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

Question

1761 views around the world

You can reuse this answer
Creative Commons License

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 $r=sqrt(x^2+y^2)$

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

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

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

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