Question

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)

Answer 1

The correct option is B.

Explanation:

If polar coordinates of point P are

`P=(r,\theta)`

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

`P=(r,\theta+2n\pi)`

`P=(-r,\theta+(2n+1)\pi)`

The given coordinates are
`P(5,-(\pi)/(6))`. So, all polar coordinates of point P are

`P=(5,-(\pi)/(6)+2n\pi)`

`P=(-5,-(\pi)/(6)+(2n+1)\pi)`

Therefore correct option is B.