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The rectangular coordinates of a point are given #(4, -4sqrt3)#, how do you find polar coordinates of the point?

1 Answer

Sep 11, 2017

Use the formulas #x^2+y^2 = r^2# and #tan theta =y/x#

#r^2=(4)^2+(-4sqrt3)^2=16+48=64#

#r=sqrt64=8#

#tan theta = y/x=(-4sqrt3)/4=(-cancel(4)sqrt3)/cancel 4=-sqrt3#

#theta=tan^-1 -sqrt3=-pi/3#

#:.(r,theta)=(8,-pi/3)#

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