Question

the equation r=3sin theta represents a circle. find the cartesian coordinates of the center

Answer 1

Hey welcome to OpenStudy!

Answer 2

\[\Large\rm r=3\sin \theta\]Umm I can show you the way `I would do it`.
There's probably a shorter way.. but this is what makes sense to me at least...

Answer 3

Multiplying both sides by r gives us,\[\Large\rm r^2=3r \sin \theta\]Then recall how we change things from polar to cartesian,\[\Large\rm r^2=x^2+y^2\]\[\Large\rm x=r \cos \theta\]\[\Large\rm y=r \sin \theta\]

Answer 4

So plugging in some stuff for the r^2 and r sin theta,\[\Large\rm x^2+y^2=3y\]

Answer 5

Move the y's to the left, and complete the square on the y's.\[\Large\rm x^2+y^2-3y=0\]Remember how to complete the square?