Solution of trigonometric function periodic formula: (1) Definition method: f(x)=f(x+C) mentioned in the title, where C is a known quantity, then C is a minimum period of this function.
(2) Formula method: If the function relation of trigonometric function is expressed as: y=Asin(ωx+φ)+h or y=Acos(ωx+φ)+h, then the period T=2π/ω. If the functional relationship is expressed as: y=Acot(ωx+φ)+h or y=Atan(ωx+φ)+h, the period is T=π/ω.
(3) Theorem method: If f(x) is the algebraic sum of several periodic functions, that is, the function f(x)=f 1(x)+f2(x), the period of f 1(x) is T 1, and the period of f2(x) is T2.
∫f(x+p 1 T2)= f 1(x+p 1 T2)+F2(x+p 1 T2)
= f 1(x+p2t 1)+F2(x+p 1 T2)
= f 1(x)+ f2(x)
=f(x)
∴P 1T2 is the period of f(x), and P2T 1 is also the period of function f(x).
When t is the period of trigonometric function, n t is also the period of trigonometric function. Where n is a positive integer other than 0.
Minimum positive period of trigonometric function If there is a minimum positive number in all periods of a function f(x), then this minimum positive number is called the minimum positive period of f(x).
(1)y=Asin(ωx+φ)+h or y=Acos(ωx+φ)+h Minimum positive period T=2π/ω.
(2)y=Acot(ωx+φ)+h or y=Atan(ωx+φ)+h Minimum positive period T=π/ω.
(3) The minimum positive period of 3)y = | sinωx | or y=|cosωx| T=π/|ω|.
(4) The minimum positive period of 4)y = | tanωx | or y=|cotωx| T=π/|ω|.