Final answer:
To write the equation x^2 + y^2 = 3y in polar form, substitute x = r * cos(θ) and y = r * sin(θ), and simplify the equation.
Step-by-step explanation:
To write the equation x^2 + y^2 = 3y in polar form, we need to express x and y in terms of polar coordinates r and θ.
We can use the equations x = r × cos(θ) and y = r × sin(θ) to do this.
Substituting these equations into the given equation, we have:
(r × cos(θ))^2 + (r × sin(θ))^2 = 3 × (r × sin(θ))
Simplifying further, we get:
r^2 × cos^2(θ) + r^2 × sin^2(θ) = 3 × r × sin(θ)
Using the trigonometric identity cos^2(θ) + sin^2(θ) = 1, we can rewrite the equation as:
r^2 = 3 × r × sin(θ)
Therefore, the equation in polar form is r^2 = 3 × r × sin(θ).