Verified answer

r = sin 2 t = 2 sin t cos t

now x = r sin t and y = r cos t

amd x^2 + y^2 =1

we need to eliimate r and t

so r = 2(x/r)(y/r) = 2xy/r^2

or r^3 = 2xy

or (x^2+y^2)^(3/2) = 2xy or (x^2+y^2)^3 = 4 x^2y^2

Rockit has a parametric form.

For the rectangular form, using sin2θ=2sinθcosθ and multiplying

by r^2 you get r^3=2(rsinθ)(rcosθ)

and r=(x^2+y^2)^(1/2), x=rcosθ,y=rsinθ so

(x^2+y^2)^(3/2)=2yx

or (x^2+y^2)^3=4y^2x^2

0 ≤ θ ≤ 2π

x = sin2θ * cosθ

y = sin2θ * sin θ

hsg