# Find the lowest period for the following

1. Apr 8, 2009

### Dell

f(x)=cos2x

so what i am looking for is the smallest x that will bring me back to my same answer, correct,,,

f(0)=1
now i can see that since we have a sqared function, and cos(pi)=-1, every time i reach pi, 2pi 3pi 4pi.... i will have the same answer

therefore
T=pi

is this correct?
how do i write it in a mathematical way?

2. Apr 8, 2009

### lanedance

hi dell, if you are looking for the period of the function, it sounds about right

maybe something write like
$$f(x)=cos^2x$$
$$f(x) = f(x+n\pi)$$ $$,\forall n \in \mathbb{Z}$$

you could also notice by using the properties of cos2x with the identity
$$f(x)=cos^2x = \frac{1+cos2x}{2}$$