Answer:
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)
