已知sin(a+π/6)+cosa=4/5倍根号3,则sin(a+π/3)=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/26 14:13:37
已知sin(a+π/6)+cosa=4/5倍根号3,则sin(a+π/3)=已知sin(a+π/6)+cosa=4/5倍根号3,则sin(a+π/3)=已知sin(a+π/6)+cosa=4/5倍根号

已知sin(a+π/6)+cosa=4/5倍根号3,则sin(a+π/3)=
已知sin(a+π/6)+cosa=4/5倍根号3,则sin(a+π/3)=

已知sin(a+π/6)+cosa=4/5倍根号3,则sin(a+π/3)=
sin(a+π/6)+cosa
=sina*(v3/2)+cosa*(1/2)+cosa
=v3[sina*(1/2)+cosa*(v3/2)]
=v3sin(a+π/3)
=(4/5)*v3,
——》sin(a+π/3)=4/5.

∵sin(a+π/6)+cos a=(4/5)√3
∴sin(a+π/6)+cos((a+π/6)-π/6)=(4/5)√3
(3/2)sin(a+π/6)+(√3/2)cos(a+π/6)=(4/5)√3
∴(√3/2) sin(a+π/6)+(1/2)cos(a+π/6)=4/5
sin(a+π/3)=sin((a+π/6)+π/6)= (√3/2)sin(a+...

全部展开

∵sin(a+π/6)+cos a=(4/5)√3
∴sin(a+π/6)+cos((a+π/6)-π/6)=(4/5)√3
(3/2)sin(a+π/6)+(√3/2)cos(a+π/6)=(4/5)√3
∴(√3/2) sin(a+π/6)+(1/2)cos(a+π/6)=4/5
sin(a+π/3)=sin((a+π/6)+π/6)= (√3/2)sin(a+π/6)+(1/2)cos(a+π/6)=4/5

收起