Find all polar coordinates of point p where p = ordered pair 3 comma negative pi divided by 4.

Solution:

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

Let us assume the point as p = (3, -π/4)

We have to find all polar coordinates of point p

Where r = 3 and θ = -π/4

All the polar coordinates of point p are

p = (3, -π/4 + 2nπ) and 

p = (-3, -π/4 + (2n + 1)π)

Therefore, all the polar coordinates of point p are (3, -π/4 + 2nπ) and (-3, -π/4 + (2n + 1)π).

Find all polar coordinates of point p where p = ordered pair 3 comma negative pi divided by 4.

Summary:

All polar coordinates of point p where p = ordered pair 3 comma negative pi divided by 3 are (3, -π/4 + 2nπ) and (-3, -π/4 + (2n + 1)π).