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

Solution:

The polar coordinate system is a two-dimensional coordinate system in which the location of each point could be traced using two references:

1. Its distance from a reference line.

2. Its angle from a reference direction

If (r, θ) are the polar coordinates of a point, then all the polar coordinates are defined as:

(r, θ + 2nπ) and (-r, θ + (2n + 1) π)

Where n ∈ Z

Given:

p = (3, -π/3)

We have to find all polar coordinates of point p

Where r = 3 and θ = -π/3

All the polar coordinates of point p are

p = (3, -π/3 + 2nπ) and

p = (-3, -π/3 + (2n + 1)π)

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

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

Summary:

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