Question

What is the polar form of `( -3,-14 )`?

Answer 1

Polar coordinate: `(14.3,4.5 " radians")` approx.

Explanation:

The point `(-3,-14)` is in quadrant 3 (Q III)
with a reference angle of `theta="arctan"((-14)/(-3))`
and a radius of `r=sqrt(((-3)^2+(-14)^2)`

Using a calculator:
`color(white)("XXX")theta ~~ 1.359702994`
`color(white)("XXXXXX")`Note: since this point is in Q III it will be
`color(white)("XXXXXX")`necessary to add `pi` to it to get the true
`color(white)("XXXXXX")`polar coordinate angle.
`color(white)("XXXXXX")theta + pi ~~4.501295647`
and
`color(white)("XXX")r~~14.31782106`