Even and odd components of a constant function
You may ask yourself first whether the function is already even or odd. If not, check whether it contains an obvious odd/even part, and then whether the remainder is itself even/odd.
Finally, you can use the hammer of the parity decomposition. A function $f(t) $ can be split into the even and odd parts:
$$f(t) =\frac{1} {2} \big[f(t)+f(-t)\big]+ \frac{1} {2} \big[f(t)-f(-t)\big] $$
but it is often better to look at the function first.