Calculus II. Urgent problem!! Please Help!!!?

Question

Convert r cosθ = sin 2θ to Cartesian coordinates.

Answer 1

The polar coordinate form is given as r cosθ = sin2θ

r cosθ = 2 sinθ cosθ

r = 2 sinθ

Multiply with r on both sides.

r² = 2 (rsinθ)

We know that r² = x²+y² and y = r sinθ.

x²+y² = 2y

x²+y² - 2y = 0

Add and subtract 1.

x²+y² - 2y + 1 - 1 = 0

x² + (y-1)² = 1

Therefore the r cosθ = sin2θ is represented as x² + (y-1)² = 1 in cartesian coordinates.