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

Question

y=2x^2

r(theta)= ?

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Answer 1 · 2018-04-08T00:27:35

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

#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)