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.
网友回答
(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)= √3
A+π/6 = π/3
A = π/6b/sinB = c/sinC
2c/sin(5π/6-C) = c/sinC
2sinC = sin(5π/6-C)
=(1/2)sinC + (√3/2)cosC
(3/2) sinC = (√3/2)cosC
tanC =√3/3
C = π/6