Question

How do you convert `(4, 4pi/3)` into rectangular forms?

Answer 1

`x=-2`
`y=-2sqrt(3)`

Explanation:

If you know the poalr coordinates `(\rho,\theta)`, then the transformation to have the rectangular ones is

`x=rcos(theta)`
`y=rsin(theta)`

In your case,

`x=4cos((4pi)/3)`
`y=4sin((4pi)/3)`

since `cos((4pi)/3)=-1/2`, and `sin((4pi)/3)=-sqrt(3)/2`, we have

`x=4*(-1/2)=-2`
`y=4*(-sqrt(3)/2)=-2sqrt(3)`