How do you convert the Cartesian coordinates (-6, 13) to polar coordinates?

1 Answer
Nov 8, 2016

Polar: (r,theta)~~(14.3,2.0)

Explanation:

In general, given the Cartesian non-zero coordinates (x,y)
the polar coordinates are (r,theta)
where
color(white)("XXX")r=sqrt(x^2+y^2)
and
color(white)("XXX")theta={("arctan"(y/x) color(white)(+pi)" if " x > 0),("arctan"(y/x)+pi" if " x < 0):}

For the given Cartesian coordinates: (-6,13)

color(white)("XXX")r=sqrt((-6)^2+13^2)~~14.3178210633
and
color(white)("XXX")theta = "arctan"(13/(-6))+pi~~2.0032041024