The problem involves converting a point in rectangular (Cartesian) form $(-3, 3)$ to polar coordinates.

Solution Process:

1. Polar Radius ($r$): The formula for the polar radius is: $r = \sqrt{x^2 + y^2}$ Substituting $x = -3$ and $y = 3$: $r = \sqrt{(-3)^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}$

2. Angle ($\theta$): The angle $\theta$ in polar coordinates is given by: $\tan\theta = \frac{y}{x}$ Substituting $x = -3$ and $y = 3$: $\tan\theta = \frac{3}{-3} = -1$ From the tangent function, an angle where $\tan\theta = -1$ in the second quadrant (where $x < 0, y > 0$) is: $\theta = \frac{3\pi}{4}$

Polar Coordinates:

The polar coordinates for the point $(-3, 3)$ are: $(3\sqrt{2}, \frac{3\pi}{4})$

Would you like more explanation or have further questions? Here are related questions to consider:

1. What is the general process to convert Cartesian coordinates to polar coordinates?
2. How do we determine the correct quadrant for the angle $\theta$?
3. What are the implications of negative $x$ or $y$ values in polar conversion?
4. How can we verify the polar coordinates by converting back to rectangular coordinates?
5. How does the polar form help in solving problems involving symmetry?

Tip: Always check the quadrant of the angle when using the