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

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

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