Does a node require Change in sign of wave function

In a quantum Chemistry course we were asked to find the number of nodes of the wave function $$\Psi=\frac{\sin^2 x}{x^2} : -3\pi \le x \le 3\pi$$ Clearly this has a removable discontinuity in x=0 so for a node it must satisfy the equation $\Psi =0$ with $x\neq 0$ we get six solutions or six nodes.But I have also noticed that the hydrogenic wave functions seem to change their sign (phase) after each node.In this case $\Psi$ doesnt seem to change its sign,so can i say there are zero nodes!?


