函数f(x)=sin(2x/3+π/2)+sin2x/3的图像相邻的两条对称轴之间的距离是

问题描述:

函数f(x)=sin(2x/3+π/2)+sin2x/3的图像相邻的两条对称轴之间的距离是


f(x) = cos(2x/3) + sin(2x/3) = √2sin(2x/3+π/4)
相邻对称轴的距离为周期的一半。
d = 1/2T = 1/2× 2π/(2/3) = 3π/2

3π/2

f(x)=cos2x/3+sin2x/3
=√2sin(2x/3+π/4)
对称轴就是取最值得地方
所以即sin(2x/3+π/4)=±1
所以相邻的就是差半个周期
T=2π/(2/3)=3π
所以距离是3π/2