I have given the following formula and need to find the intervals in which $f(t)$ for $ t \in [0, \infty]$ is negative, $f(t) <0$. Note that $\alpha, x_j >0 $
$f(t)= \sum_{j=1}^N \sin(x_jt) \coth(\alpha x_j)$
I understand how it works for the 1-dim case $N=1$ but I think I am missing something here, as I don't know how to solve this. Any help or hint would be appreciated. I thought about Fourier Series but it doesn't seem to work. Thank you