# Probably very easy - Domain/range on parametric->cartesian equation

1. Dec 11, 2012

### yesiammanu

1. The problem statement, all variables and given/known data
Convert x=tant, y=sect on ∏/2<t<∏ to rectangular system and graph. Show domain, rnage, and orientation

I use sec2=tan2+1 -> y2-x2=1 which is a hyperbolic function with the graph http://www.wolframalpha.com/input/?i=y^2-x^2%3D1

I know that the graph is only in the 3rd quadrant but I'm not sure why - also, I'm not sure what the domain/range is. I think the domain (valid X's) are -∞ to 0, and range would be -∞ to -1 based on the graph being in the third quadrnat only? How would I get that the graph is only in the 3rd quadrant (probably something to do with the boundaries), and are the domain/range correct

Last edited: Dec 11, 2012
2. Dec 11, 2012

### yesiammanu

Bump if I may, my test is in 30 minutes :)

3. Dec 11, 2012

### Staff: Mentor

On the interval [$\pi/2, \pi$] x < 0 and y ≤ -1. Sketch graphs of x = tan(t) and y = sec(t) to see this. These graphs should give you some insight into the values of x and y.