已知A(2,3),B(1,4)且1/2向量AB=(sinα,cosβ),α,β∈(-π/2,π/2),且α+β=______
问题描述：
已知A(2,3),B(1,4)且1/2向量AB=(sinα,cosβ),α,β∈(-π/2,π/2),且α+β=______
答
1/2向量AB=（ -1/2, 1/2)
所以：sinα= - 1/2 cosβ=1/2
α,β∈(-π/2,π/2) α= - π/6 β= π/3或 - π/3
α+β=π/6 或 - π/2
答
—π/2或π/6
答
1/2*AB=1/2*(1-2,4-3)=(-1/2,1/2)
sinα=-1/2
α=-π/6
cosβ=1/2
β=-π/3或π/3
α+β=-π/6+π/3=π/6
或
α+β=-π/6-π/3=-π/2
答
可知AB(-1.1) α+β=-π/2+0=-π/2