Proof process: Since du is f(x+a)=-f(x) and f(x)=-f(x-a), zhi(x+a)= f(x-a), that is, f(x+2a)=f(x), so the period is 2a.
The function period formula of sinx is T=2π, and sinx is a sine function with a period of 2π.
The function period formula of cosx is T=2π, and cosx is a cosine function with a period of 2π.
The function period formula of tanx and cotx is T=π, and tanx and cotx are tangent and cotangent respectively.
The function period formula of secx and cscx is T=2π, and secx and cscx are secant cotangent.
Y=Asin(wx+b) Periodic White Formula DUT = 2π zhi/w
Y=Acos(wx+b) periodic formula t = 2π/w.
Y=Atan(wx+b) periodic formula t = π/w.
Important inference:
If the function f(x)(x∈D) has two symmetry axes x=a and x=b in the definition domain, then the function f(x) is a periodic function with a period T=2|b-a| (not necessarily the minimum positive period).
If the function f(x)(x∈D) has two symmetrical centers A(a, 0) and B(b, 0) in the defined domain, then the function f(x) is a periodic function with a period T=2|b-a| (not necessarily the minimum positive period).
If the function f(x)(x∈D) has an axis of symmetry x=a and a center of symmetry B(b, 0)(a≠b) in the defined domain, then the function f(x) is a periodic function with a period T=4|b-a| (not necessarily the minimum positive period).