The rectangular coordinates of a point are given. Find two sets of polar coordinates for the point.

(-3,-3)

tanØ = y/x = -3/-3 = 1

Ø = π/4

x = rcosØ = (1/√2)r
-3 = (1/√2)r
r = -3√2

one is (-3√2,π/4)

I will let you find the other

To find the polar coordinates for a given point, we need to use the formulas:

r = √(x^2 + y^2)
θ = arctan(y/x)

Given the rectangular coordinates (-3, -3), we can substitute these values into the formulas to find the polar coordinates.

1. First, let's find the value of r:
r = √((-3)^2 + (-3)^2)
r = √(9 + 9)
r = √18 = 3√2

2. Next, let's find the value of θ:
θ = arctan((-3)/(-3))
θ = arctan(1)
θ = π/4 (in radians) or 45° (in degrees)

So, our first set of polar coordinates for the point (-3, -3) is (3√2, π/4).

3. Now, let's consider a second set of polar coordinates. Since we are dealing with a point in the third quadrant, we need to add π (180°) to our angle θ.

θ2 = θ + π
θ2 = π/4 + π
θ2 = 5π/4 (in radians) or 225° (in degrees)

So, our second set of polar coordinates for the point (-3, -3) is (3√2, 5π/4).