I knew hyperbolic functions and trig functions for a long time, but I often forget the definition of it. So I think I need some tricks or intuition to remember them.
$$sh \, x = \frac{e^x - e ^{-x}}{2}$$ and
$$ sin \, x = \frac{e^{ix} - e^{-ix}}{2i}$$
Just remember Euler's formula for circular trigonometric functions:
$$e^{ix} = \cos x + i\sin x$$ $$e^{-ix} = \cos -x + i\sin -x = \cos x - i\sin x$$
Then isolate $\sin x$ and $\cos x$. For the hyperbolic, remember the relationship:
$$e^x = \cosh x + \sinh x$$ $$e^{-x} = \cosh -x + \sinh -x = \cosh x - \sinh x$$
Then isolate respectively.