What is the summary of the periodic formula of function?

(1)f(x+a)=-f(x) The period is 2a. Proof process: because f(x+a)=-f(x) and f(x)=-f(x-a), so f(x+a)=f(x-a), that is, f(x+2a)=f(x), so the period is 2a.

(2) The function period formula of sinx is T=2π, and sinx is a sine function with a period of 2π.

(3) The function period formula of COSX is T=2π, and COSX is a cosine function with a period of 2π.

(4) The function period formula of Tanx and cotx is T=π, and Tanx and cotx are tangent and cotangent respectively.

(5) The function period formula of SECx and cscx is T=2π, and SECx and cscx are secant and cotangent.

Extended data:

Show the definition of function periodicity: for the function y=f(x), if there is a non-zero constant t, which makes f(x+T)=f(x) hold when x takes any value in the defined domain, the function y=f(x) is called a periodic function, and the non-zero constant t is called the period of the function.

The sentence "When the independent variable increases a certain value, the function value appears regularly" is expressed in mathematical language. For the function y=f(x), if there is a non-zero constant t, when x takes every value in the domain, f(x+T)=f(x).

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