Consider the following three functions defined for all positive integers $n \geq 0$.
\[
\begin{array}{l}
f(n)=|\sin (n)+n|, \\
g(n)=n, \\
h(n)=|\sin (n)| .
\end{array}
\]
Which of the following statements about these functions is / are true?
- $f(n)=O(g(n))$
- $g(n)=O(f(n))$
- $h(n)=O(g(n))$
- Only $\text{(i)}$ is true.
- Only $\text{(ii)}$ is true.
- Only $\text{(i)}$ and $\text{(ii)}$ are true.
- Only $\text{(ii)}$ and $\text{(iii)}$ are true
- All of $\text{(i), (ii)}$, and $\text{(iii)}$ are true.