Answer
$x=-t; y=1; z=-2t$
Work Step by Step
Since we know the velocity is:
$v(t)=r'(t)=\lt -\sin t, \cos t, 2\cos (2t)\gt$
and $v(\dfrac{\pi}{2})=\lt -1,0,-2\gt$
The velocity components of $v$ are : $v_x=-1,v_y=0,v_y=-2$
So, the parametric equations are:
$x=(-1)t+0=-t; y=(0) t+(1)=1; z=(-2)t+(0)=-2t$
Hence, $x=-t; y=1; z=-2t$
