Multiple Choice
Convert each equation to its polar form.
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15. Polar Equations
Convert Equations Between Polar and Rectangular Forms
Multiple Choice
Convert each equation to its polar form.
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Verified step by step guidance1
Start with the given Cartesian equation: x^2 + y^2 = 2y.
Recall the polar coordinate relationships: x = r * cos(θ) and y = r * sin(θ).
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)).
Simplify the equation: r^2 * cos^2(θ) + r^2 * sin^2(θ) = 2r * sin(θ).
Use the Pythagorean identity cos^2(θ) + sin^2(θ) = 1 to simplify further: r^2 = 2r * sin(θ).
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