Convert each equation to its polar form.
$x^2+y^2=2y$

• A. $r=\(\sqrt{2}\)$
• B. $r=2\(\sin\]\theta\)$
• C. $r=4\(\sin\]\theta\)$
• D. $r=2\(\cos\]\theta\)$

Answer: (B)

Verified step by step guidance

1. Start with the given Cartesian equation: x^2 + y^2 = 2y.
2. Recall the polar coordinate relationships: x = r * cos(θ) and y = r * sin(θ).
3. Substitute x = r * cos(θ) and y = r * sin(θ) into the equation: (r * cos(θ))^2 + (r * sin(θ))^2 = 2 * (r * sin(θ)).
4. Simplify the equation: r^2 * cos^2(θ) + r^2 * sin^2(θ) = 2r * sin(θ).
5. Use the Pythagorean identity cos^2(θ) + sin^2(θ) = 1 to simplify further: r^2 = 2r * sin(θ).