Question

Find all polar coordinates of point p where p= (5, pi/3)

Answer 1

The polar coordinate of any point can be written as:

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

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

The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).

When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)

When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.

Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].