用sin(α+β)=sinαcosβ+cosαsinβ找出sin(17π/12)的值

题目

用sin(α+β)=sinαcosβ+cosαsinβ找出sin(17π/12)的值
另外一道：条件tanA=2/5,如果角A在坐标象限1；cosB=-2/3,如果角B在坐标象限3.找出cos(A-B)确切的值.

答案

sin(17π/12)=sin(6π/12+9π/12)=sin(π/2+3π/4)=sinπ/2cos3π/4+cosπ/2sin3π/4=-√2/2+0=-√2/2tanA=2/5,角A在坐标象限1则sinA=2/√29,cosA=5/√29cosB=-2/3,角B在坐标象限3则sinB=-√5/3,cos(A-B)= cosAcosB+...