Why are there 44 sine curves on $\sin(n)$ with $0 < n < 10,000$ and $n$ integer (Gilbert Strang's "thousand points of light")

Question

On Gilbert Strang's Calculus book (available on the following link: http://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf), at page 34 (with subtitle "A thousand points of light"), according to the book's enumeration, (page 40 according to pdf reader enumeration) he starts reasoning about the graph of $\sin n$ with $0 < n < 10,000$ ($\sin n$ is $\sin x$ with $x$ an integer, wich means its graph will not be continuous but rather a "cloud of points").

I do not understand why the reasoning he makes leads to the final conclusion. He reasons as follows (in topics):

1. Even though the graph of sin(n) is a cloud of points, when "looking from far away" (that is, with the graph in small proportions) it looks like there is more than one curve on it;
2. I want to know how many curves there are on it;
3. The points at $n = 22$ and at $n = 44$ are close to 0 (because they're close to multiples of $\pi$, whose sine is 0);
4. The point 44 starts the middle sine curve;
5. There are 44 sin curves.

I do not understand the reasoning that leads to 4 and 5 and would appreciate if somebody could help.

Thanks in advance.