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

y=2x^2

r(theta)= ?

1 Answer
Apr 8, 2018

r(theta)=sin(theta)/(2cos^2(theta))

Explanation:

y=2x^2

2y^2+y=2x^2+2y^2

2(r(theta)sin(theta))^2+r(theta)sin(theta)=2(r(theta))^2

2(r(theta))^2sin^2(theta)+r(theta)sin(theta)=2(r(theta))^2

2r(theta)sin^2(theta)+sin(theta)=2r(theta)

2r(theta)sin^2(theta)-2r(theta)=-sin(theta)

r(theta)(2sin^2(theta)-2)=-sin(theta)

r(theta)=-sin(theta)/(2sin^2(theta)-2)

r(theta)=sin(theta)/(2-2sin^2(theta))

r(theta)=sin(theta)/(2cos^2(theta))

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