What is the rectangular form of r = −2 sin(θ)?

Use the polar identities r² = x² + y² and r sin(θ) = y. Multiplying r = −2 sin(θ) by r gives r² = −2r sin(θ), so x² + y² = −2y. Completing the square yields x² + (y + 1)² = 1, which is choice D.

AI-written and checked against the verified answer.