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

1 Answer
Jim G.
Feb 26, 2016

#x^2 = y^2#

Explanation:

Using the formulae that links Polar to Cartesian coordinates.

#• x = rcostheta rArr costheta = x/r #

#• y = rsintheta rArr sintheta = y/r#

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

#• cos(2theta) = cos^2theta - sin^2theta #

hence #: r^2(cos(2theta)) = r^2( cos^2theta - sin^2theta) = 1#

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

and 'taking out' # 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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