Verified answer

Polar: (r, Θ)

Rectangular: (x, y)

The relationships between polar and rectangular coordinates are:

tan(Θ) = y/x

r² = x² + y²

Given (4, π/6):

tan(π/6) = y/x

1/√3 = y/x

y = x/√3

4² = x² + y²

16 = x² + y²

16 = x² + (x/√3)³

16 = x² + 1/3 x²

16 = 4/3 x²

12 = x²

|x| = √12

|y| = √12/√3 = √4 = 2

(x, y) = (√12, 2) = (2√3, 2)

x = 4cospi/6 = 4(sqrt(3)/2) = 2sqrt(3)

y = 4sinpi/6 = 4(1/2) = 2

(2sqrt(3),2)