Question

函数f(x)=2sin(2x+兀/6)的对称轴对称中心

Answer 1

对称轴：2x + π/6=kπ + π/2
2x=kπ + π/3
∴x=kπ/2 + π/6，(k∈Z)
对称中心：2x + π/6=kπ
2x=kπ - π/6
x=kπ/2 - π/12
则对称中心是(kπ/2 - π/12，0)，(k∈Z)

Answer 2

f(x) = cos2wx + sqrt(3) sin2wx = 2 sin(2wx + pi/6) the period of this function is 2pi/(2w) = pi/w so w = 2 2. f(A) = 2sin(2wA+pi/6) = 1, 4A+pi/6 = 5pi/6 A = pi/6 when b=c, b+c is maximum b = sqrt(3)/sin15 = 2sqrt(3) / sqrt(2-sqrt(3))