Question

Find a Cartesian equation for the curve and identify it.
r=8tanxsecx

Answer 1

tanxsecx?
Are you sure it isn't
\[\Large r = 8\tan(\theta) \sec(\theta)\]?

Answer 2

yeah its r = 8 tan θ sec θ :d

Answer 3

Okay, these are all you really need for that:
\[\Large r= \sqrt{x^2+y^2}\]\[\Large \tan(\theta) = \frac{y}x\]
\[\Large x = r\cos(\theta)\]

Answer 4

scratch that, for this particular question, you don't actually need the first one
\[\large r = \sqrt{x^2+y^2}\]

Answer 5

(rcosθ)^2=8(rsinθ) is that right:d

Answer 6

Actually, yes. But that equation is still not Cartesian, though I have a feeling you already know how to fix that ;)

Answer 7

And also (as you well know, I guess)
\[\Large y = r\sin(\theta)\]

Answer 8

thanks.d

Answer 9

x^2 = 8y right :d

Answer 10

Yup. That's a parabola XD