Final answer:
To convert the rectangular equation y = x² to cylindrical coordinates, substitute y with r sin(θ) and x with r cos(θ) to get the equation sin(θ) = r cos²(θ).
Step-by-step explanation:
The question asks for an equation in cylindrical coordinates corresponding to the rectangular equation y = x². In cylindrical coordinates, the relationships between the rectangular and cylindrical systems are given by x = r cos(θ) and y = r sin(θ). Therefore, converting the given rectangular equation involves substituting y with r sin(θ) and x with r cos(θ). Since y = x², we substitute to get r sin(θ) = (r cos(θ))². Simplifying, the equation in cylindrical coordinates is r sin(θ) = r² cos²(θ). To remove the redundancy of r when r is not zero, we get sin(θ) = r cos²(θ), which is the desired cylindrical equation.