Trig Functions Periodicity: Which Function is Not Periodic?

[Saitama]

What you need is that you can add some constant to x and when you substitute it, you get the same values.
That is you need a constant T, such that for every x you have: f(x) = f(x+T)

As for compositions of periodic functions, try:
sin(x) + 2 sin(e x)
which is not periodic.

What's this "sin(e x)"?

That's a sum of periodic functions; I meant like (f o g)(x), such as sin(sin(x)) and cos(tan(x))

And what's this "(f o g)(x)"?

 

[I like Serena]

What's this "sin(e x)"?

"e" is Euler's number (2.71828), which is the base of the natural logarithm.
I used it because it's an irrational number other than pi.
In particular the ratio between e and pi cannot be written as the ratio of 2 whole numbers.

And what's this "(f o g)(x)"?

It's math notation for f(g(x)). It's called "function composition" or "f applied to the result of g".

 

[Saitama]

"e" is Euler's number (2.71828), which is the base of the natural logarithm.
I used it because it's an irrational number other than pi.
In particular the ratio between e and pi cannot be written as the ratio of 2 whole numbers.

Is x is raised to the power of e in sin(e x) or is x multiplied to e?

It's math notation for f(g(x)). It's called "function composition" or "f applied to the result of g".

Never came across that.

 

[I like Serena]

Is x is raised to the power of e in sin(e x) or is x multiplied to e?

What is the period in each case?

Never came across that.

You just did! And I expect it will not be the last time.

 

[Saitama]

What is the period in each case?

If its sin(ex) then the period is $\frac{2\pi}{e}$. (Found it by applying the sin (nx) rule)
If it is sin(e^x), then it's not periodic since the argument is non linear.
Right..?

 

[I like Serena]

If its sin(ex) then the period is $\frac{2\pi}{e}$. (Found it by applying the sin (nx) rule)
If it is sin(e^x), then it's not periodic since the argument is non linear.
Right..?

Right!

Since I stated it was periodic, it would have to be the first form.
(And anyway, I wouldn't write down an ambiguous expression. )

 

[Saitama]

Right!

Since I stated it was periodic, it would have to be the first form.
(And anyway, I wouldn't write down an ambiguous expression. )

Do you have some more (conceptual)questions for periodicity?

 

[I like Serena]

Do you have some more (conceptual)questions for periodicity?

No. Don't you have any?

 

[Saitama]

No. Don't you have any?

No.
(You found out the website from where i am using these emoticons. )