  Mixed trigonometric-polynomials (MTPs) are functions of the form
$f(x,\sin{x}, \cos{x})$ with $f\in\mathbb{Q}[x_1,x_2,x_3]$. In this paper, an
algorithm ``isolating" all the real roots of an MTP is provided and
implemented. It automatically divides the real roots into two parts: one
consists of finitely many ``bounded" roots in an interval $[\mu_-,\mu_+]$ while
the other consists of probably countably many ``periodic" roots in
$\mathbb{R}\backslash[\mu_-,\mu_+]$. For bounded roots, the algorithm returns
isolating intervals and corresponding multiplicities while for periodic roots,
it returns finitely many mutually disjoint small intervals
$I_i\subset[-\pi,\pi]$, integers $c_i>0$ and multisets of root multiplicity
$\{m_{j,i}\}_{j=1}^{c_i}$ such that any periodic root $t>\mu_+$ is in the set
$(\sqcup_i\cup_{k\in\mathbb{N}}(I_i+2k\pi))$ and any interval
$I_i+2k\pi\subset(\mu_+,\infty)$ contains exactly $c_i$ periodic roots with
multiplicities $m_{1,i},...,m_{c_i,i}$, respectively. The effectiveness and
efficiency of the algorithm are shown by experiments. %In particular, our
results indicate that the ``distributions" of the roots of an MTP in the
``periods" $(-\pi,\pi]+2k\pi$ sufficiently far from $0$ share a same pattern.
Besides, the method used to isolate the roots in $[\mu_-,\mu_+]$ is applicable
to any other bounded interval as well. The algorithm takes advantages of the
weak Fourier sequence technique and deals with the intervals period-by-period
without scaling the coordinate so to keep the length of the sequence short. The
new approaches can easily be modified to decide whether there is any root, or
whether there are infinitely many roots in unbounded intervals of the form
$(-\infty,a)$ or $(a,\infty)$ with $a\in\mathbb{Q}$.
