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

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Answer 1 · 2018-04-15T03:36:17

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

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

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

Substituting for x and y in polar form,

$r^2 cos^2 theta - r^2 sin ^2 theta = 1$

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

But $cos^2 theta - sin^2 theta = cos (2theta)$

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

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

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