已知cosα=-1/5,π/2<α<π,则sinα/2等于___(

问题描述:

已知cosα=-1/5,π/2<α<π,则sinα/2等于___(

π/2<α<π
π/4<α/2<π/2
√2cosα=1-2sin^2(α/2)=-1/5
sin^2(α/2)=3/5
sinα/2=√3/5=(√15)/5

π/4<a/2<π/2
锐角,sina/2>0
cosa=1-2sin²(a/2)=-1/5
即sin²(a/2)=3/5
sina/2=√15/5