The possible form of the point (6√3, - 6) in polar form are (r₁, θ₁) = (12, 11π / 6), (r₂, θ₂) = (12, - π / 6).
<h3>How to derive the polar form of a point in rectangular form</h3>
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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