Question

What other kinds of identities exist like this for integers?

cos(n pi)=(-1)^n

Answer 1

\[\cos(n \pi)=(-1)^n \]

Answer 2

\[\sin n \pi=0\]

Answer 3

and \(\sin\left(\dfrac{n\pi}{2}\right) = (-1)^{n+1}\)

Answer 4

exactly what you are looking for?

Answer 5

Just anything fun or interesting @geerky42. Maybe some factorial stuff too. =P

Answer 6

these identities are so beautiful

Answer 7

\(\large e^{\pi i (2k+1)}=-1, k \in \mathbb{Z}\) ?

Answer 8

not sure if that's what you're looking for

Answer 9

Yeah, for the most part. I don't know if that is really that much different than what's already been said though @kirbykirby