Suppose I have a vector operator which angle dependence is given by $\hat O(\theta)=A\sin\theta+B\cos\theta+C$ What can I say about $\hat O$? Sorry, I do realize that it is a bit vague. Assume $\hat O$ is an operator on the space of wavefunctions.
I can see that it is periodic with period $2\pi$, but what else?
Thank you.