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

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Answer 1 · 2017-12-13T20:37:50

#=> ( 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 #alpha# in radians

So hence #alpha = - tan^-1 ( 2 / 4 ) #

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

#=> r = sqrt(4^2 + (-2)^2 ) = 2sqrt5 #

We know the polar form is #(r , theta ) #

#=> ( 2sqrt5 , -tan^-1 ( 1/2) ) #

#=> approx (2sqrt5, -0.4637 ) #