How do you convert the cartesian coordinate (2, -4) into polar coordinates?

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Answer 1 · 2017-09-11T17:31:27

see below

Use the formulas $x^{2} + y^{2} = r^{2}$ $x^2 + y^2 =r^2$ and $tan θ = \frac{y}{x}$ $tan theta =y/x$

$r^{2} = {(2)}^{2} + {(- 4)}^{2} = 4 + 16 = 20$ $r^2=(2)^2+(-4)^2=4+16=20$

$r = \sqrt{20} = 2 \sqrt{5} \approx 4.472$ $r=sqrt20 = 2sqrt5~~4.472$

$tan θ = - \frac{4}{2}$ $tan theta = -4/2$

$θ = {tan}^{- 1} - 2$ $theta=tan^-1 -2$

$θ \approx - 1.107$ $theta ~~-1.107$

$:.(r,theta)~~ (4.472, -1.107)$