Question

Convert the rectangular coordinates to polar coordinates with r > 0 and 0 ≤ θ < 2π.

(-sqrt6, -sqrt2)

The x-coordinate is (2sqrt2), how do I get y?

Answer 1

You mean r = 2sqrt(2) and you want to find theta?
Using trigonometry. You know the adjacent and opposite sides so you can find tanz, then theta = pi + z as the line is in the bottom left segment.