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

The polar coordinates of (3,-π/3)are (√(9+π^2/9),-arctan (π/9)+2π)

Step-by-step explanation:

Given (3, -π/3)

In order to convert the point to polar coordinates, we will use the following formulas:

The point in polar coordinates is represented by (r,θ)

Where

r= √(x^2+y^2 )

and

θ=arctan  (y/x)

So,

here

x=3

y= -π/3

r= √((3)^2+(-π/3)^2 )

= √(9+π^2/9)

And

θ=arctan ((-π)/3)/3

=arctan(-π/9)

The theta will be adjusted based on the given point. If the point lies in 2nd or third quadrant then π is added and if it lies in 4th quadrant then 2π is added.

θ= -arctan (π/9)+2π

The polar coordinates of (3,-π/3)are (√(9+π^2/9),-arctan (π/9)+2π)