$\displaystyle g(z)=\frac{sin(z)}{z^2}$and $\displaystyle f(z)=\frac{cos(z)}{z^2}$ both have a pole at $\displaystyle z=0$

From the Laurent series expansion I deduced that for $\displaystyle f(z)$ this pole is of order one, while for $\displaystyle g(z)$ the pole is order two.

Was there any faster way to have noticed this (because first I thought they were of order 2 for both, since there was a square sign in the denominator....)