Question

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

Answer 1

Step-by-step explanation

Given the polar coordinate;

`\mleft(r,\theta\mright)=\mleft(4,(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 (4\pi)/(3)=4\cos ((4*180)/(3))=4\cos 240=-2 \\ y=4\sin (4\pi)/(3)=4\sin ((4*180)/(3))=4\sin 240=-2√(3) \end{gathered}`

ANSWER:

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