The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter."
$x=\sec\theta\text{ and }y=\cos\theta$
In the answer key, $0\le \theta < \pi/2$ and $\pi/2 < \theta \le \pi$. What about the angle on the unit circle that are in the third and fourth quadrant?
Also, in the answer key, $|x|\ge 1$ and $|y|\le 1$ Why are $x$ and $y$ restricted in such a way?