Question

已知a(-兀/2,兀)若函数f(x)=cos(x+兀/6+a)为奇函数,则函数y=sin(2x

Answer 1

已知α∊(-π/2,π)若函数f(x)=cos(x+π/6+α)为奇函数,则函数y=sin(2x+a)在(0,π/3)上的对称轴是?

∵f(x)=cos(x+π/6+α)为奇函数,∴π/6+α=-π/2；即α=-π/2-π/6=-2π/3；

此时f(x)=cos(x-π/2)=cos(π/2-x)=sinx是奇函数.

y=sin(2x-2π/3)在(0,π/3)上的对称轴x=π/12.