Question

Convert the polar point (r,theta) =(4, 4pi/3) to a Cartesian point(x,y)

Answer 1

Explanation

Given the polar coordinate;

$\mleft(r,\theta\mright)=\mleft(4,\frac{4\pi}{3}\mright)$

We can find its cartesian equivalent using the formula below;

$\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}$

Therefore;

$\begin{gathered} x=4\cos \frac{4\pi}{3}=4\cos (\frac{4\times180}{3})=4\cos 240=-2 \\ y=4\sin \frac{4\pi}{3}=4\sin (\frac{4\times180}{3})=4\sin 240=-2\sqrt{3} \end{gathered}$

ANSWER:

$(x,y)=(-2,-2\sqrt[]{3})$