Determining the graph a parametric function.

Question

I know that the graph of $\overline{r}(t) = \langle \cos(t), t, \sin(t)\rangle$ is a cylinder aligned along the $y$-axis, however how can I determine from $\overline{r}(t) = \langle \cos(t), -\cos(t), \sin(t)\rangle$ that is is only a circle? What about changing the $y$-coordinate from $t$ to $-\cos(t)$ causes this change in shape?