- 高二数学问题：已知向量m(cosx,
- 已知向量m(cx,-sinx),向量n(cosx,sinx-2根号3cosx),x属于R,设f(x）=m*n+2,问题1.求函数f(x）的最小值；2.若f(x)=50/13，且x属于[π/4，π/2], 求sin2x的值。3.使不等式f(x）>=3成立的x的取值范围。4.若方程f(x）=k （0
- (1) 由已知,可得f(x)=2sin(2x+π/6)+2, ∵ -1≤sin(2x-π/6)≤1, ∴ 0≤f(x)≤4, ∴ sin(2x-π/6)=-1时,f(x)有最小值0.
(2) 由2sin(2x-π/6)+2=50/13,得sin(2x+π/6)=12/13.
∵ 2π/3≤2x+π/6≤7π/6, ∴ c(2x+π/6)=-5/13.由
sin(2x)cos(π/6)+cos(2x)sin(π/6)=12/13,
cos(2x)cos(π/6)-sin(2x)sin(π/6)=-5/13,消去cos(2x)得
sin(2x)=(12√3-5)/26.
(3) 由f(x)≥3,得sin(2x+π/6)≥1/2,
∴ 2kπ+π/6≤2x+π/6≤2kπ+5π/6 kπ≤x≤kπ+2π/3,(k∈Z).
(4) 有y=k和y=2sin(2x-π/6)+2的图象知x=up/3时,y=3,vx=up/2时,y=1, ∴ 1