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

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Answer 1 · 2017-09-11T17:49:58

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

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

$r=sqrt64=8$

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

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

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

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