What is the Cartesian form of ( 6,-pi/3 )?

$\left(3 , - 3 \setminus \sqrt{3}\right)$

Explanation:

The Cartesian coordinates $\left(x , y\right)$ of the point $\left(6 , - \frac{\setminus \pi}{3}\right) \setminus \equiv \left(r , \setminus \theta\right)$ are given as follows

$x = r \setminus \cos \setminus \theta$

$= 6 \setminus \cos \left(- \frac{\setminus \pi}{3}\right)$

$= 6 \setminus \cos \left(\setminus \frac{\pi}{3}\right)$

$= 6 \setminus \cdot \frac{1}{2}$

$= 3$

$y = r \setminus \sin \setminus \theta$

$= 6 \setminus \sin \left(- \frac{\setminus \pi}{3}\right)$

$= - 6 \setminus \sin \left(\setminus \frac{\pi}{3}\right)$

$= - 6 \setminus \cdot \setminus \frac{\sqrt{3}}{2}$

$= - 3 \setminus \sqrt{3}$

hence, the Cartesian coordinates are $\left(3 , - 3 \setminus \sqrt{3}\right)$