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

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Answer 1 · 2016-12-15T02:20:08

${(x^{2} + y^{2})}^{\frac{3}{2}} = 2 x^{2}$ $(x^2+y^2)^(3/2)=2x^2$

Convert $r = 2 {(cos θ)}^{2}$ $r=2(costheta)^2$ to rectangular form.

$cos θ = \frac{x}{r}$ $costheta =x/r$

Substitute $r = 2 {(\frac{x}{r})}^{2}$ $r=2(x/r)^2$

$r = \frac{2 x^{2}}{r^{2}}$ $r=(2x^2)/r^2$

Cross multiply

$r^{3} = 2 x^{2}$ $r^3=2x^2$

Substitute $r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$

${(\sqrt{x^{2} + y^{2}})}^{3} = (2 x^{2})$ $(sqrt(x^2+y^2))^3=(2x^2)$

${({(x^{2} + y^{2})}^{\frac{1}{2}})}^{3} = (2 x^{2})$ $((x^2+y^2)^(1/2))^3=(2x^2)$

${(x^{2} + y^{2})}^{\frac{3}{2}} = 2 x^{2}$ $(x^2+y^2)^(3/2)=2x^2$

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