Question

what is r= 60+60 sin(theta) in rectangular form?

Answer 1

We know that \(r^2=x^2+y^2\) and \(y=r\sin\theta\), so that's something we can start with. Multiplying both sides of the equation by \(r\) gives us an equation that contains these two expressions.
\[r^2=60r+60r\sin\theta~~\iff~~x^2+y^2=60r+60y\]
Knowing that \(r^2=x^2+y^2\) tells us that \(r=\sqrt{x^2+y^2}\), so we can replace the \(r\) as well.
\[x^2+y^2=60\sqrt{x^2+y^2}+60y\]