Take , and divide the entire equation through by to get an identity that might help.
My textbook says:
x = 2 + 5 tan t
y = 1 + 3 sec t
By performing appropriate operations on the parametric equations, eliminate the parameter and get a Cartesian equation relating x and y. You should find that one of the Pythagorean properties will help.
I believe the question is asking for me to take the two equations and make one equation in the f(x)=x format so it may be put into a graphing calculator. If this is true, I am 100% at a loss; I cannot find any reference in the chapter that tells how to do this, and as a last resort, I even checked all of the example problems... none relate to this.
Yes, that's what you are asked to do.
You have the following system of equations:If this is true, I am 100% at a loss; I cannot find any reference in the chapter that tells how to do this, and as a last resort, I even checked all of the example problems... none relate to this.
and
Given the second equation, you can express in terms of .
You can then replace (and even ) in the first equation by terms in which does not occur anymore. Finally, solve that remaining equation (in x and y) for y.
Okay, I somewhat overlooked that I may of taken the three variable system of equations and solved for t, then y.
x=2+5tan(t)
(x-2)/5=tanT
arctan((x-2)/5)=T
y=1+3secT
1/3=1/cosT
3/1=cosT
arccos3=T
arctan((x-2)/5)=arccos3
(arctan((x-2)/5)/(arccos3)=y
Am I headed in the right direction with this work?
I think you might be able to get that approach to work. But if you do what I suggested, that is, see that then you simply solve each of your two equations for the relevant trig function, and drop them into the equation I just wrote down. Voila, you're done.
What Ackbeet was suggesting was what I erased -- I ended up getting two possible equations when I tried to solve for y, and I thought I was missing something. I'll just show you the beginning part:
Solve each equation for the corresponding trig function:
Use the pythagorean identity that Ackbeet mentioned and plug in :
EDIT: Duh, this is an equation for a hyperbola. Who says we need to solve for y? I'm such an idiot. So just put it in standard form: