The equation r is equal to 4 sine theta represents a circle. What is the radius of the circle, and what is the symmetry of the graph?

Use the polar relationships r² = x² + y² and r sin θ = y. Multiplying r = 4 sin θ by r gives x² + y² = 4y, or x² + (y − 2)² = 4. This is a circle with radius 2 and center (0, 2), so it is symmetric about the vertical line θ = π/2. The correct choice is “The radius is 2 units, and the graph is symmetric about the line θ = π/2.”

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