高中数学(必修4)的1.4节中给出了周期函数的定义,根据正弦函数和余弦函数图像及诱导公式说明了正弦函数和余弦函数都是周期函数,且周期为2kπ(k∈Z,k≠0),最小正周期为2π。正弦函数是奇函数,图像关于原点对称,由正弦函数的周期性可知图像关于点(kπ,0),k∈Z中心对称,同时图像也关于直线x=kπ+π2(k∈ The definitions of periodic functions are given in Section 1.4 of High School Mathematics (Compulsory 4). According to the sine and cosine function images and the induction formulas, it is proved that both the sine and cosine functions are periodic functions and the period is 2kπ (k∈Z, k ≠ 0), the minimum positive period is 2π. Sine function is an odd function and the image is symmetric about the origin. The periodicity of the sine function shows that the image is symmetric about the center of k∈Z (kπ, 0) and k∈Z, and the image is also symmetric about the line x = kπ + π2