Question

The polar coordinate (r,theta)= (12,4pi/3)be written in Cartesian coordinates as

Answer 1

SOLUTION:

Case: Polar to Cartesian coordinates

Method:

$\begin{gathered} r=12 \\ \theta=\frac{4\pi}{3} \end{gathered}$

Changing to the form (x,y)

$\begin{gathered} x=rcos\theta \\ x=12\cos(\frac{4\pi}{3}) \\ x=12\times-\frac{1}{2} \\ x=-6 \end{gathered}$$\begin{gathered} y=r\sin\theta \\ y=12\sin(\frac{4\pi}{3}) \\ y=12\times-\frac{\sqrt{3}}{2} \\ y=6\times-\sqrt{3} \\ y=-6\sqrt{3} \end{gathered}$

Final answer: Option (B)

(x,y) is

$(-6,-6\sqrt{3})$