Restriction Of Parametric Functions DomainThe 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 ⁡ θ and y = cos ⁡ θIn the answer key, 0 ≤ θ &lt; π / 2 and π / 2 &lt; θ ≤ π. What about the angle on the unit circle that are in the third and fourth quadrant?Also, in the answer key, | x | ≥ 1 and | y | ≤ 1. Why are x and y restricted in such a way?

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Restriction Of Parametric Functions DomainThe problem I am working on is, &quot;Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.&quot;  x  =  sec  ⁡  θ   and   y  =  cos  ⁡  θIn the answer key,   0  ≤  θ  &amp;lt;  π      /    2 and   π      /    2  &amp;lt;  θ  ≤  π. What about the angle on the unit circle that are in the third and fourth quadrant?Also, in the answer key,       |    x      |    ≥  1 and       |    y      |    ≤  1. Why are x and y restricted in such a way?

Sariah Glover · Accepted Answer

Step 1It&#039;s the curve   y  =  1      /    x restricted to those values of y that can be cos theta, or equivalently, those values of x that can be sec theta.Remember that   −  1  ≤  cos  ⁡  θ  ≤  1, and   sec  ⁡  θ is always either   ≥  1 or   ≤  −  1.Step 2As   θ goes from 0 to   π,   cos  ⁡  θ goes all the way from 1 down to -1. If we went beyond   π, we&#039;d see it going through the same set of values again, from -1 back up to +1. We would not get any new values of x or y that we didn&#039;t get the first time.

Restriction Of Parametric Functions Domain The problem I am working on is, "Sketch the curve repres

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