Find all polar coordinates of point p where p = ordered pair 1 comma pi divided by 3.

Solution:

The polar coordinate of any point can be written as

(r, θ) = (r, θ + 2nπ) (when r is positive)

(r, θ) = (-r, θ + (2n + 1)π) (when r is negative

Where n is an integer.

Given the point is (1, π/3)

When r is positive, the polar coordinate is (1, π/3 + 2nπ)

When r is negative, the polar coordinate is (-1, (2n + 1)π)

Therefore, all polar coordinates of the given point are (1, π/3 + 2nπ) and (-1, (2n + 1)π).

Find all polar coordinates of point p where p = ordered pair 1 comma pi divided by 3.

Summary:

All polar coordinates of point p where p = ordered pair 1 comma pi divided by 3 are (1, π/3 + 2nπ) and (-1, (2n + 1)π).