2. Polar to Cartesian

x = r\cos(\theta), \quad \quad y = r\sin(\theta)

r = \sqrt{x^2 + y^2}, \quad \quad \theta = \arctan{\dfrac{y}{x}}

Convert the polar coordinate $(2, \dfrac{\pi}{3})$ in their cartesian form

x = 2\cos(\dfrac{\pi}{3}) = 1 \\ \; \\ y = 2\sin(\dfrac{\pi}{3}) = \sqrt{3} \\ \; \\ \boxed{(1, \sqrt{3})}

Convert the cartesian coordinate $(1, -\sqrt{3})$ into its polar form

\theta = \arctan(-\dfrac{\sqrt{3}}{1}) = -\dfrac{\pi}{3} \\ \; \\ r = \sqrt{1^2 + (-\sqrt{3})^2} = 2 \\ \; \\ \boxed{(2, -\dfrac{\pi}{3})}