### 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 this point, we need to find the radius, which is the distance from the point $(-2,-2)$ to the origin, and the angle, which is the angle formed between the line containing the point $(-2,-2)$ and the origin and the positive $x$-axis.
We can find the radius using the distance formula.  The distance from the point $(-2,-2)$ to the origin is $\sqrt{(-2-0)^2+(-2-0)^2}=\sqrt{8}$.
To find the angle, we can use the inverse tangent function. Note that the point $(-2,-2)$ is in the third quadrant.  The inverse tangent function gives us the angle between a point and the positive $x$-axis, so we need to add $180^\circ$ to this angle to get the angle between the point $(-2,-2)$ and the positive $x$-axis.
Evaluating the inverse tangent function, we get $\tan^{-1}(\frac{-2}{-2})=\frac{\pi}{4}$, so the angle is $\frac{\pi}{4}+\pi=\frac{5\pi}{4}$.