Question

Given point M the ordered pair negative 6 comma negative 6 times the square root of 3 comma which is located on the rectangular coordinate plane, what are the representations of the point in polar form, where −2π ≤ θ ≤ 2π?

a point 12 comma negative 4 pi over 3 comma a point 12 comma 2 pi over 3 comma a point negative 12 comma negative pi over 3 comma a point negative 12 comma 5 pi over 3
a point 12 comma 4 pi over 3 comma a point 12 comma negative 2 pi over 3 comma a point negative 12 comma negative pi over 3 comma a point negative 12 comma negative 5 pi over 3
a point 12 comma pi over 6 comma a point 12 comma negative five pi over 6 comma a point negative 12 comma 11pi over 6 comma a point negative 12 comma negative pi over 6

Answer 1

To convert the given point (x, y) to polar form (r, θ), use the formulas r = √(x^2 + y^2) and θ = arctan(y/x). For the given point M (-6, -6√3), the polar representation is (12, π/3).

Step-by-step explanation:

To convert the given point (x, y) to polar form (r, θ), we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x), where arctan is the inverse tangent function.

For the given point M (-6, -6√3), we can calculate:

r = √((-6)^2 + (-6√3)^2) = √(36 + 108) = √144 = 12

θ = arctan((-6√3)/(-6)) = arctan(√3) = π/3

Therefore, the representation of the point in polar form is (12, π/3).