Question

Find the polar coordinates of a point with Cartesian coordinates (x,y)=(2√3,2).Select the correct answer below:

(4,π/6)
(2,2π/3)
(4,2π/3)
(2,7π/6)
(4,7π/6)
(2,π/6)

Answer 1

(4,π/6)

Step-by-step explanation:

The correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).

Step-by-step explanation:

Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

Plugging in the given values:

r = √((2√3)^2 + 2^2)

= √(12 + 4)

= √16

= 4

θ = atan2(2, 2√3)

≈ 0.5236 radians

However, in the polar coordinate system, angles are typically expressed in radians between 0 and 2π. The angle π/6 is equivalent to 0.5236 radians, so the correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).