1两个充要条件定理1设函数f(x)=Atan(ωx+φ)(A0,ω0)的最小正周期为T,则当自变量x在任意两个整数间(包括两个整数本身)变化时,f(x)至少有两次失去意义的充要条件是T≤12.图1证如图1,在l1与l2,l2与l3,l3与l4之间分别只有该函数的一支图象,设A(a,0),B(a+1,0),C(a+2,0)(a∈Z), 1 Two sufficient and necessary condition theorems 1 Let the function f(x) = Atan(ωx + φ) (A0, ω0) have a minimum positive period T, then when the independent variable x is between any two integers (including two integers itself ) When changing, f(x) has at least twice the significance of the loss of the necessary and sufficient condition is T ≤ 12. Figure 1 card shown in Figure 1, between l1 and l2, l2 and l3, l3 and l4 respectively, only one of the function Branch image, set A(a,0), B(a+1,0), C(a+2,0)(a∈Z),