Question

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

Answer 1

Case: Polar to Cartesian coordinates

Method:

`\begin{gathered} r=12 \\ \theta=(4\pi)/(3) \end{gathered}`

Changing to the form (x,y)

`\begin{gathered} x=rcos\theta \\ x=12\cos((4\pi)/(3)) \\ x=12*-(1)/(2) \\ x=-6 \end{gathered}`
`\begin{gathered} y=r\sin\theta \\ y=12\sin((4\pi)/(3)) \\ y=12*-(√(3))/(2) \\ y=6*-√(3) \\ y=-6√(3) \end{gathered}`

Final answer: Option (B)

(x,y) is

`(-6,-6√(3))`