Is this function periodic ? $f:[-30\pi,30\pi] \to [-1,1]$ , where $f(x)=\sin x$
Now , obviously $\sin x$ is a periodic function , I am asking this question just because according my to definition of periodic function :
A function $f$ is said to be periodic if for some constant P , it is the case that $$f(x+P)=f(x)$$ fo all values $x$ in the domain.
Now if I take $x=29\pi$ (which is in the domain of the function) , then I must have $$f(29\pi + 2\pi) = f(29\pi)$$ or , $$f(31\pi)=f(29\pi)$$ But this is not the case as $f(31\pi)$ is not defined .
So, I concluded that the given function is not periodic.
Could someone please let me know whether I am right or not , and if not , where did I go wrong ?
Thanks !