Answer
$0.669s$
Work Step by Step
We can determine the required time as follows:
$\omega=\sqrt{\frac{g}{L}}$
$\implies \omega=\sqrt{\frac{9.8m/s^2}{1.0m}}$
$\implies \omega=3.13s^{-1}$
We know that
$\theta(t)=\theta_{max} cos(\omega t)$
We plug in the known values to obtain:
$-4.0^{\circ}=8.0^{\circ}cos((3.13s^{-1})t)$
This simplifies to:
$t=0.669s$
