13问答网 > 已知π⼀4<α<3π⼀4,0<β<π⼀4,cos(π⼀4+α)=-3⼀5,sina(3π⼀4+β)=5⼀13,求sina(α+β)的值

已知π⼀4<α<3π⼀4,0<β<π⼀4,cos(π⼀4+α)=-3⼀5,sina(3π⼀4+β)=5⼀13,求sina(α+β)的值

2025-05-09 09:09:18

推荐回答（2个）

回答1：

π/4<α<3π/4 ，cos(π/4+α)=-3/5 …… sin(π/4+α)=4/5

0<β<π/4， sin(3π/4+β)=5/13…… cos(3π/4+β)= - 12/13

sina(α+β)= - sin（α+β+π）=- sin（(π/4+α)+(3π/4+β）)

= - (sin(π/4+α)*cos(3π/4+β) + cos(π/4+α)*sin(3π/4+β) )

=63/65

回答2：

π/4<α<3π/4 cos(π/4+α)=-3/5 就有 sin(π/4+α)=4/5

0<β<π/4 sin(3π/4+β)=5/13 cos(3π/4+β)= - 12/13

sina(α+β)= - sin（α+β+π）=- sin（(π/4+α)+(3π/4+β）)

= - (sin(π/4+α)*cos(3π/4+β) + cos(π/4+α)*sin(3π/4+β) )

=自己算吧