Question

Pre calculus, trigonometry Given point M the ordered pair 6 times the square root of 3 comma negative 6 comma which is located on the rectangular coordinate plane, what are the representations of the point in polar form, where −2π ≤ θ ≤ 2 π?
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 12 comma 7pi over 6
a point 12 comma pi over 3 comma a point 12 comma negative five pi over 3 comma a point negative 12 comma 2pi over 3 comma a point negative 12 comma negative 4 pi over 3
a point negative 12 comma 5 pi over 6 comma a point 12 comma 11 pi over 6 comma a point 12 comma negative pi over 6 comma a point negative 12 comma negative 7 pi over 6
a point 12 comma negative pi over 3 comma a point 12 comma five pi over 3 comma a point negative 12 comma 2pi over 3 comma a point 12 comma negative 4 pi over 3

Answer 1

The possible form of the point (6√3, - 6) in polar form are (r₁, θ₁) = (12, 11π / 6), (r₂, θ₂) = (12, - π / 6).

How to derive the polar form of a point in rectangular form

In this problem we find a point in rectangular form, that is, a point of the form (x, y). We are asked to find the polar form of the point, that is, a point described by the following expression:

(r, θ)

Where:

• r - Magnitude
• θ - Direction, in radians

The magnitude is found by Pythagorean theorem:

r =√(x² + y²)

And the direction of the point is described by the following inverse trigonometric function:

θ = tan⁻¹ (y / x)

If we know that (x, y) = (6√3, - 6), then the point in polar form is:

r = √[(6√3)² + (- 6)²]

r = 12

θ = tan⁻¹ (- 6 / 6√3)

θ = tan⁻¹ (- √3 / 3)

θ = 11π / 6 rad / θ =  - π / 6 rad

There are two possible solutions: (r₁, θ₁) = (12, 11π / 6), (r₂, θ₂) = (12, - π / 6).

To learn more on point in polar form: brainly.com/question/13103661

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