Answer
Graph I.
Work Step by Step
Because $\sin^{2}A+\cos^{2}A=1$,
the x and y coordinates satisfy
$x^{2}+y^{2}=1$
So, as z changes, this circle translates into a cylinder propagating around the z-axis. The curve will lie on this cylinder.
The values of z are between -1 and 1 (the range of cosine), so the cylinder does not extend indefinitely.
z values repeat after the period of $\pi$, while the x and y coordinates have a period of 2$\pi$.
The curve will retrace itself. These points lead to graph I.
