Question

How do you convert `r= theta - 4sintheta` to Cartesian form?

Answer 1

`x^2+y^2=sqrt(x^2+y^2)tan^(-1)(y/x)-4y`

Explanation:

The relation between polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` is given by

`x=rcostheta` and `y=rsintheta` i.e. `tantheta=y/x` and `r^2=x^2+y^2`

Hence `r=theta-4sintheta`

`hArrr^2=rtheta-4rsintheta`

or `x^2+y^2=sqrt(x^2+y^2)tan^(-1)(y/x)-4y`