$3\mathrm{.}1.$ A continuous$-$time periodic signal $x(t)$ is real valued and has a fundamental period $T=8.$ The nonzero Fourier series coefficients for $x(t)$ are

$a_1=a_{-1}=2,a_3=a_{-3}^{**}=4j$

Express $x(t)$ in the form

$x(t)={\displaystyle \underset{k=0}{\overset{}{}}}{A}_{k}cos({}_{k}t+{}_k)$