How do you write x=2sec(t) and y=3tan(t) in rectangular form?

1 Answer
May 25, 2018

x24y29=1

Explanation:

I want to be very lazy and use trig identities (instead of some form of inverse functions). The one that pops to mind is
sec2(t)=tan2(t)+1
Solving for each of these factors in the given equations yields
x2=sec(t)andy3=tan(t)
hence
(x2)2=(y3)2+1x24y29=1
This is an hyperbola with dimension 2 in the x and 3 in the y.