若A是锐角,sin(A-π/6）=1/3,则cos - 知识问答

若A是锐角,sin(A-π/6）=1/3,则cosA的值等于多少? 要过程

1个回答

cosA=cos(A-π/6+π/6)=cos(A-π/6)cosπ/6-sin(A-π/6)sinπ/6
0＜A＜π/2
-π/6＜A-π/6＜π/3
cos(A-π/6)＞0
sin(A-π/6）=1/3
cos(A-π/6）=(2√2)/3
cosA=(2√2)/3*√3/2-(1/3)*(1/2)
=√6/3-(1/6)
=[(2√6)-1]/6

相关问题