已知π/4小于4分之3π,0小于β小于π/4,cosα=5/13,sinβ=5/13,求sinα+β
问题描述:
已知π/4小于4分之3π,0小于β小于π/4,cosα=5/13,sinβ=5/13,求sinα+β
答
π/4<α<3π/4
cosα=5/13
sinα=根号(1-cos^2α)=12/13
0<β<π/4
sinβ=5/13
cosβ=根号(1-sin^2β)=12/13
sin(α+β)=sinαcosβ+cosαcosβ
= 12/13 * 12/13 + 5/13 * 5/13
= 1