Question

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

Answer 1

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`