A GRE subject trig question:
Let $p,q$ be constants and let $$f(x)=p \sin x + q x \cos x + x^2$$ for all real numbers $x$. If $f(2)=3$, find $f(-2)$.
So I plug in and obtain
$$3=\phantom{-}p \sin 2 +2q \cos 2 + 4$$ $$y=-p\sin 2 -2q \cos 2 + 4$$
Adding them, I obtain
$$3+y= 8$$
Where $y$ is what; that is, is the answer $5$?