How do you convert a polar line to a line in standard form? That being, change a line with parameters $\rho$ and $\theta$ in a polar coordinate system, to a standard form ($Ax+By=C$) in Cartesian coordinates?
[Math] How to convert the equation of a line from polar to standard form
geometrypolar coordinates
Best Answer
In even more general cases than converting a line to and from polar, you can use the substitutions $$r=\sqrt{x^2+y^2}, \theta=\tan^{-1}\left(\frac{y}{x}\right), x=r\cos\theta, y=r\sin\theta$$ Note that because $\arctan$ only takes values in $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$, the identity given for $\theta$ doesn't do all the work: you need to decide between the fourth and the second, and between the first and the third, quadrants based on the signs of $x$ and $y$.