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?
How to convert the equation of a line from polar to standard form?
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geometry
polar-coordinates
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1A *straight* line or something more general? – 2012-09-24
1 Answers
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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 $y$.