How do you change the rectangular equation $x^{2} - y^{2} = 1$ $x^2-y^2=1$ into polar form?

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Answer 1 · 2018-04-15T03:36:17

$cos (2 θ) = \frac{1}{r^{2}}$ $cos (2theta) = 1 / r^2$

$x = r cos θ, y = r sin θ$ $x = r cos theta, y = r sin theta$

Given : $x^{2} - y^{2} = 1$ $x^2 - y^2 = 1$

Substituting for x and y in polar form,

$r^{2} {cos}^{2} θ - r^{2} {sin}^{2} θ = 1$ $r^2 cos^2 theta - r^2 sin ^2 theta = 1$

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

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

$:. r^2 cos (2theta) = 1$

$cos (2theta) = 1 / r^2$

How do you change the rectangular equation x^2-y^2=1x2−y2=1x^2-y^2=1 into polar form?