How do you convert # r^2=cos2 theta# to rectangular form?

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Answer 1 · 2016-09-27T08:05:08

We know the relations

#x=rcostheta and y =rsintheta#

where r and #theta# are the polar coordinate of a point having rectangular coordinate #(x,y)#
So #r^2=x^2+y^2#

Now the given relation is

#r^2=cos2theta=cos^2theta-sin^2theta#

#=>r^4=r^2cos^2theta-r^2sin^2theta#

#=>(x^2+y^2)^2=x^2-y^2#

This is the rectangular form of the given polar equation.