Question

将函数f(x)=根号3cosx-sinx的图像按向量（-a，0）平移（a>0) 所得图像对应的函数为偶函数 则a的最小值为

Answer 1

f(x) = (√3)cosx - sinx = 2[(√3/2)cosx - (1/2)sinx] = 2[sin(π/3)cosx - cos(π/3)sinx]
= 2sin(π/3 - x)
= -2sin(x - π/3)
图像按向量(-a, 0)平移, 相当于向左平移a个单位; 现在需要找出y轴右方最近正漏的对称敬清此轴.
正弦函数的对称轴为 x = π/2 + nπ (n为整数)
n = 0: x - π/3 = π/2, x = 5π/6

n = 1: x - π/3 = 3π/2, x = 11π/6
y轴右方最近的亮迅对称轴: x = 5π/6
a = 5π/6