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#