已知向量m=(cosθ,-sinθ),n=(根号2+sinθ,cosθ),θ∈(π,3π/2),且cos(θ/2+π/8)=-4/5,求|m+n|的值谢谢

题目

已知向量m=(cosθ,-sinθ),n=(根号2+sinθ,cosθ),θ∈(π,3π/2),且cos(θ/2+π/8)=-4/5,求|m+n|的值谢谢

答案

θ∈(π,3π/2),且cos(θ/2+π/8)=-4/5,所以sin(θ/2+π/8)=-3/5因为m=(cosθ,-sinθ)和n＝(√2+sinθ,cosθ)所以m+n=（√2+sinθ+ cosθ,-sinθ+cosθ）所以|m+n|=√[(√2+sinθ+ cosθ)^2+(-sinθ+cosθ)^2]=√[(2...