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Find all polar coordinates of point P where P = ordered pair 5 comma negative pi divided by 6 .

A.(5, negative pi divided by 6 + 2nπ) or (-5, negative pi divided by 6 + 2nπ)

B.(5, negative pi divided by 6 + 2nπ) or (-5, negative pi divided by 6 + (2n + 1)π)

C.(5, negative pi divided by 6 + 2nπ) or (5, pi divided by 6 + (2n + 1)π)

D.(5, negative pi divided by 6 + (2n + 1)π) or (-5, negative pi divided by 6 + 2nπ)

Respuesta :

Answer:

The correct option is B.

Step-by-step explanation:

If polar coordinates of point P are

[tex]P=(r,\theta)[/tex]

Where, r is real number and θ is in radian, then all polar coordinates of point P are defined as

[tex]P=(r,\theta+2n\pi)[/tex]

[tex]P=(-r,\theta+(2n+1)\pi)[/tex]

The given coordinates are [tex]P(5,-\frac{\pi}{6})[/tex]. So, all polar coordinates of point P are

[tex]P=(5,-\frac{\pi}{6}+2n\pi)[/tex]

[tex]P=(-5,-\frac{\pi}{6}+(2n+1)\pi)[/tex]

Therefore correct option is B.

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