Is $x(t) = \cos t + \sin\left(\frac{1}{2}t\right)$ a periodic signal?
As for every $t_0\in\mathbb{R}$ and $k\in\mathbb{Z}$
$$
\begin{eqnarray}
  &amp;x(t_0+4k\pi)  &amp;=\cos(t_0+4k\pi)+\sin(t_0/2+2k\pi)\\
  &amp;              &amp;=\cos(t_0)+\sin(t_0/2)\\
  &amp;              &amp;=x(t_0)
\end{eqnarray}
$$
you answer is correct: $x(t)$ is periodic.