1. The problem is to convert the Cartesian coordinates $(-4,-4)$ to polar coordinates. 2. Polar coordinates $(r,\theta)$ are related to Cartesian coordinates $(x,y)$ by the formulas: $$r = \sqrt{x^2 + y^2}$$ $$\theta = \tan^{-1}\left(\frac{y}{x}\right)$$ 3. Here, $x = -4$ and $y = -4$. 4. Calculate the radius $r$: $$r = \sqrt{(-4)^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}$$ 5. Calculate the angle $\theta$: $$\theta = \tan^{-1}\left(\frac{-4}{-4}\right) = \tan^{-1}(1) = \frac{\pi}{4}$$ 6. Since both $x$ and $y$ are negative, the point lies in the third quadrant. We add $\pi$ to the angle to get the correct direction: $$\theta = \frac{\pi}{4} + \pi = \frac{5\pi}{4}$$ 7. Therefore, the polar coordinates are: $$(r, \theta) = \left(4\sqrt{2}, \frac{5\pi}{4}\right)$$ This means the point is $4\sqrt{2}$ units from the origin at an angle of $\frac{5\pi}{4}$ radians measured counterclockwise from the positive x-axis.