How do you convert $(0, −4)$ to polar form?

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Answer 1 · 2017-10-21T01:41:50

$(4, -pi/2)$

To convert from Cartesian Coordinates $(x,y)$ to Polar Coordinates $(r,theta$ ):
Where $r = sqrt( x^2 + y^2 )$ and $theta = arctan ( y / x )$

In this example: $x=0 and y=-4$

$:. r = sqrt(0^2+(-4)^2) =4$

$theta = arctan (-4/0)$ which is undefined

Consider:
$theta = arctan(lim_"x->0" -4/x)$

$= lim_"x->-oo" arctan (x)$

$= -pi/2$ [* See graph of $arctan x$ below]

Hence, $(0, -4)$ in polar coordinates is: $(4, -pi/2)$

*Graph of $arctan x$

graph{arctan x [-16.01, 16.03, -8.01, 8]}

How do you convert (0, −4) (0, −4) to polar form?