# Thread: how to replace the sinus..

1. ## how to replace the sinus..

http://i45.tinypic.com/r9lfg5.jpg

i found a_n b_n a_0
but i need to replace the sines
like (-1)^n=cos(pi*n)

i dont know how to do it which sines

2. Originally Posted by transgalactic
http://i45.tinypic.com/r9lfg5.jpg

i found a_n b_n a_0
but i need to replace the sines
like (-1)^n=cos(pi*n)

i dont know how to do it which sines

Are you actually asking what's $\displaystyle \sin\left(\frac{\pi}{2}\pm n\pi\right)=\left\{\begin{array}{rc}1&,\mbox{if } n\in 2\mathbb{Z}\\-1&,\mbox{if } n\notin 2\mathbb{Z}\end{array}\right.$ ?? This is trivial, so perhaps I misunderstood.

Tonio

3. Originally Posted by tonio
Are you actually asking what's $\displaystyle \sin\left(\frac{\pi}{2}\pm n\pi\right)=\left\{\begin{array}{rc}1&,\mbox{if } n\in 2\mathbb{Z}\\-1&,\mbox{if } n\notin 2\mathbb{Z}\end{array}\right.$ ?? This is trivial, so perhaps I misunderstood.

Tonio
Tonio, I have a quick question. What does $\displaystyle n \in 2 \mathbb{Z}$ mean ? Does it mean that $\displaystyle n = 2k$ with $\displaystyle k \in \mathbb{Z}$ ? (Sorry for my ignorance)

4. Originally Posted by Bacterius
Tonio, I have a quick question. What does $\displaystyle n \in 2 \mathbb{Z}$ mean ? Does it mean that $\displaystyle n = 2k$ with $\displaystyle k \in \mathbb{Z}$ ? (Sorry for my ignorance)
It means that n is an even integer.

CB