How do you convert #r = 2 sin theta# into cartesian form?
Make use of a few formulas and do some simplification. See below.
When dealing with transformations between polar and Cartesian coordinates, always remember these formulas:
#x=rcostheta# #y=rsintheta# #r^2=x^2+y^2#
We can also replace
We could leave it at that, but if you're interested...
If we subtract
Note that we can complete the square on
And how about that! We end up with the equation of a circle with center