Posted by Paige on .
Find a Cartesian equation for the polar curve y = 5tan(theta)sec(theta). I think I got it but I just wanted to double check. Thanks in advance!

Calc 2 
MathMate,
Would you like to post your answer if you just wanted to check?

Calc 2 
Mgraph,
y=... or r=...?

Calc 2 
MathMate,
It would be in the form:
x=f(θ),
y=g(θ)
where f and g are functions of θ. 
Calc 2 
Mgraph,
Read the terms of your problem!

Calc 2 
Mgraph,
If r=tan(theta)sec(theta)
then r(cos(theta)^2)=sin(theta)
(r*cos(theta))^2=r*sin(theta)
x^2 = y 
Calc 2 
Paige,
I am sorry, it is r = 5tan(theta)sec(theta)

Calc 2 
Paige,
Mggraph: but (r*cos(theta))^2 is not x^2, is it? I thought rcos(theta) = x^2
This is what I got:
1 = 5y/[(x^2)(square root of(x^2 + y^2))] 
Calc 2 
Mgraph,
Then all right sides multiply by 5:
x^2=5y or
y=0.2x^2 
Calc 2 
Paige,
Aha I got it! Thanks so much! :)

Calc 2 
VĂctor,
if I've this equation: r=sec theta tan theta. How is?