Answer
$f(-x)=-f(x)$
Work Step by Step
We take a look at the point where $x=\frac{\pi}{2}$
At $x=\frac{\pi}{2}$, $y=1$
Then we take a look at the point where $x=-\frac{\pi}{2}$.
At $x=-\frac{\pi}{2}$, $y=-1$
Therefore, $f(-\frac{\pi}{2})=-f(\frac{\pi}{2})$
We can take another case where $x=\frac{3\pi}{2}$ and $x=-\frac{3\pi}{2}$.
We find that $f(\frac{3\pi}{2})=-1$, while $f(-\frac{3\pi}{2})=1$
As we take a close examination, the graph has a symmetry through the point $O$, which means for a point where $x=a$ and $y=b$, the point where $x=-a$ would have $y=-b$.
In other words, $f(-x)=-f(x)$
