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)

y=mx+

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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