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]}