How do you convert (r+1)^2= 2r-theta + sin theta costheta to Cartesian form?

1 Answer
Jun 27, 2018

x^2+y^2+1=(xy)/(x^2+y^2)-tan^-1(y/x)

Explanation:

Expand and Simplify

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

Recall x^2+y^2=r^2,x=rcostheta, y=rsintheta

Therfore y/x=tan(theta) this means tan^-1(y/x)=theta

Trickery

r^2+1=-theta+((rsintheta)(rcostheta))/r^2

Substitute

x^2+y^2+1=(xy)/(x^2+y^2)-tan^-1(y/x)