Answer:
The polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).
Explanation:
To convert the rectangular coordinates (0, 6√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = tan^(-1)(y/x)
Substituting the given values, we get:
r = √(0^2 + (6√3)^2) = 6√3
θ = tan^(-1)((6√3)/0) = π/2
However, note that the angle θ is not well-defined since x=0. We can specify that the point lies on the positive y-axis, which corresponds to θ = π/2 radians.
Thus, the polar form of the rectangular coordinates (0, 6√3) is:
r = 6√3
θ = π/2
To express the angle θ in terms of θo, where 0 ≤ θo < 27 and in radians, we can write:
θ = π/2 = (π/54) × 54 ≈ (0.0292) × 54 ≈ 1.58 radians
Therefore, the polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).