What is the rectangular form of r = 8 sin(θ)?

Use the polar-coordinate identities r² = x² + y² and r sin(θ) = y. Multiplying r = 8 sin(θ) by r gives r² = 8r sin(θ), so x² + y² = 8y. Completing the square in y gives x² + (y − 4)² = 16, which is choice C.

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