How do you convert $r^{2} (cos 2 (θ)) = 1$ $r^2(cos2(theta))=1$ into cartesian form?

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How do you convert $r^{2} (cos 2 (θ)) = 1$ $r^2(cos2(theta))=1$ into cartesian form?

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Answer 1 · 2016-02-26T19:06:11

$x^{2} = y^{2}$ $x^2 = y^2$

Explanation:

Using the formulae that links Polar to Cartesian coordinates.

$∙ x = r cos θ \Rightarrow cos θ = \frac{x}{r}$ $• x = rcostheta rArr costheta = x/r$

$∙ y = r sin θ \Rightarrow sin θ = \frac{y}{r}$ $• y = rsintheta rArr sintheta = y/r$

and $Double angle formula$ $color(blue)" Double angle formula "$

$∙ cos (2 θ) = {cos}^{2} θ - {sin}^{2} θ$ $• cos(2theta) = cos^2theta - sin^2theta$

hence $: r^{2} (cos (2 θ)) = r^{2} ({cos}^{2} θ - {sin}^{2} θ) = 1$ $: r^2(cos(2theta)) = r^2( cos^2theta - sin^2theta) = 1$

$\Rightarrow r^{2} (\frac{x^{2}}{r^{2}} - \frac{y^{2}}{r^{2}}) = 1$ $rArr r^2(x^2/r^2 - y^2/r^2 ) = 1$

and 'taking out' $\frac{1}{r^{2}} as a common factor$ $1/r^2 " as a common factor "$

$rArr cancel(r^2)/cancel(r^2) (x^2 - y^2) = 1 rArr x^2 = y^2$

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How do you convert $r^{2} (cos 2 (θ)) = 1$ $r^2(cos2(theta))=1$ into cartesian form?

1 Answer

Explanation:

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How do you convert r^2(cos2(theta))=1r2(cos2(θ))=1r^2(cos2(theta))=1 into cartesian form?

1 Answer

Explanation:

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How do you convert $r^{2} (cos 2 (θ)) = 1$ $r^2(cos2(theta))=1$ into cartesian form?