How do you convert #r=1+0.5cos2(theta)# into cartesian form?

1 Answer
Sep 19, 2016

#x^2/sqrt(x^2+y^2)-x^2/(x^2+y^2)=1/2#

Explanation:

The pass equations are

#((x=rcostheta),(y=rsintheta))#

and also keeping in mind that #cos2theta =1-2sin^2theta#

#r = 1+(1-2sin^2theta)/2 = 1+1/2-sin^2theta = 1/2+cos^2theta#

then

#x/costheta = 1/2 + cos^2theta#

but #costheta = x/sqrt(x^2+y^2)#

so

#x^2/sqrt(x^2+y^2)-x^2/(x^2+y^2)=1/2#