Question

已知cos（α-π/6）+sinα=4/5 根号3,则sin(α+7/6π)=?

三角函数问题

Answer 1

cos(α-π/6)+sinα
=cosα*√3/2+1/2 *sinα+sinα
=cosα*√3/2+3/2 *sinα
=√3(sinπ/6cosα+cosπ/6sinα)
=√3sin(π/6+α)=4/5√3;

sin(α+7π/6)=-sin(α+π/6+π)=-sin(α+π/6)=-4/5
修改了一下楼上的

Answer 2

cos(α-π/6)+sinα
=cosα*√3/2-1/2 *sinα+sinα
=cosα*√3/2+1/2 *sinα
=sinπ/6cosα+cosαπ/6sinα
=sin(π/6+α);

sin(α+7π/6)=-sin(α+π/6+π)=-sin(α+π/6)=-4√3/5