题目

已知cos(θ-π/6)＝3/5,θ∈(π/6,2π/3),求sinθ

提问时间：2020-09-05

答案

∵cos(θ-π/6)＝3/5,θ∈(π/6,2π/3),求
∴θ-π/6∈(0,π/2)
sin(θ-π/6)=4/5
∴sinθ
=sin[(θ-π/6)+π/6]
=sin(θ-π/6)cosπ/6+cos(θ-π/6)sinπ/6
=4/5*√3/2+3/5*1/2
=(4√3+3)/10