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

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

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Answer 1 · 2016-02-27T05:38:34

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

Explanation:

Hence $x = r \cdot cos θ$ $x=r*costheta$ and $y = r \cdot sin θ$ $y=r*sintheta$ we have that

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

so

$r = 2 \cdot {(cos θ)}^{2} \Rightarrow \sqrt{x^{2} + y^{2}} = 2 \cdot {(\frac{x}{r})}^{2} \Rightarrow r^{2} \cdot (\sqrt{x^{2} + y^{2}}) = 2 x^{2} \Rightarrow {(x^{2} + y^{2})}^{\frac{3}{2}} = 2 x^{2}$ $r=2*(costheta)^2=>sqrt(x^2+y^2)=2*(x/r)^2=> r^2*(sqrt(x^2+y^2))=2x^2=> (x^2+y^2)^(3/2)=2x^2$

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

1 Answer

Explanation:

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How do you convert r=2(cos(theta))^2r=2(cos(θ))2r=2(cos(theta))^2 into cartesian form?

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