若角2a的中边与角π/6的中边关于Y=X对称,且a ∈（-2π,2π）,求a

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