Question

Convert the following rectangular coordinates into polar coordinates (r,θ) so that r < 0

and 0 ≤ θ ≤ 2π :

(4,−4√3)

Answer 1

$$r^2=(4)^2+(-4\sqrt{3})^2=64$$

$$r=-8$$

$$\theta=\tan^{-1}(\dfrac{-4\sqrt{3}}{4})+\pi=2\pi/3$$

$(-8, 2\pi/3)$