Rewrite the rectangular equation to a polar equation, y=2x^2, what would r(theta) equal?

y=2x^2

r(theta)= ?

1 Answer
Timber Lin
Apr 8, 2018

r(θ)=sin(θ)2cos2(θ)

Explanation:

y=2x2

2y2+y=2x2+2y2

2(r(θ)sin(θ))2+r(θ)sin(θ)=2(r(θ))2

2(r(θ))2sin2(θ)+r(θ)sin(θ)=2(r(θ))2

2r(θ)sin2(θ)+sin(θ)=2r(θ)

2r(θ)sin2(θ)−2r(θ)=−sin(θ)

r(θ)(2sin2(θ)−2)=−sin(θ)

r(θ)=−sin(θ)2sin2(θ)−2

r(θ)=sin(θ)2−2sin2(θ)

r(θ)=sin(θ)2cos2(θ)

(note: i think you can divide both sides by r(θ) in step 5 because the function r(θ) passes through the origin (r=0) anyway)

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