已知sin(π/6-θ)=﹣3/5,π/6<θ<2π/3,求sinθ与cos2θ的值!具体过程,限今晚.谢谢!

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已知sin(π/6-θ)=﹣3/5,π/6<θ<2π/3,求sinθ与cos2θ的值!具体过程,限今晚.谢谢!
已知sin(π/6-θ)=﹣3/5,π/6<θ<2π/3,求sinθ与cos2θ的值!具体过程,限今晚.谢谢!

已知sin(π/6-θ)=﹣3/5,π/6<θ<2π/3,求sinθ与cos2θ的值!具体过程,限今晚.谢谢!
sin(π/6-θ)=﹣3/5,π/6<θ<2π/3,
则cos(π/6-θ)=4/5,
sinθ=sin[π/6 -(π/6-θ)]
= sinπ/6cos(π/6-θ)- cosπ/6 sin(π/6-θ)
=(4+3√3)/10.
cos2θ=1-2 sin²θ=(7-24√3)/50.