The trigonometric function was first taught in high school. Which book does the People's Education Edition require the periodic function to be in? As a matter of fact, as mentioned in compulsory one, the function is periodic, but it is abstract. Compulsory four is an example ~

Do periodic functions have inverse functions? I read a book that the periodic function has no inverse function. But isn't the inverse of trigonometric function an inverse trigonometric function? The inverse trigonometric function is not the inverse of trigonometric function. The inverse trigonometric function has a domain, for example, the domain of arcsin(x) is-1 ~+ 1. One function value of a periodic function corresponds to the values of multiple independent variables.

There is no inverse function, because the inverse function needs one x to one y, one y to one x, the periodic function needs one y to countless x, and the inverse trigonometric function has restrictions, so it is guaranteed that one x to one y and one y to one x are not contradictory.

Is periodic function multiplied by periodic function or periodic function? This is a periodic function.

Introduction to Advanced Mathematics in China: If both f(x) and g(x) are functions with a period ω, their sum, difference, product and quotient (except the point with a denominator of 0) are still functions with a period ω.

In which book did you learn the compound function?

A periodic function multiplied by an aperiodic function is an aperiodic function, right?

Is the function a periodic function, an original function or a periodic function? Not necessarily.

For example, f(x)=cosx is a periodic function, and its original function F(x)=sinx is also a periodic function.

For example, f(x)= 1 is a periodic function, but its original function F(x)=x is not a periodic function.

The periodicity of a function has nothing to do with its original function.

Is the derivative of a periodic function a periodic function? If the derivative of a periodic function exists, it must be a periodic function, and its period is equal to that of the original function.

Function is a periodic function. Is its derivative a periodic function? I think so.

The geometric meaning of derivative function is the slope of each point.

If a function is periodic, its slope is also periodic.

It should be easy to imagine, such as y=sinx.

Let f(x) be a function with a period of t, then:

f(x)=f(x+T)

Both sides are deduced at the same time, there are

f'(x)=f'(x+T)

It is known that the derivative function of f(x) is still a periodic function.

Is f(x) a periodic function and f'(x) a periodic function? Let the period be t

f(x+T)=f(x)

Deduce f'(x+T)=f'(x)

F'(x) has a period of t.