The projection of a vector value function onto the xz-plane. Okay, so I missed CalcIII today and I'm struggling a bit here.
$r(t) = (\sin t,\cos t,7\sin t + 4\cos 2t)$
Find the projection of $r(t)$ onto the xz-plane for $−1 \leq x \leq 1$
Answer as an equation using the variables $x$, $y$, and $z$.
P.S. I clepped CalcI and II.... in 2010. Haven't done much since then so I'm just a little out of practice, need to kick my brain back into gear. 

Looks kinda like a parabola:

And with good reason.  It just so happens that the $z$-component can be rewritten:
$$7 \sin (t)+4 \cos (2 t)=4-8 \sin ^2(t)+7 \sin (t).$$
Thus, the $x$ and $z$ components satisfy the relationship $z=4+7x-8x^2$.
