# Relating to period of a function.

If we have f(k)=Asin($\frac{xa}{2}$). Then it was mentioned that f(x) is a periodic function with period $\frac{Δx.a}{2}$=π. How come?

Thanks!

Please note, A and a are constants.

Mark44
Mentor
If we have f(k)=Asin($\frac{xa}{2}$).
This should be f(x) = A sin(##\frac{xa}{2}##). The only variable here is x. k doesn't appear at all in the formula for this function.
Then it was mentioned that f(x) is a periodic function with period $\frac{Δx.a}{2}$=π. How come?
This is wrong, and I have no idea where you got this.

The sine and cosine functions are periodic. The period of both sin(x) and cos(x) is 2##\pi##. The period of sin(Kx) and cos(Kx) is ##\frac{2 \pi}{K}##.

What then would be the period of sin((a/2)x)?
Thanks!

Please note, A and a are constants.

Sorry it is x, I typed it by mistake. It should be 4π/a. But here they related the variable of the sin function "x" to the period in some way I didn't understand.. (i.e, the formula that I wrote in my first post and that you quoted second).
Thanks

Mark44
Mentor
Sorry it is x, I typed it by mistake. It should be 4π/a. But here they related the variable of the sin function "x" to the period in some way I didn't understand.. (i.e, the formula that I wrote in my first post and that you quoted second).
Thanks
If the period of sin(Kx) is ##2\pi/K##, what is the period of sin((a/2)x)?

I answered you previously, it would be 4π/a

Mark44
Mentor
You said it "should be 4π/a", which I interpreted to mean that you knew that was the answer, but didn't know how it was obtained.

You asked about the formula in your first post (and that I quoted). I have no idea what they mean by that formula, especially the part with Δx.

Yes. Neither do I. Thank you anyway!