Question

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

Answer 1

r = 8 tan(x) sec(x)

In order to solve this, we are going to use the following:
r = sqrt(x^2 + y^2) //but in this case, we don't need this.
tan(x) = Y / X
X = r cos(x)
Y = r sin(x)

(r cos x)^2 = 8(r sin x)

x^2 = 8y