已知角a的终边与π/6的终边关于直线y=x对称,且a属于(-4π,4π),则a=?答案是-11π/3,-5π/3,π/3,7π/3

题目

已知角a的终边与π/6的终边关于直线y=x对称,且a属于(-4π,4π),则a=?答案是-11π/3,-5π/3,π/3,7π/3

答案

Y=X是斜率为45度=π/4
角a的终边与π/6关于Y=X对称,则a-π/4=π/4-π/6
a=(π/4+π/4-π/6)=π/3
因为a∈（-4π,4π）,
所以在此区间内a可以取值π/3-4π,π/3-2π,π/3,π/3+2π
因此a=-11π/3或-5π/3,或π/3,或7π/3