### Instruction: Convert the point $(-2,-2)$ in rectangular coordinates to polar coordinates.  Enter your answer in the form $(r,\theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$.### Response: To convert from rectangular to polar coordinates, I need to find the distance and the angle of the point from the origin.
The distance is easy to find using the Pythagorean theorem: $r = \sqrt{x^2 + y^2} = \sqrt{(-2)^2 + (-2)^2} = \sqrt{8}.$
The angle is trickier, because I have to account for the quadrant of the point.
I know that the angle of a point $(x,y)$ in the standard position is given by $\theta = \tan^{-1}(\frac{y}{x})$, but this only works for points in the first and fourth quadrants.
Since the point $(-2,-2)$ is in the third quadrant, I have to add $\pi$ to the angle to get the correct orientation.
So, $\theta = \tan^{-1}(\frac{-2}{-2}) + \pi = \tan^{-1}(1) + \pi = \frac{\pi}{4} + \pi = \frac{5\pi}{4}.$
Therefore, the polar coordinates of the point are $(\sqrt{8}, \frac{5\pi}{4}).$