A circle in the Cartesian plane is given by the equation x2+y2=5y. In this problem you will express the circle in polar form and interpret the result.
(a) Rewrite the given Cartesian equation in polar coordinates by substituting x=rcosθ and y=rsinθ. Simplify your answer so that r is explicitly expressed as a function of θ.
(b) Determine all values of θ for which the corresponding r obtained in Part (a) is non-negative. Provide a complete algebraic justification.
(c) Describe, in words, how the restriction on θ found in Part (b) relates to the location of the circle in the Cartesian plane.