两角和与差习题sin（α-π/6）=-3/5,α∈（-π/3,π/6）,求sinα

Question

两角和与差习题
sin（α-π/6）=-3/5,α∈（-π/3,π/6）,求sinα

Answer 1

很简单的
sin（α-π/6）=3/5
则cos（α-π/6）=4/5
则sinαcosπ/6-cosαsinπ/6=3/5
cosαcosπ/6+sinαsinπ/6=4/5
则
√3/2sinα-1/2cosα=3/5 ①
√3/2cosα+1/2sinα=4/5 ②
则
①×√3+②,得
3/2sinα+1/2sinα=3√3/5+4/5
则2sinα=3√3/5+4/5
则sinα=3√3/10+2/5
采纳哦!