Question

1 设向量a=（4cosα,sinα),b=(sinβ,4cosβ),c=(cosβ,-4sinβ)求│b+c│的最大值

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