Question

Rewrite the cartesian equation y = 3 x² as a polar equation.

Answer 1

To rewrite the cartesian equation y = 3x² as a polar equation, substitute x and y with their polar coordinates. Simplify the equation using trigonometric identities.

Step-by-step explanation:

To rewrite the cartesian equation y = 3x² as a polar equation, we can substitute x and y with their respective polar coordinates using the equations x = r cos(θ) and y = r sin(θ). So, the polar equation becomes:

r sin(θ) = 3(r cos(θ))²

Now, simplifying the equation gives:

r sin(θ) = 3r² cos²(θ)

Using the trigonometric identity cos²(θ) = (1 + cos(2θ))/2, we can further simplify the equation:

r sin(θ) = 3r²(1 + cos(2θ))/2