period

**surjective** · May 3rd 2010, 05:14 PM

Hey,

I'm trying to find the period of:

$f(x)=(\cos(\pi\gamma))^{n} \hspace{0,5cm}, \gamma \in \mathbb{R}, n \in \mathbb{N}$

It seems that when $n$ is even then the $f$ has period=1 and when $n$ is odd then $f$ has period=2 .

How to show that analytically?

**TKHunny** · May 3rd 2010, 05:34 PM

As written, your function is not periodic. It's constant. Care to have another go?

**surjective** · May 3rd 2010, 05:50 PM

Hey,

My mistake. It should say:

$<br /> f(x)=(\cos(\pi x))^{n} \hspace{0,5cm}, x \in \mathbb{R}, n \in \mathbb{N}$

**TKHunny** · May 3rd 2010, 08:15 PM

Must you consider more than this?

$[cos(\pi x)]^{n+1} = [cos(\pi x)]^{n}\cdot cos(\pi x)$

If you can make conclusions about even values of n, there is not much left for odd values.

**surjective** · May 3rd 2010, 08:21 PM

Hey,

Sorry for the inconvenience. What I wanted do to was to arrive at the conclusion analytically rather than explanatory. How do I do that?

**TKHunny** · May 3rd 2010, 08:58 PM

What's the definition of "Period"?

Something like: The minimum value of 'h' such that f(x+h) = f(x).

Definitions are always good places to start. They are not always the best places to start writing programs, but for proving results, they are gold.

Thread: period

LinkBack

Thread Tools

Display

period

period

periodicity

Similar Math Help Forum Discussions

what is the period

sin(x), sin(2x), sin(1/2)....what is the period?

[SOLVED] Future value annuities with a different payment period to the compounding period.

Period : 2

Period

Search Tags