Question

How do you convert `(r+1)^2= theta + sectheta` to Cartesian form?

Answer 1

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

Explanation:

When we convert polar coordinates `(r,theta)` to Cartesian coordinates, the relation is `x=rcostheta`, `y=rsintheta` and hence `r^2=x^2+y^2` and `theta=tan^(-1)(x/y)`.

Hence `(r+1)^2=theta+sectheta` can be written as

`r^2+2r+1=theta+sectheta` or

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

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

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