已知sin(π/6-θ)=根号2/3,-5π/6

题目

已知sin(π/6-θ)=根号2/3,-5π/6

答案

-5π/6<θ<-π/3
π/3<-θ<5π/6
π/2<π/6-θ<π
sin(π/6-θ)=√2/3
cos(π/6-θ)=-√7/3
cos(5π/12-θ)
=cos[π/4+(π/6-θ)]
=cosπ/4cos(π/6-θ)-sinπ/4sin(π/6-θ)
=√2/2*(-√7/3)-√2/2*√2/3
=-√17/6-1/3