QuestionFind the polar coordinates, $0 \leq \theta<2 \pi$ and $r \geq 0$, of the point given in Cartesian A) $\left(4 \sqrt{2}, \frac{3 \pi}{4}\right)$ B) $\left(4 \sqrt{2}, \frac{7 \pi}{4}\right)$ coordinates. $(4,-4)$ C) $\left(4 \sqrt{2}, \frac{\pi}{4}\right)$ D) $\left(4 \sqrt{2}, \frac{5 \pi}{4}\right)$

Studdy Solution
Adjust $\theta$ to ensure it lies within the range $0 \leq \theta < 2\pi$.
Since $\theta = -\frac{\pi}{4}$ is negative, add $2\pi$ to adjust:
$$\theta = -\frac{\pi}{4} + 2\pi$$ $$\theta = \frac{7\pi}{4}$$
The polar coordinates of the point $(4, -4)$ are:
$$\boxed{\left(4\sqrt{2}, \frac{7\pi}{4}\right)}$$