# Thread: O(sin n), Ω(sin n), Θ(sin n) complexity

1. ## O(sin n), Ω(sin n), Θ(sin n) complexity

Hello , Do you know examples of functions belonging crowds O(sin (n)), Ω (sin (n)), Θ (sin (n)) ?

2. Originally Posted by ulita
Hello , Do you know examples of functions belonging crowds O(sin (n)), Ω (sin (n)), Θ (sin (n)) ?
Look at the definitions of big-O, Omega, and Theta notation and construct your examples. (To start you off $\displaystyle f(n)=3$ is an example of $\displaystyle \Omega(\sin(n))$ )

CB

3. I also thought about a sort of such example, but how you demonstrate the left part : 0 <= c*sin n<=3, let c=1. sin is a periodic function...which will be the n0, n>=n0 to satisfy the left inequality ?

4. Originally Posted by ulita
I also thought about a sort of such example, but how you demonstrate the left part : 0 <= c*sin n<=3, let c=1. sin is a periodic function...which will be the n0, n>=n0 to satisfy the left inequality ?
$\displaystyle |f(n)|=3\ge \sin(n)$ for all $\displaystyle n$, so putting $\displaystyle c=1$ we have:

For all $\displaystyle n>1;\ |f(n)|\ge c \sin(n)$ where $\displaystyle c=1$

$\displaystyle f(n) \in \Omega(\sin(n))$

CB

5. Thanks a lot.