rectangular and polar coodinates problem?

Question

please explain how you got the answer:

Convert the rectangular coordinates to polar coordinates with r>0 and with theta between 0 and 2pi.

(3squareroot3, -3)

Answer 1

r = √(x² + y²)
θ = tanˉ¹ (y/x)

r = √(9*3 + 9) = 6
θ = tanˉ¹ (-1/√3) = -π/6 + πn

Since it is in quadrand IV, we want θ = 5π/6.

Answer 2

rectangular coordinates (x,y) = (3sqrt3,-3)
x=3sqrt3; y=-3

r=sqrt(x^2+y^2)
=sqrt(27+9)
=sqrt(36)
r=6

theta = invtan(abs(y/x))
=invtan(3/(3sqrt3))
=invtan(0.5773..)
=30 or 150
=150 since 0

Answer 3

(3√3, -3)
tanθ = - 3/3√3
θ = - 30° = 330°
r = - 3 / sin(330°) = 6
(3√3, -3) = (6, 330°)