Parametric Equation Conversion?

Question

Convert the following equations to rectangular form and state the range of values for x and y.

x = 2sintcost, y = 3csc2t 0 < t < (Pi/2)

Answer 1

x = 2sin t cos t = sin 2t
y = 3cosec 2t = 3/sin 2t = 3/x
so y=3/x
it's a rectangular hyperbola in the form xy =c^2
where c=V3

for 0 to pi/2 it's basically filling the 1st quadrant only.

Hope this helps!

Answer 2

x = 2sintcost, y = 3csc2t 0 < t < (Pi/2)
x = sin 2t, y = 3/ sin 2t
y =3/x
xy =3

Answer 3

Somewhat larger than a bread-box.