Question

已知a,β都是锐角,sina=4/5,cos(a+β)=5/13,求sinβ的值

Answer 1

解由a,β都是锐角,sina=4/5,cos(a+β)=5/13
则cosα=3/5，sin(a+β)=12/13
则sinβ
=sin（β+α-α）
=sin（（β+α）-α）
=sin(a+β)cosα-cos(a+β)sinα
=12/13×3/5-5/13×4/5
=36/65-20/65
=16/65

追问

谢谢！顺便问下sin5π/4要怎么算

Answer 2

a,β都是锐角
a+β<π
cos(a+β)=5/13
sin(a+β)=12/13
sina=4/5
cosa=3/5
sinβ=sin(a+β-a)
=sin(a+β)cosa-cos(a+β)sina
=12/13*3/5-5/13*4/5
=16/65

追问

谢谢！顺便问下sin5π/4要怎么算

追答

sin5π/4

=sin(π+π/4)

=-sin(π/4)
=-√2/2