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

Solution:

The polar coordinates of point p are

P = (r, θ)

Where r is the real number

θ is the radian

All the polar coordinates of the point P are

P = (r, θ + 2nπ)

P = (-r, θ + (2n + 1)π)

P (5, -π/6) are the given coordinates

All the polar coordinates of the point P are

P = (5, -π/6 + 2nπ)

P = (5, -π/6 + (2n + 1)π)

Therefore, all polar coordinates of point p are P = (5, -π/6 + (2n + 1)π).

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

Summary:

All polar coordinates of point p where p = ordered pair 5 comma negative pi divided by 6 are P = (5, -π/6 + (2n + 1)π).