### 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 use the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}(y/x),$ where $\theta$ is measured from the positive $x$-axis.
In this case, $x = -2$ and $y = -2,$ so I can plug them into the formulas to get $r = \sqrt{(-2)^2 + (-2)^2} = \sqrt{8}$ and $\theta = \tan^{-1}((-2)/(-2)) = \tan^{-1}(1).$
I know that $\tan^{-1}(1)$ is equal to $\pi/4,$ but I have to be careful about the quadrant.
Since $x$ and $y$ are both negative, the point $(-2,-2)$ is in the third quadrant, which means $\theta$ is between $\pi$ and $3\pi/2.$
To get the correct angle, I need to add $\pi$ to $\pi/4,$ which gives me $\theta = 5\pi/4.$
Therefore, the polar coordinates of $(-2,-2)$ are $(\sqrt{8},5\pi/4).$