How do you convert $r=-2 theta - tan theta$ to Cartesian form?

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Answer 1 · 2018-02-18T17:32:06

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

$"Given,"r=-2theta-tantheta$

$x=rcostheta, y=rsintheta$

$tantheta=y/x$

$r=sqrt(x^2+y^2), theta=tan^-1(y/x)$

Thus,

$r=-2theta-tantheta " becomes, "$
$sqrt(x^2+y^2)=-2tan^-1(y/x)-y/x$

Rearranging

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

How do you convert r=-2 theta - tan theta r=-2 theta - tan theta to Cartesian form?