How do you convert #r=2(cos(theta))^2# to rectangular form?

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Answer 1 · 2016-12-15T02:20:08

#(x^2+y^2)^(3/2)=2x^2#

Convert #r=2(costheta)^2# to rectangular form.

#costheta =x/r#

Substitute #r=2(x/r)^2#

#r=(2x^2)/r^2#

Cross multiply

#r^3=2x^2#

Substitute #r=sqrt(x^2+y^2)#

#(sqrt(x^2+y^2))^3=(2x^2)#

#((x^2+y^2)^(1/2))^3=(2x^2)#

#(x^2+y^2)^(3/2)=2x^2#