How to find a Cartesian equation for a polar curve

How do I find a Cartesian equation for the polar curves:

A) r = 2cscΘ

B) r = 2tanΘsecΘ

If someone could show step by step how to solve this problem it would be helpful.

x = rcosΘ
y = rsinΘ

tanΘ = y/x
r = √(x² + y²)

A) r = 2cscΘ
r = 2/sinΘ
2 = rsinΘ
y = 2

B) r = 2tanΘsecΘ
r = 2tanΘ/cosΘ
rcosΘ = 2tanΘ
x = 2(y/x)
x² = 2y
y = 1/2 x²

A) y = r*sin(t)
y = 2csc(t)*sin(t) = 2
y = [2/sin(t)]*sin(t)
y = 2

B) r = 2tan(t)*1/cos(t)
x = 2tan(t)*1/cos(t)*cos(t) = 2tan(t)
tan(t) = x/2
y = 2tan(t)*1/cos(t)*sin(t) = 2tan^2(t)
y = 2*x^/4 = x^2/2
y = (1/2)*x^2