Question

The position of a particle is given by the expression x = 2.00 cos (6.00πt + 2π/5), where x is in meters and t is in seconds determine the position of the particle at t = 0.330 s

Answer 1

The position of the particle at time t is
$x(t) = 2.00 \cos (6.00 \pi t+ \frac{2}{5}\pi )$
If we substitute $t=0.330 s$, we find
$x(0.330 s)=2.00 \cos (6.00 \pi (0.330 s) + \frac{2}{5} \pi)=$
$=2.00 \cos (1.98 \pi + 0.40 \pi )=2.00 \cos (2.38 \pi) =$
$=2.00 \cdot (-0.72)=-1.45 m$