How do you convert $r=3theta - csctheta$ to Cartesian form?

Question

2139 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-14T05:31:38

$sqrt(x^2+y^2)=3arctan(y/x)-sqrt(x^2+y^2)/y$

$(r,theta)$ in polar coordinates is $(rcostheta,rsintheta)$ in rectangular coordinates and

$(x,y)$ in rectangular coordinates is $(sqrt(x^2+y^2),arctan(y/x))$ in polar coordinates.

Note that $sintheta=y/r=y/(sqrt(x^2+y^2)$

Hence $r=3theta-csctheta$ can be written as

$sqrt(x^2+y^2)=3arctan(y/x)-sqrt(x^2+y^2)/y$

How do you convert r=3theta - csctheta r=3theta - csctheta to Cartesian form?