Question

Convert r^2 sin(2 theta) = 4 to Cartesian form.

Answer 1

Hello,

xy=2 is the cartesian form.

Indeed:
x=r cos t ==>cos t=x/r
y=r sin t ==> sin t=y/r
r²*sin 2t=4  ==>r²*2 sin t cos t=4
==>r²*x/r*y/r=2==>xy=2

Answer 2

R^2 sin(2 theta) from the trigonometric identities is equal to r sin theta * r cos theta.  in this case, r sin theta  is equal to y while r cos theta is equal to x. r^2 in this expression is equal to 4 where r is equal to 2. Hence the cartesian form is equal to xy = 2