Can you explain so i can understand how it was completed?

determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°. (1 point)

(3 square root of 2 , 315°), (-3 square root of 2 , 135°)

(3 square root of 2 , 225°), (-3 square root of 2 , 45°)

(3 square root of 2 , 45°), (-3 square root of 2 , 225°)

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

Step-by-step explanation:

Hello!

We need to determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.

We know that the polar coordinate system is a two-dimensional coordinate. The two dimensions are:

So we need to find r and θ. So we know that:

      (1)

x = rcos(θ)                                   (2)

x = rsin(θ)                                    (3)

From the statement we know that (x, y) = (3, -3).

Using the equation (1) we find that:

Using the equations (2) and (3) we find that:

3 = rcos(θ)

-3 = rsin(θ)

Solving the system of equations:

θ= -45

Then:

r = 3\sqrt{2}[/tex]

θ= -45 or 315

Notice that  there are two feasible angles, they both have a tangent of -1. The X will take the positive value, and Y the negative one.

So, the solution is:

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

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step-by-step explanation: