Answer
Graph IV
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. Two graphs offer upright cylinders with circular coils, IV and VI.
When t=0, the point on the graph is (1,0,1)
When t=$\pi/4,$ a full circle was made by the x and y coordinates, while z fell to slightly more than 0.5 (this is the difference between cylinders IV and VI).
Thus, the answer is Graph IV.
