# Periodicity of functions

• Oct 23rd 2011, 09:47 AM
Fabio010
Periodicity of functions
Can somebody tell me how can i find the periodicity of:

$\displaystyle sen^2(x)$ and $\displaystyle sen\sqrt{x}$

I know that i have to equal $\displaystyle f(x)$ to $\displaystyle f(x+p)$ but i cant solve it.

Help is always appreciated :).
• Oct 23rd 2011, 10:11 AM
SammyS
Re: Periodicity of functions
Quote:

Originally Posted by Fabio010
Can somebody tell me how can i find the periodicity of:

$\displaystyle sen^2(x)$ and $\displaystyle sen\sqrt{x}$

I know that i have to equal $\displaystyle f(x)$ to $\displaystyle f(x+p)$ but i cant solve it.

Help is always appreciated :).

I assume that sen(x) is what most of us refer to as sin(x) .

Sketch a graph of each function.

Use one of the double angle identities for the cosine to find a way to express $\displaystyle \sin^2(x)$ in terms of cos(2x) .
• Oct 23rd 2011, 11:55 AM
Fabio010
Re: Periodicity of functions
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• Oct 23rd 2011, 11:59 AM
Fabio010
Re: Periodicity of functions
Quote:

Originally Posted by SammyS
I assume that sen(x) is what most of us refer to as sin(x) .

Sketch a graph of each function.

Use one of the double angle identities for the cosine to find a way to express $\displaystyle \sin^2(x)$ in terms of cos(2x) .

I never noticed that

$\displaystyle sin^2(x) = \frac{1-cos(2x)}{2}$

$\displaystyle \frac{1-cos(2x+2P)}{2} = \frac{1-cos(2x)}{2}$

$\displaystyle cos(2x+2P) = cos(2x)$ k belongs to Z

$\displaystyle 2x + 2P = 2x + 2k\pi~~\cup~~2x + 2P = -2x + 2k\pi$

$\displaystyle P = k\pi~~\cup~~P= -2x +k\pi$

So $\displaystyle P= \pi~~~right??$

The other function, is not periodic, because we can see in graphic. But how can i prove that is not periodic??
• Oct 23rd 2011, 12:22 PM
SammyS
Re: Periodicity of functions
Correct. The period is π .