# Periodic function | Change of variables

1. Nov 6, 2009

### kingwinner

"Is f(x)=sin(x2) periodic?

WHY? I believe "sin" is always periodic? Can someone please explain?

Any help is appreciated!

Last edited: Nov 7, 2009
2. Nov 6, 2009

### Staff: Mentor

On the first one, what is the definition of periodic? And when you have a non-linear argument to the sin() funtion, what is the period?

3. Nov 6, 2009

### HallsofIvy

Staff Emeritus
If x= 0, $sin(x^2)= sin(0^2)= sin(0)= 0$. When is $sin(x^2)= 0$ again? Is that a period?

4. Nov 7, 2009

### kingwinner

I know that f(x)=sin(x) has period 2pi, g(x)=sin(2x) has period pi, etc. Since I am seeing sin in the function sin(x^2), this leads me to think that sin(x^2) is periodic as well.

For sin(x^2), The zero set is {x: x^2 = (n)(pi)}, but how can I know whether it's periodic or not?
I think it's hard for me to tell whether a function given randomly to me is periodic or not. Is there any systematic way to answer this? I am not sure where to start...

Thanks!

5. Nov 7, 2009

### kingwinner

For sin(x^2), The zero set is {x: x^2 = (n)(pi)}, but how can I know whether it's periodic or not? I just can't tell...

6. Nov 7, 2009

### lanedance

periodic in my book would be
f(t+a) = f(t) for all t, for som constant a

in your case, solve for the first few zeros, and see what the difference bewteen them is (cf with a in the above) , see if there's any pattern which you can pick out which shows its not periodic