The function
\[
f(x) = \frac{\cos x}{\left\lfloor \frac{2x}{\pi} \right\rfloor + \frac{1}{2}},
\]
where \( x \) is not an integral multiple of \( \pi \) and \( \lfloor \cdot \rfloor \) denotes the greatest integer function, is:
Show Hint
A function is odd if \( f(-x) = -f(x) \) and even if \( f(-x) = f(x) \).