin(5π/6-C) = c/si...