1设向量a=（4cosα,sinα),b=(sinβ,4cosβ),c=(cosβ,-4sinβ)求│b+c│的最大值?2y=2sin2x,求f（x)在区间[-π/6,2/π]上的最大值和最小值?3设函数f(x)=sin(2x+φ)(-π

Question

1 设向量a=（4cosα,sinα),b=(sinβ,4cosβ),c=(cosβ,-4sinβ)求│b+c│的最大值?
2 y=2sin2x,求f（x)在区间[-π/6,2/π]上的最大值和最小值?
3 设函数f(x)=sin(2x+φ)(-π

Answer 1

1.|b+c|^2=(sinβ+cosβ)^2+(4cosβ-4sinβ)^2
=1+2sinβcosβ+16-32sinβcosβ
=17-15sin2β
≤17-15×(-1)
=32
|b+c|≤4√2
2.-π/6≤x≤π/2
-π/3≤2x≤π
-√3/2≤sin2≤1
-√3≤y≤12
3.f(π/8)=sin(2π/8+φ)=sin(π/4+φ)
-π