How do you convert $(4, - 2)$ $(4,-2)$ from cartesian to polar coordinates?

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Answer 1 · 2017-12-13T20:37:50

$\Rightarrow (2 \sqrt{5}, - {tan}^{- 1} (\frac{1}{2}))$ $=> ( 2sqrt5 , -tan^-1 ( 1/2) )$

I have drawn a diagram to illustate:

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Here we see a diagram where we must compute $α$ $alpha$ in radians

So hence $α = - {tan}^{- 1} (\frac{2}{4})$ $alpha = - tan^-1 ( 2 / 4 )$

We can now find $r$ $r$ the mod of the point

$\Rightarrow r = \sqrt{4^{2} + {(- 2)}^{2}} = 2 \sqrt{5}$ $=> r = sqrt(4^2 + (-2)^2 ) = 2sqrt5$

We know the polar form is $(r, θ)$ $(r , theta )$

$\Rightarrow (2 \sqrt{5}, - {tan}^{- 1} (\frac{1}{2}))$ $=> ( 2sqrt5 , -tan^-1 ( 1/2) )$

$\Rightarrow \approx (2 \sqrt{5}, - 0.4637)$ $=> approx (2sqrt5, -0.4637 )$

How do you convert (4,−2)(4,-2) from cartesian to polar coordinates?